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We present a new approach to test empirically the financial distress costs theory of corporate hedging. We estimate the ex-ante expected financial distress costs, which serve as a starting point to construct further explanatory variables in an equilibrium setting, as a fraction of the value of an asset-or-nothing put option on the firm's assets. Using single-contract data of the derivatives' use of 189 German middle-market companies that stems from a major bank as well as Basel II default probabilities and historical accounting information, we are able to explain a significant share of the observed cross-sectional differences in hedge ratios. Hence, our analysis adds further support for the financial distress costs theory of corporate hedging from the perspective of a financial intermediary., J Bus Fin Account;48(3-4)

Pooling individual customers with different inception dates into a single legal entity may generate intergenerational subsidies that are accentuated when the insurer has limited liability. This article aims to investigate whether an insurer can charge fair premiums while simultaneously ensuring identical levels of default risk—measured by the value of the default put option ratio—for all generations. The decision variables for achieving these goals are asset allocation and the amount of the insurer's equity capital. We propose an accounting framework where the insurer controls for insolvency positions annually after the first contract is issued. Additionally, a run‐off framework is developed where the insurer does not declare bankruptcy in case of an insolvency, but instead stops issuing new policies and runs the company until the assets are exhausted or the last policyholder is paid. We find that intergenerational subsidies and different levels of default risk per generation cannot be avoided whenever we face a positive default risk.

The reverse mortgage is a very useful financial product for senior citizens who own homes but do not have a cash income, while it is a high-risk product from the lender's perspective. One of benefits of reverse mortgages is that the debt limit is restricted to the scope of the disposition price of the collateralized house, which is considered a put option to borrowers. The present study evaluates the option value of the reverse mortgage in Hong Kong through an empirical analysis using the Black–Scholes option-pricing model. Moreover, the present study shows specific monetary values through option matching to the consumer situation, contributing to the increased understanding of reverse mortgages from the consumer's point of view.

After reviewing the notion of Systemically Important Financial Institution (SIFI), we propose a first principles way to compute the price of the implicit put option that the State gives to such an institution. Our method is based on important results from Extreme Value Theory (EVT), one for the aggregation of heavy tailed distributions and the other one for the tail behavior of the Value-at-Risk (VaR) versus the Tail-Value-at-Risk (TVaR). We show how to value in practice is proportional to the VaR of the institution and thus would provide the wrong incentive to the banks even if not explicitly granted. We conclude with a proposal to make the institution pay the price of this option to a fund, whose task would be to guarantee the orderly bankruptcy of such an institution. This fund would function like an insurance selling a cover to clients.

In this paper, we present a pricing model for catastrophe equity put options with default risk by assuming that the default of the option issuer may occur at any time prior to maturity of the option. Catastrophic events are assumed to occur according to a doubly stochastic Poisson process, and stock price is affected by the catastrophe losses, which follow the compound doubly stochastic Poisson process. As for default risk, we adopt typical structural approaches, and we also allow the correlation between the underlying stock and the assets of the option issuer. Under this framework, we derive a pricing formula for catastrophe equity put options with default risk. Finally, numerical analysis is presented to illustrate effects of default risk on catastrophe equity put option prices.

Both CDS and out-of-money put option can protect investors against downside risk, so they are related while not being mutually replaceable. This study provides a straightforward linkage between corporate CDS and equity option by inferring stock volatility from CDS spread and, thus, enables a direct analogy with the implied volatility from option price. I find CDS inferred volatility (CIV) and option implied volatility (OIV) are complementary, both containing some information that is not captured by the other. CIV dominates OIV in forecasting stock future realized volatility. Moreover, a trading strategy based on the CIV–OIV mean reverting spreads generates significant risk-adjusted return. These findings complement existing empirical evidence on cross-market analysis. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark

We study the determinants of fails-to-deliver in the period before and after the implementation of Rule 203 (elimination of option market maker exception from the locate and close-out requirement) and Rule 204 (t+3 close-out rule) in September 2008. We find a positive relation between short selling and fails-to-deliver that weakens after the implementation of these rules. Fails-to-deliver are higher for stocks with low institutional ownership, low book-to-market, small market capitalization, high turnover, and put option availability. The relation between short selling and these measures of borrowing costs is also weaker after the implementation of these rules.

This paper proposes a unique framework for the determination of the exercise boundary of American put option utilizing the mean value theorem for integration. We have isolated the path-dependent feature of the problem through a small term, and formulated an iteration procedure that avoids an explicit integration over the exercise boundary in the integral representation of the pricing. Our method outperforms other methods in the literature in terms of accuracy and efficiency for the pricing of American put options with maturity in the region of most practical uses. © 2015 Wiley Periodicals, Inc. Jrl Fut Mark

We develop a theory of robust pricing and hedging of a weighted variance swap given market prices for a finite number of co‐maturing put options. We assume the put option prices do not admit arbitrage and deduce no‐arbitrage bounds on the weighted variance swap along with super‐ and sub‐replicating strategies that enforce them. We find that market quotes for variance swaps are surprisingly close to the model‐free lower bounds we determine. We solve the problem by transforming it into an analogous question for a European option with a convex payoff. The lower bound becomes a problem in semi‐infinite linear programming which we solve in detail. The upper bound is explicit. We work in a model‐independent and probability‐free setup. In particular, we use and extend Follmer's pathwise stochastic calculus. Appropriate notions of arbitrage and admissibility are introduced. This allows us to establish the usual hedging relation between the variance swap and the “log contract” and similar connections for weighted variance swaps. Our results take the form of a FTAP: we show that the absence of (weak) arbitrage is equivalent to the existence of a classical model which reproduces the observed prices via risk‐neutral expectations of discounted payoffs.

The literature contains four explanations for the private placement discount. I find that all four contribute to the discount: loss of option value due to transfer restrictions, equity ownership con-centration, information gathering, and overvaluation and expected underperformance post-issue. An average-strike put option model calculates marketability discounts that are consistent with empirical private placement discounts when observed discounts are adjusted for equity ownership concentration, information, and overvaluation effects. In contrast to the positive signaling effect of traditional private placement announcements, there is a negative signaling effect for private investments in public equity when the firm commits to register the shares promptly. [ABSTRACT FROM AUTHOR]

U.S. exchange-traded stock options are exercisable before expiration. While put options should frequently be exercised early to earn interest, they are not. In this paper, we derive an early exercise decision rule and then examine actual exercise behavior during the period January 1996 through September 2008. We find that more than 3.96 million puts that should have been exercised early remain unexercised, representing over 3.7% of all outstanding puts. We also find that failure to exercise cost put option holders $1.9 billion in forgone interest income and that this interest is systematically captured by market makers and proprietary firms.

In this thesis, we prove that the optimal exercise boundary of the American put option is not convex when the dividend rate of the underlying assetwhich follows a geometric Brownian motion, is slightly larger than the risk-free interest rate. We show that the non-convex region occurs very near the expiry time. Numerical evidence is also provided which suggests that the convexity of the optimal exercise boundary is restored when the dividend rate is sufficiently larger than the interest rate. In addition we provide the near-expiry and far-from-expiry behavior of the boundary. To complete the rigorous proofs, we also show that the optimal exercise boundary has $C^infty$ regularity.

We investigate the risk-return characteristics of merger arbitrage in the Australian market for corporate control, whereby hedge fund managers acquire companies subject to a takeover offer. On average, a strategy of buying target companies and short-selling bidders making scrip offers would have generated an annual return of 30per cent from 1985 to 2008, excluding transaction costs, compared to the return on the broader market of 12per cent. However, performance is not market neutral, being positively associated with market returns during downturns and inversely related to market movements during rising markets. The payoffs to this strategy are analogous to a short straddle, whereby the investor is short a call and put option at the same exercise price. These results are consistent with large-sample evidence from the United States and the United Kingdom and have not previously been documented in Australia, in which prior evidence is based only on cash deals during the 1990s. © 2011 The Authors. Accounting and Finance

Corporate bond prices are known to be influenced by default and term structure risk in addition to non-default risks such as illiquidity. Putable corporate bonds allow investors to sell their holdings back to the issuer and may thus provide insurance against all of these risks. We first document empirically that embedded put option values are related to proxies for all three. In a second step, we develop a valuation model that simultaneously captures default and interest rate risk. We use this model to disentangle the reduction in yield spread enjoyed by putable bonds that can be attributed to each risk. Perhaps surprisingly, the most important reduction is due to mitigated default or spread risk, followed by term structure risk. The reduction in the non-default component is present but rather small.

State and local public sector employee pensions are widely known to be underfunded, but pension financial reports do not reveal the true extent of funding shortfalls. Pension accounting methods assume that plan investments can earn high returns without taking any account of the market risk involved. This gives a false sense of the financial strength of public sector pensions and understates risks to taxpayers. Since accrued pension benefits are legally and constitutionally protected, any pension funding shortfalls must be met by taxpayers. This benefit guarantee amounts to an effective put option on plan investments, the cost of which is not disclosed under current actuarial accounting. This paper uses an options pricing method to calculate the market value of taxpayer guarantees underlying public sector pensions. The average funding ratio declines from 83 percent under actuarial accounting to 45 percent under this options pricing approach. The typical state has unfunded public pension liabilities three times larger than its explicit government debt. Public pension shortfalls equal an average of 27 percent of state gross domestic product, posing a significant fiscal challenge in coming years. Accurate measures of public pension liabilities are important for policy makers, taxpayers, investors considering the economic environment in which to start or locate a business, and bond purchasers considering the risk premia appropriate to municipal government bonds that are in practice subordinate to public pension liabilities.

This paper offers new evidence on informed trading around merger and acquisition announcements from the UK equity and options market. The analysis suggests that in about 25–33% of events there is abnormal option trading volume during the month that precedes the announcement. Such evidence is found in both call and put option volumes, is robust to different “estimation” and “event window” lengths, to different sub-samples, and to liquidity considerations. These results support the argument that informed investors will transact in both the options and the stock market, and are comparable to results reported by the FSA in the cash market.

In takeovers bidders offer a premium to target firm shareholders but the determinants of such premium are not clearly identified. Among the factors previously examined in the literature are prior target undervaluation, expected synergy and overpayment due to behavioural biases like hubris. In this paper we use an option pricing approach to decompose the observed takeover premia. We also test the implications of recent real options-based models of takeover premia and risk changes surrounding takeovers. We model the observed target stock price as a portfolio of unobserved stock price and a put option whose value depends on a number of target and deal characteristics that impinge on the probability of bid success. For a sample of over 200 UK cash takeover bids during 1990–2004, we estimate the put value using the Black-Scholes option pricing model and find that target firm revaluation accounts for a substantial part of the observed takeover premium and the put value accounts for a smaller, but still significant, proportion. The latter is higher in hostile, failed and longer bids. The put option value is also significantly correlated with the relative riskiness of bidders and targets, and synergy as predicted by Lambrecht (2004). Movements in betas in the run up to takeover announcements and in the post-announcement period are consistent with the real options-based predictions of Hackbarth and Morellec (2008). This study contributes to a better understanding of the true determinants of takeover premium and demonstrates the usefulness of option pricing models and provides a preliminary test of real options models in understanding and measuring the impact of UK takeovers on firm risk and shareholder gains.

During the credit and liquidity crisis in 2007 and 2008, banks found themselves largely unable to raise significant new equity quickly from parties other than sovereign wealth funds and governments. Some banks have thus recently begun to consider contingent capital as a means of pre-arranging recapitalizations for future crises. Contingent capital is a type of put option that entitles a company to issue new securities on pre-negotiated terms, often following the occurrence of one or more risk-based triggering events. This article compares the economic merits of a new security—a “contingent reverse convertible” or CRC—against more traditional forms of contingent capital. In November 2009, Lloyds Banking Group plc issued “Enhanced Capital Notes”—subordinated debt that converts into common stock if Lloyds's core regulatory capital falls below 5% of its regulatory risk-weigh ted assets. This CRC is not strictly speaking a form of contingent capital, but it does give banks the potential to recapitalize themselves quickly in the face of a crisis without having to turn to governments and taxpayers. One important limitation of CRCs is that because they do not generate new cash for a bank at the time of conversion, they are unlikely to stop a liquidity crisis once it has begun. More traditional contingent capital facilities, by contrast, do put cash in the hands of the issuer at the time the facility is drawn. But even for those inclined to use CRCs, it may be unrealistic to expect many other institutions to imitate the structure of the Lloyds offering. Persuading existing investors to take a more subordinated position in a bank's capital structure and write a put option to the bank on its own stock will be neither cheap nor easy. For this reason, the more traditional solutions used to date may have more success with banks, though arriving at a price that helps issuers and satisfies investors will be a challenge for those structures as well.

The two main legal forms of insurance companies are stock companies and mutual companies. The main characteristic of a mutual company is that it is owned and controlled, at least in theory, by its policyholders. In a context of growth, one major handicap inherent in the mutual form is its limited access to the equity market. A new type of insurance organization was recently allowed in the province of Quebec, Canada, so that an insurance company would have access to the equity market while aiming at preserving the mutual philosophy. According to this new scheme, the voting rights of the policyholders are transferred from the insurance company to an upstream holding whose sole purpose is to control the insurance company transformed from a mutual to a stock company. Outside investors are then allowed to hold a minority interest in this new stock company. This type of organization will be described in more detail later on. It is believed that this new scheme will attract the capital necessary to achieve growth objectives, while leaving the control of the stock insurance company in the hands of the policyholders. The relative advantages of the stock and mutual forms of insurance companies have been studied from different standpoints, and therefore contributions can be found in the actuarial, legal, and financial economic literature. While some authors have focused on technical and performance issues related to the legal form of the company, and to the conversion of stock to mutual or vice-versa (Cameron, 1981; Gold, 1975; Plumley, 1984; Spiller, 1972), a great deal of research has been devoted to issues of governance, incentive conflicts, and the determinants of ownership structure in stock and mutual companies (Carter & Stover, 1990; Doherty & Dionne, 1987; Gingras, 1984; Hansmann, 1985; Lamm-Tennant & Starks, 1989; Mayers & Smith, 1981, 198; McNamara & Rhee, 1992). Most of this literature put into evidence the widespread agency problems in the insurance industry, which can be related, to some degree, to the high level of asymmetry of information between the seller and the buyer in this industry. The asymmetry of information is not surprising, given that a life insurance policy is an intangible product, based on a probabilistic reasoning not easily grasped. The history of the North American life insurance industry unveils a non-negligible number of mutualisations and demutualisations. These have been rationalized along different lines, often related to agency problems, and are often associated with wealth transfers from the policyholders to the shareholders. Let us recall here the Armstrong-Hughes investigation at the beginning of the century, which resulted in a large number of mutualisations. This investigation was set up following, notably, the detection of widespread use of disguised tontine plans where the owners of the insurance company were the main beneficiaries at the expense of the policyholders. A wave of mutualisations in Canada at the end of the 1950s and the beginning of the 1960s was officially justified by the fear of foreign takeovers. However, it could as well be argued that some mutualisations served as a pretext for private stockholders to make a good deal at the expense of future policyholders. A main issue in most demutualisations was the estimation of an appropriate compensation to the policyholders, in order to avoid wealth transfers from the policyholders to the stockholders. The new form of insurance organization analyzed in this paper also carries with it potential wealth transfers at the expense of the policyholders, in the form of a put option given to external investors. It will be argued, however, that in this special case, it can actually be rational for the policyholders to subsidize external shareholders, in order to avoid bankruptcy costs. Bearing in mind the potential wealth transfers associated with a change of legal form, the purpose of this paper is to analyze this new form of organization where mutualist and capitalist shareholders coexist. …

In the past several years, many exchanges in North America and Europe have introduced options on foreign stock indexes. The most popular are Nikkei put warrants (hereafter, NPWs). In Canada, six NPWs have been listed on the Toronto Stock Exchange (see the Appendix for details). The mushrooming of NPWs around the turn of the decade was mainly due to the belief that the Japanese stocks were seriously overvalued. That belief was subsequently confirmed by the movement of the Nikkei index: Over the last three years, it has dropped by about 50%. As a result, most of the NPWs have been exercised. Although the creation of NPWs was mainly motivated by an assessment of the market movement, many similar products have been introduced for other reasons.(1) One important rationale is the ability of investors to participate in the foreign stock market without incurring otherwise prohibitive transaction costs. In fact, some of the foreign index warrants allow investors to participate in the foreign stock index movements without incurring exchange rate risk. Given the globalization of the world financial markets, it is logical to foresee more development and creation of cross-currency instruments such as NPWs. Despite the popularity of these innovative products, the literature has been lacking in formal treatments of the new instruments. Although some authors have examined the theoretical pricing of cross-currency products, very few have examined the empirical evidence in this market.(2) There are two exceptions. Chen, Sears, and Shahrokhi (1992) studied the price behaviour of NPWs traded on the American Stock Exchange. Wei (1992a) empirically tested pricing models, using NPWs traded on the Toronto Stock Exchange. The question of market efficiency of the NPW market is largely unanswered. The purpose of this paper is to investigate efficiency of the NPW market. Specifically, NPWs traded on the Toronto Stock Exchange were used to evaluate two trading strategies designed to make arbitrage profits. In the remainder of the paper, we will present the NPWs and their pricing models, describe the data and testing methodologies, and report empirical results. NIKKEI PUT WARRANTS AND THEIR VALUATION An NPW is an American put option written on the Nikkei 225 index. Although the index the underlying asset is denominated in Japanese yen, the warrants are traded in dollars. Therefore, it matters as to how the Japanese yen payoff is converted into dollars. Existing NPWs can be classified into three different categories, according to conversion scheme. We will use the following notation. S = Nikkei 225 index level in yen; X = current Cdn$/JapY exchange rate; X sub 0 = pre-specified, fixed exchange rate; K = exercise price in yen; r = Canadian risk-free interest rate; r sub f = Japanese risk-free interest rate; sigma sub s , = volatility of the Nikkei index; sigma sub x , = volatility of the exchange rate; rho = correlation coefficient between the index and the exchange rate; q = continuous dividend yield on the Nikkei index; t = current time; T = maturity date. In terms of payoffs, the three categories can be characterised as follows. Category--Payoff upon exercise in dollars Category I NPWs--Max [0, X sub T (K - S sub T )] Category II NPWs--Max [0, X sub 0 (K - S sub T )] Category III NPWs--Max [0, X sub 0 K - X sub T S sub T ] It is seen that the exchange rate enters the payoff function in different ways. For category I NPWs, the exchange rate simply serves as a currency conversion factor. Therefore, holding a category I NPW is exactly like holding an ordinary Japanese index put option. This is because the spot exchange rate at the time of exercise is always used to convert the yen payoff. It is, however, not the case with a category III NPW. Here, the exercise price is converted upfront, at exchange rate X sub 0 , which is constant throughout the life of the warrant, but the Nikkei index is converted at the spot exchange rate at the time of exercise. …

For stocks of a listed company subject to a takeover offer, a premium must be paid by the bidder to induce acceptance of the offer. For partial takeovers, this premium can be modelled as a put option. While the takeover is current, temporary support for the stock may materialize, possibly resulting in increased prices. The price of options or warrants over the target stock can be used as a means of estimating the ex-takeover stock price, the takeover premium and any extra support that temporarily may be in the observed market price. This leads to an evaluation of the probable success of the takeover.

Real options are valuable sources of flexibility that are either inherent in, or can be built into, corporate assets. The value of such options are generally not captured by the standard discounted cash flow (DCF) approach, but can be estimated using a variant of financial option pricing techniques. This article provides an overview of the basics of real option valuation by examining four important kinds of real options: 1The option to make follow-on investments. Companies often cite “strategic” value when taking on negative-NPV projects. A close look at the payoffs from such projects reveals call options on follow-on projects in addition to the immediate cash flows from the projects. Today's investments can generate tomorrow's opportunities. 2The option to wait (and learn) before investing. This is equivalent to owning a call option on the investment project. The call is exercised when the firm commits to the project. But often it's better to defer a positive-NPV project in order to keep the call alive. Deferral is most attractive when uncertainty is great and immediate project cash flows—which are lost or postponed by waiting—are small. 3The option to abandon. The option to abandon a project provides partial insurance against failure. This is a put option; the put's exercise price is the value of the project's assets if sold or shifted to a more valuable use. 4The option to vary the firm's output or its production methods. Companies often build flexibility into their production facilities so that they can use the cheapest raw materials or produce the most valuable set of outputs. In this case they effectively acquire the option to exchange one asset for another. The authors also make the point that, in most applications, real-option valuation methods are a complement to, not a substitute for, the DCF method. Indeed DCF, which is best suited to and usually sufficient for safe investments and “cash cow” assets, is typically the starting point for real-option analyses. In such cases, DCF is used to generate the values of the “underlying assets”—that is, the projects when viewed without their options or sources of flexibility.

We study the fair price of American put option with regime-switching volatility. Assuming that volatility σ(t) takes two different values σ1 and σ2, applying Δ hedging technique we obtain a system of evolutionary variational inequalities, which possesses two free boundaries (optimal exercise boundaries). The following are the main results of this paper. 1. Two free boundaries are monotonic and infinitely differentiable. 2. The optimal exercise boundary of American put option with regime-switching volatility in the bearish (or bullish) market is smaller (or higher) than the one of standard American put option. And the price of American put option with regime-switching volatility in the bearish (or bullish) market is higher (or smaller) than the one of standard American put option. 3. The solution of problem (1) is unique. These results are original in the option pricing with regime-switching volatility, the proof is technical. Copyright © 2008 John Wiley & Sons, Ltd.

We show that the optimal exercise boundary for the American put option with non-dividend-paying asset is convex. With this convexity result, we then give a simple rigorous argument providing an accurate asymptotic behavior for the exercise boundary near expiry.

Introduced by Kifer (2000), game options function in the same way as American options with the added feature that the writer may also choose to exercise, at which time they must pay out the intrinsic option value of that moment plus a penalty. In Kyprianou (2004) an explicit formula was obtained for the value function of the perpetual put option of this type. Crucial to the calculations which lead to the aforementioned formula was the perpetual nature of the option. In this paper we address how to characterize the value function of the finite expiry version of this option via mixtures of other exotic options by using mainly martingale arguments.

There is a close correspondence between buffer stock stabilization of primary commodity prices and hedging strategies using futures or options markets. In particular, bandwidth stabilization, employed in most buffer stock agreements, closely resembles the strategy obtained by purchasing a put option and writing a call option at prices symmetrically below and above the central price. This suggests that the choice between hedging and stabilization should depend less on th e properties of hedged and stabilized revenues under ideal conditions than on the implications of departures from these conditions. Copyright 1988 by Blackwell Publishing Ltd and the Board of Trustees of the Bulletin of Economic Research

In this article, the authors derive explicit formulas for European foreign exchange (FX) call and put option values when the exchange rate dynamics are governed by jump-diffusion processes. The authors use a simple general equilibrium international asset pricing model with continuous trading and frictionless international capital markets. The domestic and foreign price level are introduced as state variables that contain jumps caused by monetary shocks and catastrophic events such as 9/11 or Hurricane Katrina. The domestic and foreign interest rates are stochastic and endogenously determined in the model and are shown to be critically affected by the jump risk of the foreign exchange. The model shows that the behavior of FX options is affected through the impact of state variables and parameters on the nominal interest rates. The model contrasts with those of M. Garman and S. Kohlhagen (1983) and O. Grabbe (1983), whose models have exogenously determined interest rates. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:669–695, 2007

Lenders are frequently accused of mispricing the put option embedded in nonrecourse lending. Prior research shows one lender's incentives to underprice. Here, we identify the conditions for a marketwide underpricing equilibrium. We demonstrate that, in a market with many players, given sufficient time, a race to the bottom and marketwide mispricing are inevitable. Underpricing occurs because bank managers and shareholders exploit mispriced deposit insurance. We show that the probability of the underpricing equilibrium increases with time since the previous market crash and that the more volatile the underlying asset market, the more likely it is subject to underpricing.

Two standard-setting approaches have emerged globally to guide the choice of accounting for securitizations: the control and components approach (SFAS No. 125 and SFAS No. 140) and the risks and rewards transfer approach (IAS No. 39). A lack of consensus about derecognition accounting is a major impediment to achieving convergence in global standards that must be resolved. Thus, both SFAS No. 140 and IAS No. 39 will be reexamined, and evidence pertinent to the debate is timely and important. In this study, we present evidence consistent with the view of credit-rating analysts, who view many securitizations as, in substance, secured borrowings. Specifically, for a sample of originators applying sale accounting guidance in SFAS No. 125/140 during the period 1997-2003, we show that off-balance-sheet debt related to securitizations has, on average, the same risk-relevance for explaining market measures of risk (that is, CAPM beta) as on-balance-sheet debt. We also find that, in a returns and earnings association framework, the pricing multiple on securitization gains declines as the amount of off-balance-sheet debt increases, implying that investors take off-balance-sheet debt into account when assessing the valuation-relevance of such gains. For those who advocate the control and components approach to securitization accounting, our results suggest that, at least for frequent securitizers, the put option arising from implicit recourse is a "missing piece" that is not currently accounted for when calculating securitization gains. Our results challenge the extant measurement standards in SFAS No. 140.

The purpose of this paper is to explain why leases have a purchase option and how the exercise price of this option is determined. We follow Demski and Sappington's (1991) approach by using a double moral hazard setting. One limitation of their model is that the agent has unlimited liability. The agent has to have enough wealth and the obligation to buy the firm when the principal decides to exercise the put option. In our paper, this problem is resolved by using a call option, which is a feature of many lease contracts. We show that leases with a purchase option can completely resolve the double moral hazard problem even if all the variables in the model are unverifiable. It is the threat of being the residual claimant that induces the lessor to provide an efficient level of effort. On the other hand, it is the opportunity of being the residual claimant that induces the lessee to maintain the asset efficiently. Finally, the model predicts that certain leased assets are not properly accounted for under the current accounting standards for leasing.

We find that the long-term equity premium is consistent with both GDP growth and portfolio insurance. We use a supply-side growth model and demonstrate that the arithmetic average stock market return and the returns on corporate assets and debt depend on GDP per capita growth. The implied equity premium matches the U.S. historical average over 1926‐ 2001. Separately, we find that the equity premium tracks the value of a put option on the S&P 500. Our theory predicts a smaller equity premium in the future, assuming that the recent regime shifts in dividend policies, interest rates, and tax rates are permanent.

Variable annuity contracts frequently have many options and option-like features embedded in the contracts. Some are obvious, such as guaranteed minimum death benefits (GMDBs), while others are less obviously option-ike. In this article, we consider the effect of the real option to transfer funds between fixed and variable accounts. If a GMDB rider is considered in isolation, it is sometimes in the policyholder's interest to transfer to the fixed fund if the fixed fund earns less than the variable fund in a risk-neutral world. On the other hand, the option to transfer will not be used if the entire annuity and rider are considered together. INTRODUCTION There have been a number of papers in recent years dealing with the valuation of guaranteed minimum death benefits (GMDBs) embedded in annuity contracts. These riders guarantee some minimum benefit at death, which is frequently the return of premiums paid or a fixed percentage rollup on that premium. They resemble a sequence of European put options, as the annuitant cannot choose the time of his own death. A few papers discuss option pricing from an actuarial standpoint. Gerber and Shiu (1994) discuss methods of obtaining closed-form option prices using Esscher transforms. Tiong (2000) uses this approach to value equity-indexed annuities. Milevsky and Promislow (2001) and Milevsky and Posner (2001) extend the discussion to cases more specifically related to insurance and annuity contracts by looking at the option to annuitize and the valuation of GMDBs. There has recently been recognition of the fact that even GMDBs have features of American options. Milevsky and Salisbury (2001) note that policyholders have a real option to lapse their policy and reinstate the death benefit when their policy is out of the money and this option should be priced for. They assume that policyholders exercise their option optimally in that they would lapse and reinstate immediately if there were no surrender charges to prevent it. With this assumption, they calculate the surrender charge necessary to fully compensate the insurance company for this loss of income. This surrender charge is one where the individual owning the policy would be indifferent between maintaining the policy and lapsing it. A second option that is frequently available in these contracts is the option to transfer funds between a variable account and an attached fixed account that earns a guaranteed rate. A particular worry is that individual policyholders will choose to transfer their money from the variable account to the fixed account when the GMDB is in-the-money and thereby lock in a positive GMDB for a substantial period into the future. This option to transfer would behave very much like an American option to lock in a GMDB at a time of the policyholder's own choosing. Unlike an American option, however, the decision to transfer is not irreversible. Another American-type option exists, which allows the policyholder to transfer back to variable account. Clearly, this option has value if the fixed fund were to rise to the value of the GMDB strike, as the value would be zero if the funds were in the fixed account and positive if the funds were in the variable account. The transfer option in these contracts bears some similarity to passport options that have attracted attention recently. They are even more similar to vacation put options introduced by Shreve and Vecer (2000). These options are special cases of call options on a traded account. The individual owning the account starts with an initial wealth [[pi].sub.0] and is allowed to invest a value [q.sub.t] in an asset that follows a geometric Brownian motion process. At maturity time T, the investor receives the maximum of 0 and the value [[pi].sub.T]. The value [q.sub.t] is constrained to be in the range [less than or equal to] [q.sub.t] [less than or equal to] [beta]. The case = [beta] = 1 corresponds to a European call option, and a = [beta] = -1 corresponds to a European put option. …

Risk management techniques such as value at risk and conditional value at risk focus attention on protecting the downside exposures without penalizing the upside exposures. The implied welfare functions are equivalent to an otherwise risk neutral agent with a put option exposure on the downside. The correspondence can be exploited to design smoother loss measures and numerically based solutions for optimal hedge ratios. A statistically well-adapted hedge object for the firm is the corporate terms of trade, which balances up output and expense prices as a single index related to the net profit margin. The methods are applied to the NZ dairy industry to derive optimal foreign exchange forwards based hedges. It is not always optimal to rely solely on forward discounts or premiums. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:1059–1088, 2006

A continuous-time mean-variance portfolio selection problem is studied where all the market coefficients are random and the wealth process under any admissible trading strategy is not allowed to be below zero at any time. The trading strategy under consideration is defined in terms of the dollar amounts, rather than the proportions of wealth, allocated in individual stocks. The problem is completely solved using a decomposition approach. Specifically, a (constrained) variance minimizing problem is formulated and its feasibility is characterized. Then, after a system of equations for two Lagrange multipliers is solved, variance minimizing portfolios are derived as the replicating portfolios of some contingent claims, and the variance minimizing frontier is obtained. Finally, the efficient frontier is identified as an appropriate portion of the variance minimizing frontier after the monotonicity of the minimum variance on the expected terminal wealth over this portion is proved and all the efficient portfolios are found. In the special case where the market coefficients are deterministic, efficient portfolios are explicitly expressed as feedback of the current wealth, and the efficient frontier is represented by parameterized equations. Our results indicate that the efficient policy for a mean-variance investor is simply to purchase a European put option that is chosen, according to his or her risk preferences, from a particular class of options. © 2005 Blackwell Publishing Inc.

We show how the change-of-variable formula with local time on curves derived recently in Peskir (2002) can be used to prove that the optimal stopping boundary for the American put option can be characterized as the unique solution of a nonlinear integral equation arising from the early exercise premium representation. This settles the question raised in Myneni (1992) and dating back to McKean (1965).

Empirical research on mortgage default in the single-family market has focused on the value of the borrower's put option using house price indices to estimate contemporaneous loan-to-value ratio or the probability of negative equity. But since the borrower possesses the option to increase leverage by taking on additional debt secured by junior liens subsequent to loan origination (a phenomenon termed here equity dilution), even a perfect house price adjustment cannot be expected to accurately measure changes in borrower equity over time. Since junior liens are generally unobservable to senior debt holders, proxies are required in empirical applications. This paper employs an independent estimate of junior lien probability developed from the 1998 Survey of Consumer Finances combined with loan level mortgage performance data to examine the role junior liens play in increasing default risk.

The reset right embedded in an option contract is the privilege given to the option holder to reset certain terms in the contract according to specified rules at the moment of shouting, where the time to shout is chosen optimally by the holder. For example, a shout option with strike reset right entitles its holder to choose the time to take ownership of an at-the-money option. This paper develops the theoretical framework of analyzing the optimal shouting policies to be adopted by the holder of an option with reset right on the strike price. It is observed that the optimal shouting policy depends on the time dependent behaviors of the expected discounted value of the at-the-money option received upon shouting. During the time period when the theta of the expected discounted value of the new option received is positive, it is never optimal for the holder to shout at any level of asset value. At those times when the theta is negative, we show that there exists a threshold value for the asset price above which the holder of a reset put option should shout optimally. For the shout floor, we obtain an analytic representation of the price function. For the reset put option, we derive the integral representation of the shouting right premium and analyze the asymptotic behaviors of the optimal shouting boundaries at time close to expiry and infinite time from expiry. We also provide numerical results for the option values and shouting boundaries using the binomial scheme and recursive integration method. Accuracy and run time efficiency of these two numerical schemes are compared.

In this article we deal with the problem of pricing a guaranteed life insurance participating policy, sold in the Italian market, which embeds a surrender option. This feature is an American-style put option that enables the policyholder to sell back the contract to the insurer at the cash surrender value. Employing a recursive binomial formula patterned after the Cox, Ross, and Rubinstein (1979) discrete option pricing model we compute, first of all, the total price of the contract, which also includes a compensation for the participation feature ("participation option," henceforth). Then this price is split into the value of three components: the basic contract, the participation option, and the surrender option. The numerical implementation of the model allows us to catch some comparative statics properties and to tackle the problem of suitably fixing the contractual parameters in order to obtain the premium computed by insurance companies according to standard actuarial practice.

In this paper, we apply a copula function pricing technique to the evaluation of credit derivatives, namely a vulnerable default put option and a credit switch. Also in this case, copulas enable one to separate the specification of marginal default probabilities from their dependence structure. Their use is based here on no–arbitrage arguments, which provide pricing bounds and easy–to–implement super–replication strategies. At a second stage, we specify the copula function to be a mixture one. In this case, we obtain closed form prices and hedges, which we calibrate on real market data. For the sake of comparison, we add a Clayton calibration. (J.E.L: G11, G12).

The main option pricing bounds in the literature were originally obtained through various disparate methods. I show that those bounds can be derived from a single analytical framework. The key to this synthesis lies in the use of a general expression for the price of a call option depending on the corresponding put option's discount factor. Although the put's discount factor is unknown, it can be bounded from below. I use this lower bound on the put's discount factor to derive traditional lower bounds for call prices. In addition, I extend the literature by finding a new tighter lower bound.

High Yield Equity Notes are securities that provide the noteholder with a cash flow stream that comprises a fixed yield and a short position in a European put option on the shares of an Australian company. This paper examines the pricing of these securities and finds apparent overpricing compared with expectations given standard pricing relationships. This apparent overpricing is consistent with the low transaction costs incurred by purchasers of High Yield Equity Notes.

Explicit expressions valid near expiry are derived for the values and the optimal exercise boundaries of American put and call options on assets with dividends. The results depend sensitively on the ratio of the dividend yield rate D to the interest rate r. For D>r the put boundary near expiry tends parabolically to the value rK/D where K is the strike price, while for D≤r the boundary tends to K in the parabolic-logarithmic form found for the case D=0 by Barles et al. (1995) and by Kuske and Keller (1998). For the call, these two behaviors are interchanged: parabolic and tending to rK/D for D