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We introduce a new class of dynamic utilities that are generated forward in time. We discuss the associated value functions, optimal investments, and indifference prices and we compare them with their traditional counterparts, implied by backward dynamic utilities. [ABSTRACT FROM AUTHOR]

We study the effect of risk aversion on the valuation of credit derivatives. Using the technology of utility-indiffierence valuation in intensity-based models of default risk, we analyze resulting yield spreads for single-name defaultable bonds and a simple representative two-name credit derivative. The impact of risk averse valuation on prices and yield spreads is expressed in terms of "effective correlation." [ABSTRACT FROM AUTHOR]

The one-factor Gaussian model is well known not to fit the prices of the different tranches of a collateralized debt obligation (CDO) simultaneously, leading to the implied correlation smile. Recently, other one-factor models based on different distributions have been proposed. Moosbrucker [12] used a one-factor Variance-Gamma (VG) model, Kalemanova et al. [7] and Guégan and Houdain [6] worked with a normal inverse Gaussian (NIG) factor model, and Baxter [3] introduced the Brownian Variance-Gamma (BVG) model. These models bring more flexibility into the dependence structure and allow tail dependence. We unify these approaches, describe a generic one-factor Lévy model, and work out the large homogeneous portfolio (LHP) approximation. Then we discuss several examples and calibrate a battery of models to market data. [ABSTRACT FROM AUTHOR]

A new approach to credit risk modelling is introduced that avoids the use of inaccessible stopping times. Default events are associated directly with the failure of obligors to make contractually agreed payments. Noisy information about impending cash flows is available to market participants. In this framework, the market filtration is modelled explicitly, and is assumed to be generated by one or more independent market information processes. Each such information process carries partial information about the values of the market factors that determine future cash flows. For each market factor, the rate at which true information is provided to market participants concerning the eventual value of the factor is a parameter of the model. Analytical expressions that can be readily used for simulation are presented for the price processes of defaultable bonds with stochastic recovery. Similar expressions can be formulated for other debt instruments, including multi-name products. An explicit formula is derived for the value of an option on a defaultable discount bond. It is shown that the value of such an option is an increasing function of the rate at which true information is provided about the terminal payoff of the bond. One notable feature of the framework is that it satisfies an overall dynamic consistency condition that makes it suitable as a basis for practical modelling situations where frequent recalibration may be necessary. [ABSTRACT FROM AUTHOR]

The goals of the paper are as follows: (i) review some qualitative properties of oil and gas prices in the last 15 years; (ii) propose some mathematical elements towards a definition of mean reversion that would not be reduced to the form of the drift in a stochastic differential equation; (iii) conduct econometric tests in order to conclude whether mean reversion still exists in the energy commodity price behavior. Regarding the third point, a clear "break" in the properties of oil and natural gas prices and volatility can be exhibited in the period 2000-2001. [ABSTRACT FROM AUTHOR]

We derive forward partial integrodifferential equations (PIDEs) for pricing up-and-out and down-and-out call options when the underlying is a jump diffusion. We assume that the jump part of the returns process is an additive process. This framework includes the Variance-Gamma, finite moment logstable, Merton jump diffusion, Kou jump diffusion, Dupire, CEV, arcsinh normal, displaced diffusion, and Black-Scholes models as special cases. [ABSTRACT FROM AUTHOR]

In an affine term structure framework with stochastic volatility, we derive the characteristic function of the log swap rate. Having the characteristic function, we employ the fast Fourier transform (FFT) to price swaptions. Using ten years of swap rates and swaption premiums, model parameters are estimated using a square-root unscented Kalman filter. We investigate the relationship between model premiums and interest rate factors, as well as between market premiums and interest factors, to conclude that long-dated swaptions are highly correlated to the shape of the curve. [ABSTRACT FROM AUTHOR]

We review the Lévy-driven interest rate theory that has been developed in recent years. The intimate relations between the various approaches, as well as the differences, are outlined. The main purpose of this paper is to elaborate on calibration in the real world as well as in the risk-neutral setting. [ABSTRACT FROM AUTHOR]

Most financial asset-pricing models assume frictionless competitive markets that imply the absence of arbitrage opportunities. Given the absence of ar-bitrage opportunities and complete asset markets, there exists a unique martingale measure that implies martingale pricing formulae and replicating asset portfolios. In incomplete markets, or markets with transaction costs, these results must be modified to admit nonunique measures and the possibility of imperfectly replicating portfolios. Similar di3culties arise in markets with taxation. Some theoretical research has argued that some taxation functions will imply arbitrage opportunities and the nonexistence of a competitive asset economy. In this paper we construct a multiperiod, discrete time/state general equilibrium model of asset markets with transaction costs and taxes. The transaction cost technology and the tax system are quite general, so that we can include most discrete time/state models with transaction costs and taxation. We show that a competitive equilibrium exists. Our results require careful modeling of the government budget constraints to rule out tax arbi-trage possibilities. [ABSTRACT FROM AUTHOR]

This paper reviews and extends the mathematical finance literature on bubbles in complete markets. We provide a new characterization theorem for bubbles under the standard no-arbitrage framework, showing that bubbles can be of three types. Type 1 bubbles are uniformly integrable martingales, and these can exist with an infinite lifetime. Type 2 bubbles are nonuniformly integrable martingales, and these can exist for a finite, but unbounded, lifetime. Last, Type 3 bubbles are strict local martingales, and these can exist for a finite lifetime only. When one adds a no-dominance assumption (from Merton [24]), only Type 1 bubbles remain. In addition, under Merton's no-dominance hypothesis, put-call parity holds and there are no bubbles in standard call and put options. Our analysis implies that if one believes asset price bubbles exist and are an important economic phenomena, then asset markets must be incomplete. [ABSTRACT FROM AUTHOR]

This paper provides a brief tutorial on the notions of a zero volatility (ZV) spread and an option adjusted spread (OAS), as applied to fixed income securities. Using the standard definitions, it is shown that the zero volatility spread measures the percentage of a security's spread due to any embedded options and any mispricings. The mispricings could be due to either market or model error. In contrast, the OAS only measures the percentage of the security's spread due to mis-pricings. Refinements and alternative measures of a bond's embedded optionality and mispricings are also provided. [ABSTRACT FROM AUTHOR]

This article reviews the theory of fractional Brownian motion (fBm) in the white noise framework, and we present a new approach to the proof of Itô-type formulas for the stochastic calculus of fractional Brownian motion. [ABSTRACT FROM AUTHOR]

To prove their formulae for the moments of the characteristic polynomial of the generic matrix of U(N), Keating and Snaith [8] (see also Keating [7]) use Selberg's integrals as a ‘black box.' In this note, we point out some identities in law which are equivalent to the expressions of Selberg's integrals and which involve beta, gamma, and normal variables. However, this is a mere probabilistic translation of Selberg's results, and does not provide an independent proof of them. An outcome of some of these translations is that certain logarithms of (Vandermonde) random discriminants are self-decomposable, which hinges on the self-decomposability of the logarithms of the beta (a, b) (2a +b = ≥ 1) and gamma (a > 0) variables. Such self-decomposability properties have been of interest in some joint papers with D. Madan. [ABSTRACT FROM AUTHOR]

A number of remarkable properties of gamma processes are gathered in this paper, including realisation of their bridges, absolute continuity relationships, realisation of a gamma process as an inverse local time, and the effect of a gamma process as a time change. Some of them are put in perspective with their Brownian counterparts. [ABSTRACT FROM AUTHOR]

The Variance-Gamma (VG) process was introduced by Dilip B. Madan and Eugene Seneta as a model for asset returns in a paper that appeared in 1990, and subsequently used for option pricing in a 1991 paper by Dilip and Frank Milne. This paper serves as a tutorial overview of VG and Monte Carlo, including three methods for sequential simulation of the process, two bridge sampling methods, variance reduction via importance sampling, and estimation of the Greeks. [ABSTRACT FROM AUTHOR]

Dilip Madan and I worked on stochastic process models with stationary independent increments for the movement of log-prices at the University of Sydney in the period 1980-1990, and completed the 1990 paper [21] while respectively at the University of Maryland and the University of Virginia. The (symmetric) Variance- Gamma (VG) distribution for log-price increments and the VG stochastic process first appear in an Econometrics Discussion Paper in 1985 and two journal papers of 1987. The theme of the pre-1990 papers is estimation of parameters of log-price increment distributions that have real simple closed-form characteristic function, using this characteristic function directly on simulated data and Sydney Stock Exchange data. The present paper reviews the evolution of this theme, leading to the definitive theoretical study of the symmetric VG process in the 1990 paper. [ABSTRACT FROM AUTHOR]