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This paper proposes a novel equity‐price‐tree‐based convertible bond (CB) pricing model based on the first‐passage default model under stochastic interest rates. By regarding equity values as down‐and‐out call options on firm values (FVs), at each tree node, we solve the implied FV and equity‐price volatility (EPV), and then endogenously settle the default probability (DP) and also the dilution effect subject to CB conversions with the implied FV and capital structure. Our model captures the stylized negative (positive) relationships between the stochastically evolving DP and FV or EP (EPV) that cannot be fully achieved by existing CB pricing models. [ABSTRACT FROM AUTHOR]

Options can be priced by the lattice model, the results of which converge to the theoretical option value as the lattice's number of time steps n approaches infinity. The time complexity of a common dynamic programming pricing approach on the lattice is slow (at least O n 2 ), and a large n is required to obtain accurate option values. Although O n -time combinatorial pricing algorithms have been developed for the classical binomial lattice, significantly oscillating convergence behavior makes them impractical. The flexibility of trinomial lattices can be leveraged to reduce the oscillation, but there are as yet no linear-time algorithms on trinomial lattices. We develop O n -time combinatorial pricing algorithms for polynomial options that cannot be analytically priced. The commonly traded plain vanilla and power options are degenerated cases of polynomial options. Barrier options that cannot be stably priced by the binomial lattice can be stably priced by our O n -time algorithm on a trinomial lattice. Numerical experiments demonstrate the efficiency and accuracy of our O n -time trinomial lattice algorithms. [ABSTRACT FROM AUTHOR]

Item concept modeling is commonly achieved by leveraging textual information. However, many existing models do not leverage the inferential property of concepts to capture word meanings, which therefore ignores the relatedness between correlated concepts, a phenomenon which we term conceptual “correlation sparsity.” In this paper, we distinguish between word modeling and concept modeling and propose an item concept modeling framework centering around the item concept network (ICN). ICN models and further enriches item concepts by leveraging the inferential property of concepts and thus addresses the correlation sparsity issue. Specifically, there are two stages in the proposed framework: ICN construction and embedding learning. In the first stage, we propose a generalized network construction method to build ICN, a structured network which infers expanded concepts for items via matrix operations. The second stage leverages neighborhood proximity to learn item and concept embeddings. With the proposed ICN, the resulting embedding facilitates both homogeneous and heterogeneous tasks, such as item-to-item and concept-to-item retrieval, and delivers related results which are more diverse than traditional keyword-matching-based approaches. As our experiments on two real-world datasets show, the framework encodes useful conceptual information and thus outperforms traditional methods in various item classification and retrieval tasks. [ABSTRACT FROM AUTHOR]

A catastrophe equity put (CatEPut) is constructed to recapitalize an insurance company that suffers huge compensation payouts due to catastrophic events (CEs). The company can exercise its CatEPut to sell its stock to the counterparty at a predetermined price when its accumulated loss due to CEs exceeds a predetermined threshold and its own stock price falls below the strike price [ABSTRACT FROM AUTHOR]

With the rapid growth and the deregulation of financial markets, many complex derivatives have been structured to meet specific financial goals. Unfortunately, most complex derivatives have no analytical formulas for their prices, particularly when there is more than one market variable. As a result, these derivatives must be priced by numerical methods such as lattice. However, the nonlinearity error of lattices due to the nonlinearity of the derivative's value function could lead to oscillating prices. To construct an accurate, multivariate lattice, this study proposes a multiphase method that alleviates the oscillating problem by making the lattice match the 'critical locations,' locations where nonlinearity of the derivative's value function occurs. Moreover, our lattice has the ability to model the jumps in the market variables such as regular withdraws from an investment account, which is hard to deal with analytically. Numerical results for vulnerable options, insurance contracts guaranteed minimum withdrawal benefit (GMWB), and defaultable bonds show that our methodology can be applied to the pricing of a wide range of complex financial contracts. [ABSTRACT FROM AUTHOR]

Alzheimer's disease is a neurodegenerative illness. The Mini Mental State Examination (MMSE), Cognitive Abilities Screening Instrument (CASI) and Clinical Dementia Rating (CDR) are applied to assess whether a person suffers Alzheimer's disease and determine its severity. There are many confounding factors within those assessments, medical professionals need to bear in mind the pitfalls when evaluating the data and the patient.