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Adaptive Continuous time Markov Chain Approximation Model toGeneral Jump-Diffusions
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TLDR
In this paper, a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications are proposed.Abstract:
We propose a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications. Our approach also accommodates state-dependent jump intensity and jump distribution, a flexibility that is very hard to achieve with other numerical methods. The Kologorov-Smirnov test shows that the proposed Markov chain transition density converges to the one given by the likelihood expansion formula as in Ait-Sahalia (2008). We provide numerical examples for European stock option pricing in Black and Scholes (1973), Merton (1976) and Kou
(2002).read more
Citations
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Journal ArticleDOI
Numerical methods for stochastic control problems in continuous time
TL;DR: K Kushner and P.H. Dupuis as discussed by the authors have published a book called "Kushner and Duyguluis, 1992: A History of the World Wide Web".
Journal ArticleDOI
Bayesian inference for discretely sampled Markov processes with closed-form likelihood expansions
TL;DR: A new Bayesian Markov chain Monte Carlo (MCMC) methodology for estimation of a wide class of multidimensional jump-diffusion models based on the closed-form likelihood approximations of Ait-Sahalia (2002, 2008).
Posted Content
USLV: Unspanned Stochastic-Local Volatility Model
Igor Halperin,Andrey Itkin +1 more
TL;DR: In this article, the authors propose a new framework for modeling stochastic local volatility, with potential applications to modeling derivatives on interest rates, commodities, credit, equity, FX etc., as well as hybrid derivatives.
Posted Content
Is Nonlinear Drift Implied by the Short-End of the Term Structure?
TL;DR: In this paper, nonlinear drift models of the short-rate are estimated using data on the short end of the term structure, where the cross-sectional relation is obtained by an analytical approximation.
Local Volatility Calibration with the Markov Chain Approximation
TL;DR: In this paper, the authors propose a method for calibrating the local volatility surface that relaxes the computational complexity associated with many models and prices options consistently with the volatility skew under a continuous time semi-closed form solution based on the Markov chain approximation of Kushner (1990).
References
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Journal ArticleDOI
The Pricing of Options and Corporate Liabilities
Fischer Black,Myron S. Scholes +1 more
TL;DR: In this paper, a theoretical valuation formula for options is derived, based on the assumption that options are correctly priced in the market and it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks.
Journal ArticleDOI
A Theory of the Term Structure of Interest Rates.
TL;DR: In this paper, the authors use an intertemporal general equilibrium asset pricing model to study the term structure of interest rates and find that anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices.
Journal ArticleDOI
Option pricing when underlying stock returns are discontinuous
TL;DR: In this article, an option pricing formula was derived for the more general case when the underlying stock returns are generated by a mixture of both continuous and jump processes, and the derived formula has most of the attractive features of the original Black-Scholes formula.
Journal ArticleDOI
The valuation of options for alternative stochastic processes
John C. Cox,Stephen A. Ross +1 more
TL;DR: In this paper, the authors examined the structure of option valuation problems and developed a new technique for their solution and introduced several jump and diffusion processes which have not been used in previous models.
Book
Numerical Methods for Stochastic Control Problems in Continuous Time
TL;DR: In this paper, a Markov chain is used to approximate the solution of the optimal stochastic control problem for diffusion, reflected diffusion, or jump-diffusion models, and a general method for obtaining a useful approximation is given.
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