Convex order for path-dependent American options using the Euler scheme of martingale jump diffusion process
نویسنده
چکیده
We explore the functional convex order of martingale diffusions and stochastic integrals with respect to their diffusion coefficient in both a Brownian and a jump framework. We finally extend this result to the Snell envelope of functionals of these process i.e. to American options with pathwise payoffs.
منابع مشابه
Pricing Options in Jump-Diffusion Models: An Extrapolation Approach
We propose a new computational method for the valuation of options in jump-diffusion models. The option value function for European and barrier options satisfies a partial integrodifferential equation (PIDE). This PIDE is commonly integrated in time by implicit-explicit (IMEX) time discretization schemes, where the differential (diffusion) term is treated implicitly, while the integral (jump) t...
متن کاملConvex order for path-dependent derivatives: a dynamic programming approach
We investigate the (functional) convex order of for various continuous martingale processes, either with respect to their diffusions coefficients for Lévy-driven SDEs or their integrands for stochastic integrals. Main results are bordered by counterexamples. Various upper and lower bounds can be derived for pathwise European option prices in local volatility models. In view of numerical applica...
متن کاملOption Pricing Under a Mixed-Exponential Jump Diffusion Model
This paper aims at extending the analytical tractability of the Black-Scholes model to alternative models with arbitrary jump size distributions. More precisely, we propose a jump diffusion model for asset prices whose jump sizes have a mixed-exponential distribution, which is a weighted average of exponential distributions but with possibly negative weights. The new model extends existing mode...
متن کاملJump-Diffusion Models for Asset Pricing in Financial Engineering
In this survey we shall focus on the following issues related to jump-diffusion models for asset pricing in financial engineering. (1) The controversy over tailweight of distributions. (2) Identifying a risk-neutral pricing measure by using the rational expectations equilibrium. (3) Using Laplace transforms to pricing options, including European call/put options, path-dependent options, such as...
متن کاملA fast high-order sinc-based algorithm for pricing options under jump-diffusion processes
An implicit-explicit Euler scheme in temporal direction is employed to discretize a partial integro-differential equation, which arises in pricing options under jumpdiffusion process. Then the semi-discretized equation is approximated in space by the Sinc-Galerkin method with exponential accuracy. Meanwhile, the domain decomposition method is incorporated to handle the non-smoothness of the pay...
متن کامل