Numerical analysis of American option pricing in a jump-diffusion model
Mathematics of Operations Research
Numerical analysis on binomial tree methods for a jump-diffusion model
Journal of Computational and Applied Mathematics
A Jump-Diffusion Model for Option Pricing
Management Science
A penalty method for American options with jump diffusion processes
Numerische Mathematik
Convergence of the Binomial Tree Method for American Options in a Jump-Diffusion Model
SIAM Journal on Numerical Analysis
A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models
SIAM Journal on Numerical Analysis
On the rate of convergence of the binomial tree scheme for American options
Numerische Mathematik
Optimal convergence rate of the explicit finite difference scheme for American option valuation
Journal of Computational and Applied Mathematics
Numerical valuation of options with jumps in the underlying
Applied Numerical Mathematics
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An American put option with jump diffusion can be modeled as an integro-variational inequality. With a penalization approximation and under the stability condition $\frac{\sigma^2 \Delta t}{\Delta x^2}\le 1$, where $\Delta x ={\rm ln}\,\frac {S_{n+1}}{S_n}$ ($S_t$-underlying asset price), we obtain the optimal convergence rate $O((\Delta x)+(\Delta t)^{1/2})$ of the binomial tree scheme for this variational inequality. Moreover, we define an approximate optimal exercise boundary within the framework of the binomial tree scheme and derive the convergence rate estimate $O((\Delta t)^{1/4})$ to the actual free boundary.