Convergence rates of moving mesh methods for moving boundary partial integro–differential equations from regime-switching jump–diffusion Asian option pricing

Ma, Jingtang; Wang, Han

doi:10.1016/j.cam.2019.112598

Cited by 11 publications

(2 citation statements)

References 21 publications

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“…Obviously, the approximation of the integral is second‐order accurate. Another way to discrete the integral term is by using piecewise linear interpolation to approximate the function

u

(see, e.g., [39, 40]), and also has second‐order accuracy.…”

Section: Fully Discretizationmentioning

confidence: 99%

A variable step‐size extrapolated Crank–Nicolson method for option pricing under stochastic volatility model with jump

Mao,

Tian,

Wang

2023

Math Methods in App Sciences

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This paper studies the numerical solution of the stochastic volatility model with jumps under European options. This model can be transformed into a partial integro‐differential equation (PIDE) with spatial mixed derivative terms. Due to the nonsmoothness of the initial function, the variable step‐size extrapolated Crank–Nicolson (CN) method, which explicitly discretizes the jump term and implicitly the rest, is proposed to solve this model. The finite difference method is used to discretize the spatial differential operator, the composite trapezoidal rule to calculate the jump integral, and then a linear system with a nine‐diagonal coefficient matrix is obtained, which is easy to solve. The stability of the variable step‐size extrapolated CN method is then proved. Based on realistic regularity assumptions on the data, the consistency error and global error bounds of the variable step‐size extrapolated CN method are derived in norm. Compared with the variable step‐size IMEX BDF2 method and the variable step‐size IMEX MP method, the numerical results show the efficiency of the proposed variable step‐size extrapolated CN method.

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“…Obviously, the approximation of the integral is second‐order accurate. Another way to discrete the integral term is by using piecewise linear interpolation to approximate the function

u

(see, e.g., [39, 40]), and also has second‐order accuracy.…”

Section: Fully Discretizationmentioning

confidence: 99%

A variable step‐size extrapolated Crank–Nicolson method for option pricing under stochastic volatility model with jump

Mao,

Tian,

Wang

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…For details, one can refer to [4][5][6]. These schemes are applied to many fields, such as option pricing [7][8][9][10], portfolio optimization [11,12], and so on. Ruijter and Oosterlee [13] extended the Fourier cos method to two-dimensional FBSDE, named Fourier cos-cos method, and gave a numerical scheme to pricing European option and Bermudan option under GBM model and Heston stochastic volatility.…”

Section: Introductionmentioning

confidence: 99%

A regression-based Monte Carlo method to solve two-dimensional forward backward stochastic differential equations

Zhu

et al. 2021

Adv Differ Equ

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The purpose of this paper is to investigate the numerical solutions to two-dimensional forward backward stochastic differential equations(FBSDEs). Based on the Fourier cos-cos transform, the approximations of conditional expectations and their errors are studied with conditional characteristic functions. A new numerical scheme is proposed by using the least-squares regression-based Monte Carlo method to solve the initial value of FBSDEs. Finally, a numerical experiment in European option pricing is implemented to test the efficiency and stability of this scheme.

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Fast and Accurate Computation of the Regime-Switching Jump-Diffusion Option Prices Using Laplace Transform and Compact Difference with Convergence Guarantee

Chen¹

2023

Comput Econ

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Convergence rates of moving mesh methods for moving boundary partial integro–differential equations from regime-switching jump–diffusion Asian option pricing

Cited by 11 publications

References 21 publications

A variable step‐size extrapolated Crank–Nicolson method for option pricing under stochastic volatility model with jump

A variable step‐size extrapolated Crank–Nicolson method for option pricing under stochastic volatility model with jump

A regression-based Monte Carlo method to solve two-dimensional forward backward stochastic differential equations

Fast and Accurate Computation of the Regime-Switching Jump-Diffusion Option Prices Using Laplace Transform and Compact Difference with Convergence Guarantee

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