In this paper,we construct and analyze a Crank-Nicolson fitted finite volume scheme for pricing European options under regime-switching Kou’s jumpdiffusion model which is governed by a system of partial integro-diffe...In this paper,we construct and analyze a Crank-Nicolson fitted finite volume scheme for pricing European options under regime-switching Kou’s jumpdiffusion model which is governed by a system of partial integro-differential equations(PIDEs).We show that this scheme is consistent,stable and monotone as the mesh sizes in space and time approach zero,hence it ensures the convergence to the solution of continuous problem.Finally,numerical experiments are performed to demonstrate the efficiency,accuracy and robustness of the proposed method.展开更多
This work presents a comparison study of different numerical methods to solve Black-Scholes-type partial differential equations(PDE)in the convectiondominated case,i.e.,for European options,if the ratio of the risk-fr...This work presents a comparison study of different numerical methods to solve Black-Scholes-type partial differential equations(PDE)in the convectiondominated case,i.e.,for European options,if the ratio of the risk-free interest rate and the squared volatility-known in fluid dynamics as P´eclet number-is high.For Asian options,additional similar problems arise when the"spatial"variable,the stock price,is close to zero.Here we focus on three methods:the exponentially fitted scheme,a modification of Wang’s finite volume method specially designed for the Black-Scholes equation,and the Kurganov-Tadmor scheme for a general convection-diffusion equation,that is applied for the first time to option pricing problems.Special emphasis is put in the Kurganov-Tadmor because its flexibility allows the simulation of a great variety of types of options and it exhibits quadratic convergence.For the reduction technique proposed by Wilmott,a put-call parity is presented based on the similarity reduction and the put-call parity expression for Asian options.Finally,we present experiments and comparisons with different(non)linear Black-Scholes PDEs.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11971354,and 11701221)the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities’Association(No.2019FH001-079)the Fundamental Research Funds for the Central Universities(No.22120210555).
文摘In this paper,we construct and analyze a Crank-Nicolson fitted finite volume scheme for pricing European options under regime-switching Kou’s jumpdiffusion model which is governed by a system of partial integro-differential equations(PIDEs).We show that this scheme is consistent,stable and monotone as the mesh sizes in space and time approach zero,hence it ensures the convergence to the solution of continuous problem.Finally,numerical experiments are performed to demonstrate the efficiency,accuracy and robustness of the proposed method.
文摘This work presents a comparison study of different numerical methods to solve Black-Scholes-type partial differential equations(PDE)in the convectiondominated case,i.e.,for European options,if the ratio of the risk-free interest rate and the squared volatility-known in fluid dynamics as P´eclet number-is high.For Asian options,additional similar problems arise when the"spatial"variable,the stock price,is close to zero.Here we focus on three methods:the exponentially fitted scheme,a modification of Wang’s finite volume method specially designed for the Black-Scholes equation,and the Kurganov-Tadmor scheme for a general convection-diffusion equation,that is applied for the first time to option pricing problems.Special emphasis is put in the Kurganov-Tadmor because its flexibility allows the simulation of a great variety of types of options and it exhibits quadratic convergence.For the reduction technique proposed by Wilmott,a put-call parity is presented based on the similarity reduction and the put-call parity expression for Asian options.Finally,we present experiments and comparisons with different(non)linear Black-Scholes PDEs.
