Laplace Transform Method for Pricing American CEV Strangles Option with Two Free Boundaries

Zhiqiang Zhou,Hongying Wu

doi:10.1155/2018/5908646

Abstract

Laplace transform method (LTM) has a lot of applications in the evaluation of European-style options and exotic options without early exercise features. However the Laplace transform methods for pricing American options have unsatisfactory accuracy and suffer from the instability. The aim of this paper is to develop a Laplace transform method for pricing American Strangles options with the underlying asset price following the constant elasticity volatility (CEV) models. By approximating the free boundaries, the Laplace transform is taken on a fixed space region to replace the moving boundaries space. After solving the linear system in Laplace space, Gaver-Stehfest formula (GSF) and hyperbola contour integral method (HCIM) are applied to compute the Laplace inversion. Numerical results show that the LTM-HCIM outperform the LTM-GSF in regard to the accuracy and stability for the option values.

Highlights

The Laplace transform methods for option pricing originate from the idea of randomizing the maturity in [1]
The Laplace transform methods are applied in the pricing options without early exercise features: Pelsser [2] for pricing double barrier options, Davydov and Linetsky [3] for pricing and hedging path dependent options under constant elasticity of variance (CEV) models, Sepp [4] for pricing double barrier options under double-exponential jump diffusion models, Cai and Kou [5] for pricing European options under mixedexponential jump diffusion models, and Cai and Kou [6] for pricing Asian options under hyperexponential jump diffusion models
The remaining parts of this paper are arranged as follows: In Section 2, we develop the Laplace transform method for pricing American CEV Strangles option; in Section 3, we discuss the hyperbola contour integral method to compute inverse Laplace and give some stable conditions for HCIM

Summary

Introduction

The Laplace transform methods for option pricing originate from the idea of randomizing the maturity in [1]. A simple framework for Laplace transform methods is introduced by Zhu [8] for pricing American options under GBM models This framework is later developed for evaluation of finite-lived Russian options by Kimura [9], pricing American options under CEV models by Wong and Zhao [10] and by Pun and Wong [11], pricing American options under hyperexponential jump-diffusion model by Leippold and Vasiljevic [12], pricing stock loan (essentially an American option with time-dependent strike) by Lu and Putri [13], and pricing American options with regime switching by Ma et al [14]. The remaining parts of this paper are arranged as follows: In Section 2, we develop the Laplace transform method for pricing American CEV Strangles option; in Section 3, we discuss the hyperbola contour integral method to compute inverse Laplace and give some stable conditions for HCIM.

Evaluation of American Strangles under CEV Model

Hyperbolic Contour Integral Method for Laplace Inversion

Numerical Examples

Conclusions