Pricing Vulnerable Options with Market Prices of Common Jump Risks under Regime-Switching Models

Miao Han,Xuefeng Song,Shengwu Zhou,Huawei Niu

doi:10.1155/2018/8545841

Abstract

This paper investigates the valuation of vulnerable European options considering the market prices of common systematic jump risks under regime-switching jump-diffusion models. The way of regime-switching Esscher transform is adopted to identify an equivalent martingale measure for pricing vulnerable European options. Explicit analytical pricing formulae for vulnerable European options are derived by risk-neutral pricing theory. For comparison, the other two cases are also considered separately. The first case considers all jump risks as unsystematic risks while the second one assumes all jumps risks to be systematic risks. Numerical examples for the valuation of vulnerable European options are provided to illustrate our results and indicate the influence of the market prices of jump risks on the valuation of vulnerable European options.

Highlights

Along with the development of the OTC market, people have recognized the influence of credit risk on financial derivatives pricing and attempted to establish all kinds of credit risk models
Tian et al [12] divide the jumps into individual jumps for each asset price and common jumps that affect the prices of all assets
In this paper, considering the market prices of common systematic jump risks regardless of individual jump risks, we develop an equivalent martingale measure for two regime-switching jump-diffusion processes with correlated jumps via regimeswitching Esscher transform and consider the differences between the physical jump-diffusion processes and the riskneutral jump-diffusion processes

Summary

Introduction

Along with the development of the OTC market, people have recognized the influence of credit risk on financial derivatives pricing and attempted to establish all kinds of credit risk models. Over the past decade or two, dozens of empirical evidences have revealed that risky asset prices present sudden shocks due to the arrival of important new information in financial markets and exhibit different behaviors in different time periods due to the time-inhomogeneity generated by the financial market For the former case, Merton [9] introduces the jump-diffusion models with compound Poisson processes into option pricing (see Kou [10], Xu et al [11], Tian et al [12], etc.).

The Model Description

Numerical Results

Conclusion