An analytical approach to the pricing of an exchange option with default risk under a stochastic volatility model

被引：1

作者：

Jeon, Jaegi ^{[1
]}

Huh, Jeonggyu ^{[2
]}

Kim, Geonwoo ^{[3
]}

机构：

[1] Chonnam Natl Univ, Grad Sch Data Sci, Gwangju 61186, South Korea

[2] Chonnam Natl Univ, Dept Stat, Gwangju 61186, South Korea

[3] Seoul Natl Univ Sci & Technol, Sch Nat Sci, Seoul 01811, South Korea

来源：

ADVANCES IN CONTINUOUS AND DISCRETE MODELS | 2023年 / 2023卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

Exchange option; Default risk; Stochastic volatility; Asymptotic expansion; VULNERABLE OPTIONS; MULTISCALE; FORMULA;

D O I：

10.1186/s13662-023-03783-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The exchange option, which has two correlated underlying assets, is one of the most popular exotic options in the over-the-counter markets. This paper studies the valuation of exchange options with default risk of option issuer, where default is allowed only at maturity. Moreover, we consider three underlying assets with stochastic volatilities and assume that fast mean-reverting processes determine the stochastic volatilities. Based on the partial differential equation approach, we derive the analytical pricing formula of the exchange option price with default risk using the asymptotic expansion. To verify the accuracy and efficiency of our pricing formula, we compare the results by our pricing formula with those by Monte Carlo simulation, which is considered a benchmark. In addition, we provide several graphs to illustrate the properties of the option for significant parameters.

引用

页数：18

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