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Article

A Stochastic-Volatility Model for Pricing Power Variants of Exchange Options

Weixuan Xia
The Journal of Derivatives Summer 2019, jod.2019.1.074; DOI: https://doi.org/10.3905/jod.2019.1.074
Weixuan Xia
is PhD student in mathematical finance department at Boston University Questrom School of Business, in Boston, USA
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  • For correspondence: tonyxia1018@163.com
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Abstract

In this article, we present a model with jumps and stochastic volatility, based on two correlated variance-gamma processes combined with an Ornstein-Uhlenbeck process with gamma innovations. Our objective is to analyze pricing methods for a European-style equity option to exchange one stock for another, as well as two important classes of its variants that raise the stock prices and the standard option payoff, respectively, to certain powers. These option variants are particularly useful in adjusting the risk level of exchange options and can also be viewed as generalizations of traditional power-type options. The pricing formulas are obtained under risk neutrality in terms of characteristic functions and are thus independent from the model distribution. Numerical results are given for illustrating the efficiency of the presented formulas along with various advantages of the proposed stochastic-volatility model.

TOPICS: Options, statistical methods, performance measurement

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The Journal of Derivatives: 28 (2)
The Journal of Derivatives
Vol. 28, Issue 2
Winter 2020
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A Stochastic-Volatility Model for Pricing Power Variants of Exchange Options
Weixuan Xia
The Journal of Derivatives Apr 2019, jod.2019.1.074; DOI: 10.3905/jod.2019.1.074

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A Stochastic-Volatility Model for Pricing Power Variants of Exchange Options
Weixuan Xia
The Journal of Derivatives Apr 2019, jod.2019.1.074; DOI: 10.3905/jod.2019.1.074
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    • MODEL FRAMEWORK
    • EXCHANGE OPTION PRICING
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