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PRICING TIMER OPTIONS: SECOND-ORDER MULTISCALE STOCHASTIC VOLATILITY ASYMPTOTICS

Part of: Mathematical finance Equations of mathematical physics and other areas of application Mathematical economics

Published online by Cambridge University Press:  23 August 2021

XUHUI WANG Open the ORCID record for XUHUI WANG [Opens in a new window] ,
SHENG-JHIH WU Open the ORCID record for SHENG-JHIH WU [Opens in a new window]  and
XINGYE YUE Open the ORCID record for XINGYE YUE [Opens in a new window]
XUHUI WANG*
Affiliation:
Center for Advanced Statistics and Econometrics Research, School of Mathematical Sciences, Soochow University, 1 Shi-Zi Street, Suzhou, 215000, China
SHENG-JHIH WU
Affiliation:
Independent Researcher, Taiwan; e-mail: shemsjw@gmail.com.
XINGYE YUE
Affiliation:
Center for Financial Engineering, School of Mathematical Sciences, Soochow University, 1 Shi-Zi Street, Suzhou, 215000, China; e-mail: xyyue@suda.edu.cn.
*
e-mail: xhwang@alu.suda.edu.cn
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Abstract

We study the pricing of timer options in a class of stochastic volatility models, where the volatility is driven by two diffusions—one fast mean-reverting and the other slowly varying. Employing singular and regular perturbation techniques, full second-order asymptotics of the option price are established. In addition, we investigate an implied volatility in terms of effective maturity for the timer options, and derive its second-order expansion based on our pricing asymptotics. A numerical experiment shows that the price approximation formula has a high level of accuracy, and the implied volatility in terms of its effective maturity is illustrated.

Keywords

timer optionstochastic volatilityimplied volatilitymultiscale asymptoticssingular perturbation

MSC classification

Primary: 91B70: Stochastic models
Secondary: 91G20: Derivative securities 35Q91: PDEs in connection with game theory, economics, social and behavioral sciences
Type
Research Article
Information
The ANZIAM Journal , Volume 63 , Issue 2 , April 2021 , pp. 249 - 267
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Copyright
© Australian Mathematical Society 2021

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