Pricing timer options: second-order multiscale stochastic volatility asymptotics

Xuhui Wang; Sheng-Jhih Wu; Xingye Yue

doi:10.21914/anziamj.v63.15291

Authors

Xuhui Wang Soochow University https://orcid.org/0000-0002-5330-1128
Sheng-Jhih Wu Independent Researcher http://orcid.org/0000-0002-3207-8465
Xingye Yue Soochow University https://orcid.org/0000-0001-5683-6286

DOI:

https://doi.org/10.21914/anziamj.v63.15291

Keywords:

timer option, stochastic volatility, implied volatility, multiscale asymptotics , singular perturbation

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.

doi:10.1017/S1446181121000249

Author Biographies

Xuhui Wang, Soochow University

Center for Advanced Statistics and Econometrics Research, School of Mathematical Sciences, Soochow University, Suzhou, China.

Xingye Yue, Soochow University

Center for Financial Engineering, School of Mathematical Sciences, Soochow University, Suzhou, China.