Pricing of American timer options

Timer options are financial derivatives and were first introduced by Société Générale Corporate and Investment Banking in 2007. They enable investors to exercise options on a random date based on the level of realized variance, which is in contrast to vanilla options exercised at a prescribed maturity date. This study investigates American timer option prices under stochastic volatility (SV), wherein the volatility is driven by a fast mean-reverting Ornstein–Uhlenbeck (OU) process. By making use of the asymptotic analysis proposed by Fouque et al. (2011), we obtain the analytic formulas for the option values and the free boundary prices under a finite stochastic variance clock, which practically serves as a time-to-maturity for American timer option. Moreover, we conduct numerical experiments to demonstrate the effect of SV on the American timer option in terms of the model parameters and verify that our explicit approximated option price is derived accurately and efficiently through comparisons with the solution obtained from a Monte-Carlo simulation.