Valuing of timer path-dependent options

Timer options are financial instruments, first proposed by Société Générale Corporate and Investment Banking in 2007, which allow investors to exercise the options randomly under the level of volatility, unlike a vanilla style option exercised at a fixed maturity date. In this article, we study the problem of valuing the timer path-dependent options where the volatility is governed by a fast-mean reverting process. Specifically, extending and developing the study by Saunders (2010), we derive analytical formulas for path-dependent timer options by using the method of images as shown in Buchen (2001) and the technique of asymptotic expansions as described in Fouque et al. (2011). Moreover, we verify the pricing accuracy of the analytic formulas of path-dependent options by comparing our solutions with the ones from the Monte Carlo simulations. Finally, we experiment with the numerical studies on the timer-path dependent options to demonstrate the pricing sensitivities with respect to the model parameters.