Analytic Approximation of Finite-Maturity Timer Option Prices

We develop an approximation technique for pricing finite-maturity timer options under Heston-like stochastic volatility models. By approximating the distributions of the accumulated variance and the random variance budget exceeding time, we obtain analytic expressions for timer option prices under zero correlation. For nonzero correlation, we use a simple linear combination approximation which matches the asymptotic correlation behavior. Numerical analysis using the Heston model shows that the method is fairly accurate, especially when the volatility of variance is small or the maximum maturity is large.