Pricing timer options

In this paper a newly introduced exotic derivative called the “timer option” is discussed. Instead of being exercised at a fixed maturity date as a vanilla option, it has a random date of exercise linked to the realized variance of the underlying stock. Unlike common quadratic-variation-based derivatives, the price of a timer option generally depends on the assumptions on the underlying variance process and its correlation with the stock (unless the risk-free rate is equal to zero). In a general stochastic volatility model, we first show how the pricing of a timer call option can be reduced to a one-dimensional problem. We then propose a fast and accurate almost-exact simulation technique coupled with a powerful (model-free) control variate. Examples are derived in the Hull–White and the Heston stochastic volatility models.