Pricing Timer Options
Grenoble Ecole de Management
Stevens Institute of Technology
August 22, 2010
Journal of Computational Finance, Vol. 15, No. 1, 2011
In this paper, we discuss a newly introduced exotic derivative called the “Timer Option”. Instead of being exercised at a fixed maturity date as a vanilla option, it has a random date of exercise linked to the accumulated 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 and White and in the Heston stochastic volatility models.
Number of Pages in PDF File: 37
Keywords: Stochastic volatility, Volatility derivative, timer option, quadratic variation, correlation, Heston model, Hull and White model.
JEL Classification: G12, G13
Date posted: May 19, 2010 ; Last revised: January 24, 2012