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Pricing Timer Options

Journal of Computational Finance, Vol. 15, No. 1, 2011

37 Pages Posted: 19 May 2010 Last revised: 24 Jan 2012

Carole Bernard

Grenoble Ecole de Management

Zhenyu Cui

Stevens Institute of Technology

Date Written: August 22, 2010

Abstract

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.

Keywords: Stochastic volatility, Volatility derivative, timer option, quadratic variation, correlation, Heston model, Hull and White model.

JEL Classification: G12, G13

Suggested Citation

Bernard, Carole and Cui, Zhenyu, Pricing Timer Options (August 22, 2010). Journal of Computational Finance, Vol. 15, No. 1, 2011. Available at SSRN: https://ssrn.com/abstract=1612014

Carole Bernard (Contact Author)

Grenoble Ecole de Management ( email )

12, rue Pierre Sémard
Grenoble Cedex, 38003
France

Zhenyu Cui

Stevens Institute of Technology ( email )

School of Business
Castle Point in the Hudson
Hoboken, NJ 07030
United States
(201) 216-3726 (Phone)

HOME PAGE: http://sites.google.com/site/zhenyucui86/

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