Derivatives Models on Models

7

Resetting Strikes, Barriers and Time^*

with Jørgen Haug

We suggest a simple technique to price a large class of European reset options. Options where the strike is reset during their lifetime are traded actively in the OTC equity market. They are considered difficult to value because of the inherent path dependency. Our solution shows you how to price these options in a surprisingly simple and intuitive way, by extending the binomial tree of Cox, Ross and Rubinstein (1979) and Rendleman and Bartter (1979). Not only can our method be used to price standard reset strike options, but also to price reset barrier options, and even to reset time itself.

1 Introduction

In a plain vanilla reset call (put) option the strike is reset to the asset price at a predetermined future time, if the asset price is below (above) the initial strike price. More generally the strike can be reset to any function of the asset price at future dates. This makes the strike path-dependent. Gray and Whaley (1999) have derived a closed form solution for the price of European reset strike options.¹ They assume that the asset price follows a geometric Brownian motion dS_t = μS_tdt + σS_tdz_t, S₀ = S The price of the call option is then given by

while the price of the put option is given by

b is the cost of carry of ...