Valuation of Razorback Executive Stock Options: A Simulation Approach

Abstract

Executive stock options with a time-varying strike price are a recent innovation in Australia and New Zealand, and possibly other parts of the world. These options have a strike price that increases at a prespecified rate and also have a dividend protection feature that reduces the strike price by the amount of any dividend payment. With an upward trend and dividend-induced drops, the path of the strike price over time appears jagged. Hence the label 'razorback' options. Standard option pricing methodology is not easily applied to value razorback options, since the strike price is typically a path-dependent function of the stock price. For example, suppose the company pays a dividend yield as a constant percentage of the stock price. In this case, the cumulative dividend adjustment to the strike price depends on the particular path of the stock price. While analytic valuation appears intractable, these path-dependent options can be valued using a least squares Monte Carlo approach developed by Longstaff and Schwartz (2001). We examine the effects of changing volatility, maturity, vesting period and dividend yield on these executive stock option values. Our results indicate that valuations can differ quite significantly from those obtained from standard Black-Scholes valuations.