Pricing Arithmetic Average Reset Options With Control Variates

Stock markets around the world have fallen sharply in recent years, leaving many stock options that were issued in better times deep out of the money. Some firms with employee stock options outstanding have chosen simply to adjust the strikes downward, toward current market levels. Reset options offer this kind of protection automatically, by specifying one or more stock price levels at which the option's strike price will be reset. Liao and Wang examine the problem of pricing reset options, taking into account some real-world features, including multiple reset levels and arithmetic Asian payoffs, that may be present but present difficulties for valuation. They show how a standard reset contract may be valued as a package of barrier options, and they offer a control variate technique for Asian contracts. One important feature of reset options is the fact that delta is discontinuous at the reset points.