Employee stock option valuation with repricing features

Repricing of an employee stock option refers to the practice of lowering the strike price and /or extending the maturity date of a previously granted employee stock option. Normally, firms reprice after a period of significant stock price decline that renders the employee stock options deeply out-of-the-money. By modeling various repricing mechanisms based on some form of Brownian functional of the stock price process, we investigate the impact of the embedded repricing flexibility on the market value of the employee stock options. We manage to derive analytic representation of the price functions of the repriceable options. We also construct the lattice tree type option valuation algorithms by applying the forward shooting grid technique to incorporate the path dependent feature of the Brownian functional in the repriceable option models. Our calculations show that the repricing flexibility may have varying degrees of impact on the option values and their comparative statics. The option delta (option vega) values of the repriceable options are seen to be lower (higher) than those of the vanilla options.