Options with combined reset rights on strike and maturity

Reset clauses on the strike price and maturity date are commonly found in derivative contracts, like insurance segregated funds, bonds and executive warrants. We analyze the optimal reset policy adopted by the holder of an option that possesses the reset rights on the strike price and date of maturity. The optimal reset policy relates closely to the temporal rate of change of the value of the new option received by the holder at the reset moment. The characterization of the optimal reset policy requires the solution of a free boundary value problem. As part of the solution procedure, we determine the critical asset price for a given time to expiry at which the holder chooses to activate the reset clause optimally. Depending on the specific nature of the reset clauses, the reset policies exhibit a wide variety of behaviors. We also manage to obtain analytic price formulas for several specific types of reset options.