Infinite Reload Options: Pricing and Analysis
نویسندگان
چکیده
Infinite reload options allow the user to exercise his reload right as often as he chooses during the lifetime of the contract. Each time a reload occurs, the owner receives new options where the strike price is set to the current stock price. We consider a modified version of the infinite reload option contract where the strike price of the new options received by the owner is increased by a certain percentage; we refer to this new contract as an increased reload option. The pricing problem for this modified contract is characterized as an impulse control problem resulting in a Hamilton-Jacobi-Bellman equation. We use fully implicit timestepping and prove that the discretized equations are monotone, stable and consistent, implying convergence to the viscosity solution. We also derive a globally convergent iterative method for solving the non-linear discrete equations. Numerical examples show that both the exercise policy and the option value are very sensitive to the percentage increase in the reload strike.
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