A Free-Boundary Model with Permanent American Capped Call Option

The no-arbitrage principle and Ito's Lemma are emploied to derive a pricing model for the permanent American capped call option and then the analytical solution is obtained. Meanwhile, it presents both mathematical proof and financial interpretation of the option price's monotonicity dependence on the model parameters. Finally, some properties of non-permanent American capped call option based on the previously mentioned results are derived.