Pricing Permanent American Capped-Call Option in EVG Model

A capped-call option is a conventional option with a pre-defined profit cap written into the contract, which will be automatically exercised when the underlying security price climbs up to the cap. It has been observed that the theoretical price of capped option always overestimate the market price in HongKong, which is the motivation of our research. This paper attempts to apply the exponential variance gamma (EVG) model into the pricing framework of permanent American capped-call option, and obtain an explicit solution to the option price and optimal exercise boundary, which would be helpful to both of the theoretical research and empirical exercise.