Perpetual Cancellable American Call Option

TL;DR

This paper analyzes the valuation of a perpetual American-style call option with a cancellation feature, considering dividends and interest rates, revealing new explicit valuation formulas and their impact on option sensitivity.

Contribution

It provides explicit valuation formulas for perpetual Game-style call options with dividends, highlighting differences based on interest rate and dividend yield relationships.

Findings

Value function is not convex when r > d.

Explicit valuation formulas depend on interest rate and dividend yield.

Numerical results show impact on option vega.

Abstract

This paper examines the valuation of a generalized American-style option known as a Game-style call option in an infinite time horizon setting. The specifications of this contract allow the writer to terminate the call option at any point in time for a fixed penalty amount paid directly to the holder. Valuation of a perpetual Game-style put option was addressed by Kyprianou (2004) in a Black-Scholes setting on a non-dividend paying asset. Here, we undertake a similar analysis for the perpetual call option in the presence of dividends and find qualitatively different explicit representations for the value function depending on the relationship between the interest rate and dividend yield. Specifically, we find that the value function is not convex when $r>d$. Numerical results show the impact this phenomenon has upon the vega of the option.