Compound Option Valuation with Maturity Varying Volatility, Maturity Varying Yields, and Maturity Varying Interest Rates

Abstract

In this paper, a detailed proof is provided for the value of compound options based on geometric Brownian motion with maturity varying yields, maturity varying volatility, and maturity varying interest rates. Most research papers focused on compound options do not address yields on the underlying option nor maturity varying parameters. The purpose of this paper is to fill this gap in the literature. The model is also illustrated along with important implementation insights. Various intriguing avenues of research are also indicated.

Keywords: compound options, options, geometric Brownian motion, maturity varying parameters

JEL Classification: G13