Issues in Simulation for Valuing Long-Term Forwards

Abstract

This paper explores valuing long-term equity forward-contracts or futures where both the underlying volatility and the interest rates are modeled as stochastic random variables. For each future, the underlying is an equity or index with no dividends. A key computational question we wish to understand is the relationship between (1) stochastically modeling the interest rates using different interest rate models while holding the volatility fixed and (2) stochastically modeling the underlying volatility using a volatility model while holding the interest rates fixed. In other words, let a “pure-X model” be a futures model where X varies stochastically while all else is fixed. Given a single future to model, this paper works towards understanding when a pure-interest rate model is equivalent to a pure-volatility model. This paper is focused on simulation and modeling issues and does not offer economic interpretation.