Face Value Convergence for Stochastic Bond Price Processes: A Note on Merton's Partial Equilibrium Option Pricing Model

Abstract

This paper considers Merton's (1973) model for partial equilibrium bond option pricing when stochastic bond price processes are involved. A log-normal process with a stochastic drift is suggested that allows the price of a pure discount bond to converge to its face value upon maturity. The stochastic process for the instantaneous short rate implicit in the bond price dynamics is identified. A necessary condition for our approach to be consistent with the arbitrage-free martingale pricing results of Harrison and Kreps (1979) is that the excess holding period bond return and the standard deviation of the bond return are both continuously differentiable with respect to time.