Rolli'n Back in Monte Carlo

Abstract

This paper proposes a simple roll-back scheme for calculating the conditional trade values for future time horizons under a Monte Carlo setup. It is independent of the nature of the trade and does not require any basis functions; as it is currently required using standard regression methods. The underlying idea is the fact that, according to Central Limit Theorem, only the first two moments of the distribution are relevant in calculating the unconditional mean. The fundamental approximation resulting from this insight is to model the cash flows as a normal distribution defined on a set of Markovian supports. Conditional values of the trade is then formulated based on the conditional expectations of these correlated supports. To give a more practical description of the approach, two simple examples of an interest rate note, and an American put option, are presented in a step-by-step manner. Its application to counterparty risk is shown by comparing the counterparty risk exposure measures obtained using the analytical pricing formula and the roll-back approach for a single vanilla interest rate swap. Valuation of a simple American put option with different moneyness, volatility and maturities using the roll-back and Least Squares Monte Carlo are compared against Finite Difference method. The average and the standard deviation of the differences between the roll-back and Finite Difference method is promising. The author is seeking feedback. Please contact the author for an updated copy.

Keywords: Longstaff-Schwarts, LSM, Monte Carlo, Stopping Time, Bermudan option, American Option

JEL Classification: G12