Published online by Cambridge University Press: 04 August 2010
In this chapter we introduce a new simulation methodology for the empirical analysis of financial market data. The purpose of the new methodology is to build a bridge between the theoretical developments in recent years in mathematical finance and the econometric models employed in empirical finance. The powerful theoretical concepts we explore center around the idea of an equivalent martingale measure, as introduced by Harrison and Kreps (1979) and Harrison and Pliska (1981), i.e., a probability measure under which suitably discounted security price processes are martingales. The existence of an equivalent martingale measure allows convenient contingent claims pricing without reference to the mean return or drift parameters. For our purposes, this implies that simulation under the equivalent martingale measure can be accomplished without specifying the drifts of the price processes.
Given the emphasis on simulation, the econometric framework we consider is cast in terms of the method of moments, where the unbiasedness of simulators as approximations to expectations is most readily exploited. However, our methodology does not merely amount to integration by simulation in the method of moments. Rather, we use simulation as a tool to operationalize the advances in theoretical finance associated with the martingale pricing model.
The chapter is organized as follows. In section 2, the simulation methodology is introduced and discussed. Numerous advantages of the new methodology are listed in section 3. Thus, the lack of need to estimate drift parameters is taken up in section 3.1.