Book contents
- Frontmatter
- Contents
- List of contributors
- Foreword by M. Hashem Pesaran
- Part I Simulation-based inference in econometrics: methods and applications
- Part II Microeconometric methods
- Part III Time series methods and models
- Introduction
- 7 Simulated moment methods for empirical equivalent martingale measures
- 8 Exact maximum likelihood estimation of observation-driven econometric models
- 9 Simulation-based inference in non-linear state-space models: application to testing the permanent income hypothesis
- 10 Simulation-based estimation of some factor models in econometrics
- 11 Simulation-based Bayesian inference for economic time series
- Part IV Other areas of application and technical issues
- Index
7 - Simulated moment methods for empirical equivalent martingale measures
Published online by Cambridge University Press: 04 August 2010
- Frontmatter
- Contents
- List of contributors
- Foreword by M. Hashem Pesaran
- Part I Simulation-based inference in econometrics: methods and applications
- Part II Microeconometric methods
- Part III Time series methods and models
- Introduction
- 7 Simulated moment methods for empirical equivalent martingale measures
- 8 Exact maximum likelihood estimation of observation-driven econometric models
- 9 Simulation-based inference in non-linear state-space models: application to testing the permanent income hypothesis
- 10 Simulation-based estimation of some factor models in econometrics
- 11 Simulation-based Bayesian inference for economic time series
- Part IV Other areas of application and technical issues
- Index
Summary
Introduction
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.
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- Simulation-based Inference in EconometricsMethods and Applications, pp. 183 - 204Publisher: Cambridge University PressPrint publication year: 2000
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