RFS Advance Access originally published online on March 2, 2009
Review of Financial Studies 2009 22(9):3669-3705; doi:10.1093/rfs/hhp009
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Simulation-Based Estimation of Contingent-Claims Prices
Yale University, University of Auckland, University of York, and Singapore Management University
Singapore Management University
Send correspondence to Jun Yu, School of Economics, Singapore Management University, 90 Stamford Road, Singapore 178903. E-mail: yujun{at}smu.edu.sg.
JEL Classification: C11, C15, G12
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Abstract |
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A new methodology is proposed to estimate theoretical prices of financial contingent claims whose values are dependent on some other underlying financial assets. In the literature, the preferred choice of estimator is usually maximum likelihood (ML). ML has strong asymptotic justification but is not necessarily the best method in finite samples. This paper proposes a simulation-based method. When it is used in connection with ML, it can improve the finite-sample performance of the ML estimator while maintaining its good asymptotic properties. The method is implemented and evaluated here in the Black-Scholes option pricing model and in the Vasicek bond and bond option pricing model. It is especially favored when the bias in ML is large due to strong persistence in the data or strong nonlinearity in pricing functions. Monte Carlo studies show that the proposed procedures achieve bias reductions over ML estimation in pricing contingent claims when ML is biased. The bias reductions are sometimes accompanied by reductions in variance. Empirical applications to U.S. Treasury bills highlight the differences between the bond prices implied by the simulation-based approach and those delivered by ML. Some consequences for the statistical testing of contingent-claim pricing models are discussed.
We thank Joel Hasbrouck (the editor), David Bates, Jin-Chuan Duan, Nengjiu Ju, James MacKinnon, Adrian Pagan, Mitch Warachka, and participants at the 2007 Singapore Econometric Study Group meeting, 2007 International Symposium on Econometric Theory and Applications, 2007 International Symposium on Financial Engineering and Risk, and 2008 China International Conference in Finance for helpful discussions. The comments from an anonymous referee were especially helpful and led to significant improvements in the paper. Phillips gratefully acknowledges support from the National Science Foundation under grant nos. SES 04-142254 and SES 06-47086. Yu gratefully acknowledges support from the Singapore Ministry of Education AcRF Tier 2 fund under grant no. T206B4301-RS.