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Simulation-Based Estimation of Contingent-Claims Prices

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  • Peter C. B. Phillips
  • Jun Yu

Abstract

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. The Author 2009. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org., Oxford University Press.

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Article provided by Society for Financial Studies in its journal The Review of Financial Studies.

Volume (Year): 22 (2009)
Issue (Month): 9 (September)
Pages: 3669-3705

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Handle: RePEc:oup:rfinst:v:22:y:2009:i:9:p:3669-3705

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Cited by:
  1. Xiaohu Wang & Peter C.B. Phillips & Jun Yu, 2011. "Bias in Estimating Multivariate and Univariate Diffusions," Cowles Foundation Discussion Papers 1778, Cowles Foundation for Research in Economics, Yale University.
  2. Jun Yu, 2009. "Bias in the Estimation of the Mean Reversion Parameter in Continuous Time Models," Working Papers 16-2009, Singapore Management University, School of Economics.
  3. Mario Cerrato & Chia Chun Lo & Konstantinos Skindilias, 2011. "Adaptive continuous time Markov chain approximation model to general jump-diffusions," Working Papers 2011_16, Business School - Economics, University of Glasgow.
  4. Tore Selland Kleppe & Jun Yu & Hans J. Skaug, 2011. "Simulated Maximum Likelihood Estimation for Latent Diffusion Models," Working Papers CoFie-04-2011, Sim Kee Boon Institute for Financial Economics.
  5. Christian Gouriéroux & Peter C. B. Phillips & Jun Yu, 2006. "Indirect Inference for Dynamic Panel Models," Development Economics Working Papers 22421, East Asian Bureau of Economic Research.
  6. Laurini, Márcio Poletti & Hotta, Luiz Koodi, 2013. "Indirect Inference in fractional short-term interest rate diffusions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 109-126.
  7. Huang, Shirley J. & Yu, Jun, 2010. "Bayesian analysis of structural credit risk models with microstructure noises," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2259-2272, November.
  8. Xiao, Wei-Lin & Zhang, Wei-Guo & Yao, Zheng & Wang, Xiao-Hui, 2013. "The impact of issuing warrant and debt on behavior of the firm's stock," Economic Modelling, Elsevier, vol. 31(C), pages 635-641.

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