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Simulation-based Estimation of Contingent Claims Prices

Author

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  • Peter C.B.Phillips

    (Yale University, University of Auckland,University of York & Singapore Management University)

  • Jun Yu

    (Sim Kee Boon Institute for Financial Economics, Singapore Management University)

Abstract

A new methodology is proposed to estimate theoretical prices of financial contin- gent 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 imple- mented 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 bi- ased. The bias reductions are sometimes accompanied by reductions in variance. Empirical applications to U.S. Treasury bills highlight the di?erences 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.

Suggested Citation

  • Peter C.B.Phillips & Jun Yu, "undated". "Simulation-based Estimation of Contingent Claims Prices," Working Papers CoFie-05-2008, Singapore Management University, Sim Kee Boon Institute for Financial Economics.
  • Handle: RePEc:skb:wpaper:cofie-05-2008
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    3. Wang, Xiaohu & Xiao, Weilin & Yu, Jun, 2023. "Modeling and forecasting realized volatility with the fractional Ornstein–Uhlenbeck process," Journal of Econometrics, Elsevier, vol. 232(2), pages 389-415.
    4. Sherrill Shaffer, 2011. "Strategic risk aversion," Applied Financial Economics, Taylor & Francis Journals, vol. 21(13), pages 949-956.
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    6. Cerrato, Mario & Lo, Chia Chun & Skindilias, Konstantinos, 2011. "Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions," SIRE Discussion Papers 2011-53, Scottish Institute for Research in Economics (SIRE).
    7. Gouriéroux, Christian & Phillips, Peter C.B. & Yu, Jun, 2010. "Indirect inference for dynamic panel models," Journal of Econometrics, Elsevier, vol. 157(1), pages 68-77, July.
    8. Tore Selland Kleppe & Jun Yu & Hans J. skaug, 2011. "Simulated Maximum Likelihood Estimation for Latent Diffusion Models," Working Papers 10-2011, Singapore Management University, School of Economics.
    9. 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.
    10. Yu, Jun, 2012. "Bias in the estimation of the mean reversion parameter in continuous time models," Journal of Econometrics, Elsevier, vol. 169(1), pages 114-122.
    11. Wang, Xiaohu & Yu, Jun, 2016. "Double asymptotics for explosive continuous time models," Journal of Econometrics, Elsevier, vol. 193(1), pages 35-53.
    12. 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.
    13. Maria Kyriacou & Peter C. B. Phillips & Francesca Rossi, 2017. "Indirect inference in spatial autoregression," Econometrics Journal, Royal Economic Society, vol. 20(2), pages 168-189, June.
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    15. Michael B. Gordy & Pawel J. Szerszen, 2015. "Bayesian Estimation of Time-Changed Default Intensity Models," Finance and Economics Discussion Series 2015-2, Board of Governors of the Federal Reserve System (U.S.).
    16. 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.
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    18. Juan Huang & Geoffrey Qiping Shen, 2017. "Residential housing bubbles in Hong Kong: identification and explanation based on GSADF test and dynamic probit model," Journal of Property Research, Taylor & Francis Journals, vol. 34(2), pages 108-128, April.

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    More about this item

    Keywords

    Bias Reduction; Bond and Bond Option Pricing; Indirect Inference; Option Pricing; Simulation-based Estimation.;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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