Advanced Search
MyIDEAS: Login to save this paper or follow this series

Simulation-based Estimation of Contingent Claims Prices

Contents:

Author Info

  • 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.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.smu.edu.sg/institutes/skbife/downloads/CoFiE/Working%20Papers/Simulation-based%20Estimation%20of%20Contingent%20Claims%20Prices.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Sim Kee Boon Institute for Financial Economics in its series Working Papers with number CoFie-05-2008.

as in new window
Length: 62 Pages
Date of creation:
Date of revision:
Publication status: Published in SMU-SKBI CoFie Working Paper
Handle: RePEc:skb:wpaper:cofie-05-2008

Contact details of provider:
Postal: 50 Stamford Road, Singapore 178903
Phone: (65) 6828 0877
Fax: (65) 6828 0888
Web page: http://www.smu.edu.sg/institutes/skbife/index.asp
More information through EDIRC

Order Information:
Email:

Related research

Keywords: Bias Reduction; Bond and Bond Option Pricing; Indirect Inference; Option Pricing; Simulation-based Estimation.;

Other versions of this item:

Find related papers by JEL classification:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Ait-Sahalia, Yacine & Kimmel, Robert L., 2008. "Estimating Affine Multifactor Term Structure Models Using Closed-Form Likelihood Expansions," Working Paper Series 2008-19, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
  2. James G. MacKinnon & Anthony A. Smith Jr., 1995. "Approximate Bias Correction in Econometrics," Working Papers 919, Queen's University, Department of Economics.
  3. Geyer, Alois L J & Pichler, Stefan, 1999. "A State-Space Approach to Estimate and Test Multifactor Cox-Ingersoll-Ross Models of the Term Structure," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 22(1), pages 107-30, Spring.
  4. Peter C. B. Phillips, 2005. "Jackknifing Bond Option Prices," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 707-742.
  5. Andersen, Torben G., 2000. "Simulation-Based Econometric Methods," Econometric Theory, Cambridge University Press, vol. 16(01), pages 131-138, February.
  6. 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.
  7. 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.
  8. Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
  9. Egorov, Alexei V. & Li, Haitao & Xu, Yuewu, 2003. "Maximum likelihood estimation of time-inhomogeneous diffusions," Journal of Econometrics, Elsevier, vol. 114(1), pages 107-139, May.
  10. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  11. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
  12. Bakshi, Gurdip & Ju, Nengjiu & Ou-Yang, Hui, 2006. "Estimation of continuous-time models with an application to equity volatility dynamics," Journal of Financial Economics, Elsevier, vol. 82(1), pages 227-249, October.
  13. Ball, Clifford A. & Torous, Walter N., 1996. "Unit roots and the estimation of interest rate dynamics," Journal of Empirical Finance, Elsevier, vol. 3(2), pages 215-238, June.
  14. Andersen, Torben G. & Chung, Hyung-Jin & Sorensen, Bent E., 1999. "Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 91(1), pages 61-87, July.
  15. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January.
  16. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  17. Samuel Thompson, 2008. "Identifying Term Structure Volatility from the LIBOR-Swap Curve," Review of Financial Studies, Society for Financial Studies, vol. 21(2), pages 819-854, April.
  18. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
  19. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S85-118, Suppl. De.
  20. Tang, Cheng Yong & Chen, Song Xi, 2009. "Parameter estimation and bias correction for diffusion processes," Journal of Econometrics, Elsevier, vol. 149(1), pages 65-81, April.
  21. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
  22. David A. Chapman & Neil D. Pearson, 2000. "Is the Short Rate Drift Actually Nonlinear?," Journal of Finance, American Finance Association, vol. 55(1), pages 355-388, 02.
  23. Boyle, Phelim P. & Ananthanarayanan, A. L., 1977. "The impact of variance estimation in option valuation models," Journal of Financial Economics, Elsevier, vol. 5(3), pages 375-387, December.
  24. Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford.
  25. Knight, John L & Satchell, Stephen E., 1997. "Existence of Unbiased Estimators of the Black/Scholes Option Price, Other Derivatives, and Hedge Ratios," Econometric Theory, Cambridge University Press, vol. 13(06), pages 791-807, December.
  26. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 297-316, July.
  27. Butler, J. S. & Schachter, Barry, 1986. "Unbiased estimation of the Black/Scholes formula," Journal of Financial Economics, Elsevier, vol. 15(3), pages 341-357, March.
  28. Lo, Andrew W., 1988. "Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data," Econometric Theory, Cambridge University Press, vol. 4(02), pages 231-247, August.
  29. Monfort, Alain, 1996. "A Reappraisal of Misspecified Econometric Models," Econometric Theory, Cambridge University Press, vol. 12(04), pages 597-619, October.
  30. Brandt, Michael W. & Santa-Clara, Pedro, 2002. "Simulated likelihood estimation of diffusions with an application to exchange rate dynamics in incomplete markets," Journal of Financial Economics, Elsevier, vol. 63(2), pages 161-210, February.
  31. Peter C.B. Phillips & Jun Yu, 2007. "Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance," Cowles Foundation Discussion Papers 1597, Cowles Foundation for Research in Economics, Yale University.
  32. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-65, January.
  33. Egorov, Alexei V. & Li, Haitao & Ng, David, 2011. "A tale of two yield curves: Modeling the joint term structure of dollar and euro interest rates," Journal of Econometrics, Elsevier, vol. 162(1), pages 55-70, May.
  34. Jun Yu, 2007. "Automated Likelihood Based Inference for Stochastic Volatility Models," Working Papers 01-2007, Sim Kee Boon Institute for Financial Economics.
  35. Phillips, P C B, 1972. "The Structural Estimation of a Stochastic Differential Equation System," Econometrica, Econometric Society, vol. 40(6), pages 1021-41, November.
  36. Pierce, James L, 1984. "Did Financial Innovation Hurt the Great Monetarist Experiment?," American Economic Review, American Economic Association, vol. 74(2), pages 392-96, May.
  37. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  38. Lo, Andrew W., 1986. "Statistical tests of contingent-claims asset-pricing models : A new methodology," Journal of Financial Economics, Elsevier, vol. 17(1), pages 143-173, September.
  39. Tripathi, Gautam, 2000. "Econometric Methods," Econometric Theory, Cambridge University Press, vol. 16(01), pages 139-142, February.
  40. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
  41. Smith, A A, Jr, 1993. "Estimating Nonlinear Time-Series Models Using Simulated Vector Autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S63-84, Suppl. De.
  42. repec:cup:etheor:v:12:y:1996:i:4:p:597-619 is not listed on IDEAS
  43. Darrell Duffie & Lasse Heje Pedersen & Kenneth J. Singleton, 2003. "Modeling Sovereign Yield Spreads: A Case Study of Russian Debt," Journal of Finance, American Finance Association, vol. 58(1), pages 119-159, 02.
  44. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  45. Yacine Aït-Sahalia, 1999. "Transition Densities for Interest Rate and Other Nonlinear Diffusions," Journal of Finance, American Finance Association, vol. 54(4), pages 1361-1395, 08.
  46. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
  47. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
  48. Chiara Monfardini, 1998. "Estimating stochastic volatility models through indirect inference," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages C113-C128.
  49. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
  50. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-52, July.
  51. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-09, March.
  52. Ball, Clifford A & Torous, Walter N, 1984. "The Maximum Likelihood Estimation of Security Price Volatility: Theory, Evidence, and Application to Option Pricing," The Journal of Business, University of Chicago Press, vol. 57(1), pages 97-112, January.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. 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.
  2. Christian Gourieroux & Peter C. B. Phillips & Jun Yu, 2006. "Indirect Inference for Dynamic Panel Models," Cowles Foundation Discussion Papers 1550, Cowles Foundation for Research in Economics, Yale University.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. Tore Selland Kleppe & Jun Yu & Hans J. Skaug, 2012. "Simulated Maximum Likelihood Estimation for Latent Diffusion Models," Working Papers 12-2012, Singapore Management University, School of Economics.
  8. 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.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:skb:wpaper:cofie-05-2008. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sim Kee Boon Institute for Financial Economics).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.