IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v01y1998i04ns0219024998000242.html
   My bibliography  Save this article

Minimum-Relative-Entropy Calibration of Asset-Pricing Models

Author

Listed:
  • Marco Avellaneda

    (Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, 10012, USA)

Abstract

We present an algorithm for calibrating asset-pricing models to the prices of benchmark securities. The algorithm computes the probability that minimizes the relative entropy with respect to a prior distribution and satisfies a finite number of moment constraints. These constraints arise from fitting the model to the prices of benchmark prices are studied in detail. We find that the sensitivities can be interpreted as regression coefficients of the payoffs of contingent claims on the set of payoffs of the benchmark instruments. We show that the algorithm has a unique solution which is stable, i.e. it depends smoothly on the input prices. The sensitivities of the values of contingent claims with respect to varriations in the benchmark instruments, in the risk-neutral measure. We also show that the minimum-relative-entropy algorithm is a special case of a general class of algorithms for calibrating models based on stochastic control and convex optimization. As an illustration, we use minimum-relative-entropy to construct a smooth curve of instantaneous forward rates from US LIBOR swap/FRA data and to study the corresponding sensitivities of fixed-income securities to variations in input prices.

Suggested Citation

  • Marco Avellaneda, 1998. "Minimum-Relative-Entropy Calibration of Asset-Pricing Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 447-472.
    • Handle: RePEc:wsi:ijtafx:v:01:y:1998:i:04:n:s0219024998000242
    DOI: 10.1142/S0219024998000242
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024998000242
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024998000242?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Buchen, Peter W. & Kelly, Michael, 1996. "The Maximum Entropy Distribution of an Asset Inferred from Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(1), pages 143-159, March.
    2. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. "Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-1632, December.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. Marco Avellaneda & Craig Friedman & Richard Holmes & Dominick Samperi, 1997. "Calibrating volatility surfaces via relative-entropy minimization," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 37-64.
    5. Eckhard Platen & Rolando Rebolledo, 1996. "Principles for modelling financial markets," Published Paper Series 1996-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    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


    Cited by:

    1. Minzhi Wu & Emili Tortosa-Ausina, 2020. "Bank Diversification and Focus in Disruptive Times: China, 2007–2018," Working Papers 2020/21, Economics Department, Universitat Jaume I, Castellón (Spain).
    2. Pierre Henry-Labordere, 2019. "From (Martingale) Schrodinger bridges to a new class of Stochastic Volatility Models," Papers 1904.04554, arXiv.org.
    3. Shulin Lan & Ming-Lang Tseng, 2018. "Coordinated Development of Metropolitan Logistics and Economy Toward Sustainability," Computational Economics, Springer;Society for Computational Economics, vol. 52(4), pages 1113-1138, December.
    4. Xiaohong Chen & Lars Peter Hansen & Peter G. Hansen, 2020. "Robust identification of investor beliefs," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 117(52), pages 33130-33140, December.
    5. Vladislav Kargin, 2003. "Consistent Estimation of Pricing Kernels from Noisy Price Data," Papers math/0310223, arXiv.org.
    6. Yuri S. Popkov & Yuri A. Dubnov & Alexey Yu. Popkov, 2023. "Reinforcement Procedure for Randomized Machine Learning," Mathematics, MDPI, vol. 11(17), pages 1-14, August.
    7. Fard, Farzad Alavi & Siu, Tak Kuen, 2013. "Pricing participating products with Markov-modulated jump–diffusion process: An efficient numerical PIDE approach," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 712-721.
    8. Marcel Nutz & Johannes Wiesel & Long Zhao, 2022. "Martingale Schr\"odinger Bridges and Optimal Semistatic Portfolios," Papers 2204.12250, arXiv.org.
    9. Lelièvre, Tony & Samaey, Giovanni & Zieliński, Przemysław, 2020. "Analysis of a micro–macro acceleration method with minimum relative entropy moment matching," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3753-3801.
    10. Sebastian Jaimungal & Silvana M. Pesenti & Leandro S'anchez-Betancourt, 2022. "Minimal Kullback-Leibler Divergence for Constrained L\'evy-It\^o Processes," Papers 2206.14844, arXiv.org, revised Aug 2022.
    11. Farzad Alavi Fard & Firmin Doko Tchatoka & Sivagowry Sriananthakumar, 2021. "Maximum Entropy Evaluation of Asymptotic Hedging Error under a Generalised Jump-Diffusion Model," JRFM, MDPI, vol. 14(3), pages 1-19, February.
    12. Meucci, A. & Nicolosi, M., 2016. "Dynamic portfolio management with views at multiple horizons," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 495-518.
    13. Evgeny Danilov, 2023. "Impact of Market Changes and Regulatory Measures on Accuracy of Bond Valuation in Portfolios of Russian Credit Institutions," Russian Journal of Money and Finance, Bank of Russia, vol. 82(4), pages 108-125, December.
    14. Alexander Veremyev & Peter Tsyurmasto & Stan Uryasev & R. Rockafellar, 2014. "Calibrating probability distributions with convex-concave-convex functions: application to CDO pricing," Computational Management Science, Springer, vol. 11(4), pages 341-364, October.
    15. Marcel Nutz & Johannes Wiesel & Long Zhao, 2023. "Martingale Schrödinger bridges and optimal semistatic portfolios," Finance and Stochastics, Springer, vol. 27(1), pages 233-254, January.
    16. José L. Vilar-Zanón & Olivia Peraita-Ezcurra, 2019. "A linear goal programming method to recover risk neutral probabilities from options prices by maximum entropy," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 259-276, June.
    17. Pierre Henry-Labordere, 2019. "From (Martingale) Schrodinger bridges to a new class of Stochastic Volatility Models," Working Papers hal-02090807, HAL.
    18. Vinicius Albani & Adriano De Cezaro & Jorge P. Zubelli, 2017. "Convex Regularization Of Local Volatility Estimation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-37, February.
    19. Alavi Fard, Farzad & He, Jian & Ivanov, Dmitry & Jie, Ferry, 2019. "A utility adjusted newsvendor model with stochastic demand," International Journal of Production Economics, Elsevier, vol. 211(C), pages 154-165.
    20. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
    21. Paul Glasserman & Bin Yu, 2005. "Large Sample Properties of Weighted Monte Carlo Estimators," Operations Research, INFORMS, vol. 53(2), pages 298-312, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. A. Monteiro & R. Tütüncü & L. Vicente, 2011. "Estimation of risk-neutral density surfaces," Computational Management Science, Springer, vol. 8(4), pages 387-414, November.
    2. Coutant, Sophie & Jondeau, Eric & Rockinger, Michael, 2001. "Reading PIBOR futures options smiles: The 1997 snap election," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 1957-1987, November.
    3. Vladislav Kargin, 2003. "Consistent Estimation of Pricing Kernels from Noisy Price Data," Papers math/0310223, arXiv.org.
    4. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    5. João Nunes, 2011. "American options and callable bonds under stochastic interest rates and endogenous bankruptcy," Review of Derivatives Research, Springer, vol. 14(3), pages 283-332, October.
    6. Monteiro, Ana Margarida & Tutuncu, Reha H. & Vicente, Luis N., 2008. "Recovering risk-neutral probability density functions from options prices using cubic splines and ensuring nonnegativity," European Journal of Operational Research, Elsevier, vol. 187(2), pages 525-542, June.
    7. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    8. Carr, Peter & Geman, Helyette & Madan, Dilip B., 2001. "Pricing and hedging in incomplete markets," Journal of Financial Economics, Elsevier, vol. 62(1), pages 131-167, October.
    9. Jarno Talponen, 2013. "Matching distributions: Asset pricing with density shape correction," Papers 1312.4227, arXiv.org, revised Mar 2018.
    10. Tapiero, Oren J., 2013. "A maximum (non-extensive) entropy approach to equity options bid–ask spread," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3051-3060.
    11. Robert R Bliss & Nikolaos Panigirtzoglou, 2000. "Testing the stability of implied probability density functions," Bank of England working papers 114, Bank of England.
    12. Shi-jie Jiang & Mujun Lei & Cheng-Huang Chung, 2018. "An Improvement of Gain-Loss Price Bounds on Options Based on Binomial Tree and Market-Implied Risk-Neutral Distribution," Sustainability, MDPI, vol. 10(6), pages 1-17, June.
    13. Shane Barratt & Jonathan Tuck & Stephen Boyd, 2020. "Convex Optimization Over Risk-Neutral Probabilities," Papers 2003.02878, arXiv.org.
    14. Ram Bhar & Carl Chiarella, 1996. "Bootstrap Results From the State Space From Representation of the Heath-Jarrow-Morton Model," Working Paper Series 66, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    15. Salazar Celis, Oliver & Liang, Lingzhi & Lemmens, Damiaan & Tempère, Jacques & Cuyt, Annie, 2015. "Determining and benchmarking risk neutral distributions implied from option prices," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 372-387.
    16. Smimou, K. & Bector, C.R. & Jacoby, G., 2007. "A subjective assessment of approximate probabilities with a portfolio application," Research in International Business and Finance, Elsevier, vol. 21(2), pages 134-160, June.
    17. Ruijun Bu & Kaddour Hadri, 2005. "Estimating the Risk Neutral Probability Density Functions Natural Spline versus Hypergeometric Approach Using European Style Options," Working Papers 200510, University of Liverpool, Department of Economics.
    18. Egorov, Alexei V. & Hong, Yongmiao & Li, Haitao, 2006. "Validating forecasts of the joint probability density of bond yields: Can affine models beat random walk?," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 255-284.
    19. Xiaoquan Liu, 2007. "Bid-ask spread, strike prices and risk-neutral densities," Applied Financial Economics, Taylor & Francis Journals, vol. 17(11), pages 887-900.
    20. Yu, Xisheng & Xie, Xiaoke, 2015. "Pricing American options: RNMs-constrained entropic least-squares approach," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 155-173.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:ijtafx:v:01:y:1998:i:04:n:s0219024998000242. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.