Метод оценки риск-нейтральной плотности вероятности по котировкам опционов

Тарас Громницкий, Виктор Лапшин

Abstract


В данной работе разработан метод построения риск-нейтральной плотности вероятности по котировкам опционов, позволяющий дать оценку точности искомой плотности. Риск-нейтральная плотность представляется сплайном, который
1) минимизирует расстояние Кульбака-Лейблера до логнормальной плотности (что обеспечивает связь с моделью Блека-Шоулза),
2) минимизирует отклонение цен, восстановленных по полученной плотности, от действительных цен опционов.

Неопределенность, возникающая из-за Bid-Ask спреда не позволяет однозначно  построить кривую плотности, поэтому методом Монте Карло строится оценка точности. При построении оценки используется факторный анализ приращений «улыбок» волатильности, меняющихся с течением времени. Результаты факторного анализа позволяют генерировать свойственные рынку кривые, которые и составляют оценку точности.


Full Text:

PDF

References


Hull John C. 2008, Options, futures, and other derivatives, Prentice-Hall inc.

Abadir, K., and M. Rockinger. “Density-Embedding Functions.” Working paper, HEC, 1997.

Abken, P., D. Madan, and S. Ramamurtie. “Pricing S&P 500 Index Options Using a Hilbert Space Basis.” Working paper, Federal Reserve Bank of Atlanta, 1996b.

Ait-Sahalia, Y., and A. Lo. “Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices.” Journal of Finance, 53, No. 2 (1998a), pp. 499-547.

Ait-Sahalia, Y., and A. Lo. “Nonparametric Risk Management and Implied Risk Aversion.” Working paper, University of Chicago, 1998b.

Aparicio, S., and S. Hodges. “Implied Risk-Neutral Distribution: A Comparison of Estimation Methods.” Working paper, Warwick University, 1998.

Bahra, B. “Implied Risk-Neutral Probability Density Functions from Option Prices: Theory and Application.” Working paper, Bank of England, 1997.

Bookstaber, R., and J. McDonald. “A General Distribution for Describing Security Price Returns.” Journal of Business, 60, No. 3 (1987), pp. 401-424.

Breeden, D., and R. Litzenberger. “Prices of State-Contingent Claims Implicit in Options Prices.” Journal of Business, 51 (1978), pp. 621-651.

Brenner, M., and Y. Eom. “No-Arbitrage Option Pricing: New Evidence on the Validity of the Martingale Property.” Working paper, New York University, 1997.

Brown, G., and K.B. Toft. “Constructing Binomial Trees from Multiple Implied Probability Distributions.” Journal of Derivatives, 7, No. 2 (1999).

Buchen, P., and M. Kelly. “The Maximum Entropy Distribution of an Asset Inferred from Option Prices.” Journal of Financial and Quantitative Analysis, 31, No. 1 (1996), pp. 143-159.

Campa, J., K. Chang, and R. Reider. “Implied Exchange Rate Distributions: Evidence from OTC Option Markets.” Journal of International Money and Finance, 17, No. 1 (1998), pp. 117-160.

Cont, R. “Beyond Implied Volatility.” In J. Kertesz and I. Kondor, eds., Econophysics. Dordrecht: Kluwer, 1997.

Corrado, C., and T. Su. “Implied Volatility Skews and Stock Index Skewness and Kurtosis Implied by S&P 500 Index Option Prices.” Journal of Derivatives, 4, No. 4 (1997), pp. 8-19.

Coutant, S., E. Jondeau, and M. Rockinger. “Reading Interest Rate and Bond Futures Options’ Smiles: How PIBOR and Notional Operators Appreciated the 1997 French Snap Election.” Working paper, HEC, 1998.

Hartvig, N., J. Jensen, and J. Pedersen. “Risk Neutral Densities of the ‘Christmas Tree’ Type.” Working paper, Centre for Mathematical Physics and Stochastics, Aarhus University, 1999.

Jackwerth, J. “Recovering Risk Aversion from Option Prices and Realized Returns.” Review of Financial Studies, forthcoming, 1999.

Jackwerth, J., and M. Rubinstein. “Recovering Probability Distributions from Option Prices.” Journal of Finance, 51 (1996), pp. 1611-1631.

Jarrow, R., and A. Rudd. “Approximate Valuation for Arbitrary Stochastic Processes.” Journal of Financial Economics, 10, No. 3 (1982), pp. 347-369.

Johnson, N. “Systems of Frequency Curves Generated by Methods of Translation.” Biometrika, 36 (1949), pp. 149-176.

Jondeau, E., and M. Rockinger. “Estimating Gram-Charlier Expansions under Positivity Constraints.” Working paper, HEC, 1998a.

Longstaff, F. “Option Pricing and the Martingale Restriction.” Review of Financial Studies, 8, No. 4 (1995), pp. 1091-1124.

Malz, A. “Estimating the Probability Distribution of the Future Exchange Rate from Option Prices.” Journal of Derivatives, 5, No. 2 (1997), pp. 18-36.

Malz, A. “Using Option Prices to Estimate Realignment Probabilities in the European Monetary System: The Case of Sterling-Mark.” Journal of International Money and Finance, 15, No. 5 (1996), pp. 717-748.

Mayhew, S. “On Estimating the Risk-Neutral Probability Distribution Implied by Option Prices.” Working paper, Purdue University, 1995.

Melick, W., and C. Thomas. “Recovering an Asset’s Implied PDF from Option Prices: An Application to Crude Oil During the Gulf Crisis.” Journal of Financial and Quantitative Analysis, 32 (1997), pp. 91-115.

Posner, S., and M. Milevsky. “Valuing Exotic Options by Approximating the SPD with Higher Moments.” Journal of Financial Engineering, 7, No. 2 (1998), pp. 109-125.

Potters, M., R. Cont, and J. Bouchaud. “Financial Markets as Adaptive Systems.” Europhysics Letters, 41, No. 3 (1998), pp. 239-244.

Pritsker, M. “Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models.” Working paper, Federal Reserve Board, Washington, DC, 1997.

Ritchey, R. “Call Option Valuation for Discrete Normal Mixtures.” Journal of Financial Research, 13, No. 4 (1990), pp. 285-295.

Rookley, C. “Fully Exploiting the Information Content of Intra Day Option Quotes: Applications in Option Pricing and Risk Management.” Working paper, University of Arizona, 1997.

Rosenberg, J. “Pricing Multivariate Contingent Claims Using Estimated Risk-Neutral Density Functions.” Working paper, University of California, San Diego, 1996.

Rosenberg, J., and R. Engle. “Option Hedging Using Empirical Pricing Kernels.” Working paper, New York University, 1997.

Rubinstein, M. “Edgeworth Binomial Trees.” Journal of Derivatives, 5, No. 3 (1998), pp. 20-27.

Sherrick, B., P. Garcia, and V. Tirupattur. “Recovering Probabilistic Information from Option Markets: Tests of Distributional Assumptions.” Working paper, University of Illinois at Urbana-Champaign, 1995.

Sherrick, B., S. Irwin, and D. Forster. “An Examination of Option-Implied S&P 500 Futures Price Distributions.” Financial Review, 31, No. 3 (1996), pp. 667-694.

Sherrick, B., S. Irwin, and D. Forster. “Option-Based Evidence of the Nonstationarity of Expected S&P 500 Futures Price Distributions.” Journal of Futures Markets, 12, No. 3 (1992), pp. 275-290.

Shimko, D. “Bounds on Probability.” Risk, 6 (1993), pp. 33-37.

Stutzer, M. “A Simple Nonparametric Approach to Derivative Security Valuation.” Journal of Finance, 51 (1996), pp. 1633-1652.


Refbacks

  • There are currently no refbacks.


Abava  Кибербезопасность MoNeTec 2024

ISSN: 2307-8162