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A Nonparametric Option Pricing Model Using Higher Moments

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  • Cayton, Peter Julian

Abstract

A nonparametric model that includes non-Gaussian characteristics of skewness and kurtosis is proposed based on the cubic market capital asset pricing model. It is an equilibrium pricing model but risk-neutral valuation can be introduced through return data transformation. The model complies with the put-call parity principle of option pricing theory. The properties of the model are studied through simulation methods and compared with the Black-Scholes model. Simulation scenarios include cases on nonnormality in skewness and kurtosis, nonconstant variance, moneyness, contract duration, and interest rate levels. The proposed model can have negative prices in cases of out-of-money options and in simulation cases that are different from real-market situations, but the frequency of negative prices is reduced when risk-neutral valuation is implemented. The model is more adaptive and more conservative in pricing options compared to the Black-Scholes model when nonnormalities exist in the returns data.

Suggested Citation

  • Cayton, Peter Julian, 2015. "A Nonparametric Option Pricing Model Using Higher Moments," MPRA Paper 63755, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:63755
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    References listed on IDEAS

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    1. Barone-Adesi, Giovanni, 1985. "Arbitrage Equilibrium with Skewed Asset Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(3), pages 299-313, September.
    2. Fang, Hsing & Lai, Tsong-Yue, 1997. "Co-Kurtosis and Capital Asset Pricing," The Financial Review, Eastern Finance Association, vol. 32(2), pages 293-307, May.
    3. I. D. Hill & R. Hill & R. L. Holder, 1976. "Fitting Johnson Curves by Moments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(2), pages 180-189, June.
    4. Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
    5. Robert A. Jarrow & Dilip B. Madan, 1997. "Is Mean-Variance Analysis Vacuous: Or was Beta Still Born?," Review of Finance, European Finance Association, vol. 1(1), pages 15-30.
    6. Stoll, Hans R, 1969. "The Relationship between Put and Call Option Prices," Journal of Finance, American Finance Association, vol. 24(5), pages 801-824, December.
    7. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    8. Robert F. Dittmar, 2002. "Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns," Journal of Finance, American Finance Association, vol. 57(1), pages 369-403, February.
    9. Ren-Raw Chen & Oded Palmon, 2005. "A Non-Parametric Option Pricing Model: Theory and Empirical Evidence," Review of Quantitative Finance and Accounting, Springer, vol. 24(2), pages 115-134, January.
    10. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    11. 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 637-654, May-June.
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    More about this item

    Keywords

    Capital Asset Pricing Model; Call Options; Kurtosis; Skewness;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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