Designing and Applying a Nonparametric Option Valuation Model

Jan Vlachý

Abstract

This paper derives, tests and discusses a comprehensive and easy to use nonparametric option-valuation model, using a representative set of historical data on underlying asset returns jointly with an assumption of minimalistic implied information on current market trend and volatility expectations. Its testing on empirical data from Warsaw Stock Exchange trading for two distinct periods of 2014 suggests that such distribution-free models are capable of delivering useful market insights as well as applicability features, in particular wherever derivative markets are relatively new, incomplete, illiquid, or with regard to the valuation of real options.

Keywords

option pricing, nonparametric simulation, inefficient markets, Warsaw Stock Exchange, WIG 20 Index

References

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Aït-Sahalia, Y., Lo, A. (1998). Nonparametric Estimation of State-Price Densities in Financial Asset Prices. Journal of Finance, 53(2), pp. 499-547. https://doi.org/10.1111/0022-1082.215228

Alcock, J., Carmichael, T. (2008). Nonparametric American Option Pricing. Journal of Futures Markets, 28(8), pp. 717-748. https://doi.org/10.1002/fut.20335

Allen & Overy (2014). How the Polish Pension Fund Reform Will Affect the Fund’s Investments. Retrieved from: http://www.allenovery.com/SiteCollectionDocuments/Publication_OFE_Investment_after_the_reform.pdf. (Nov. 30, 2014.)

Bates, D. S. (1996). Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options. Review of Financial Studies, 9(1), pp. 69-107. https://doi.org/10.1093/rfs/9.1.69

Bates, D. S. (2000). Post-’87 Crash Fears in the S&P 500 Futures Option Market. Journal of Econometrics, 94(1/2), pp. 181-238. https://doi.org/10.1016/S0304-4076(99)00021-4

Bates, D. S. (2003). Empirical Option Pricing: A Retrospection. Journal of Econometrics, 116(1/2), pp. 387-404. https://doi.org/10.1016/S0304-4076(03)00113-1

Berkowitz, J. (2010). On Justifications for the ad hoc Black-Scholes Method of Option Pricing. Studies in Nonlinear Dynamics & Econometrics, 14(1) [on-line].

Black, F. (1976). The Pricing of Commodity Contracts. Journal of Financial Economics, 3(1/2), pp. 167-179. https://doi.org/10.1016/0304-405X(76)90024-6

Black, F., Scholes, M. (1972). The Valuation of Option Contracts and a Test of Market Efficiency. Journal of Finance, 27(2), pp. 399-417. https://doi.org/10.2307/2978484

Black, F., Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), pp. 637-659. https://doi.org/10.1086/260062

Campbell, J. Y., Lo, A. W., Mackinlay, A. C. (1997). The Econometrics of Financial Markets, Princeton: Princeton University Press.

Chen, R., Palmon, O. (2005). A Non-Parametric Option Pricing Model: Theory and Empirical Evidence. Review of Quantitative Finance and Accounting, 24(2), pp. 115-134. https://doi.org/10.1007/s11156-005-6333-2

Chow, Y., Mcaleer, M., Sequeira, J. M. (2000). Pricing of Forward and Future Contracts. Journal of Economic Surveys, 14(2), pp. 215-253. https://doi.org/10.1111/1467-6419.00110

Cox, J. C., Ingersoll, J. E., Ross, S. A. (1985). An Intertemporal General Equilibrium Model of Asset Prices. Econometrica, 53(2), pp. 363-384. https://doi.org/10.2307/1911241

Cox, J. C., Ross, S.A. (1976). Valuation of Options for Stochastic Processes. Journal of Financial Economics, 4(3), pp. 145-166. https://doi.org/10.1016/0304-405X(76)90023-4

Das, S.R., Sundaram, R.K. (1999). Of Smiles and Smirks: A Term Structure Perspective. Journal of Financial and Quantitative Analysis, 34(2), pp. 211-239. https://doi.org/10.2307/2676279

Dumas, B., Fleming, J., Whaley, R.E. (1998). Implied Volatility Functions: Empirical Tests. Journal of Finance, 53(6), pp. 2059-2106. https://doi.org/10.1111/0022-1082.00083

Grossman, S.J., Stiglitz, J.E. (1980). On the Impossibility of Informationally Efficient Markets. American Economic Review, 70(3), pp. 393-408.

Harrison, J.M., Kreps, D.M. (1979). Martingales and Arbitrage in Multiperiod Securities Markets. Journal of Economic Theory, 20(3), pp. 381-408. https://doi.org/10.1016/0022-0531(79)90043-7

Hull, J.C. (2012). Options, Futures and Other Derivatives. 8th ed. New Jersey: Prentice Hall.

Hull, J.C., White, A. (1987). The Pricing of Options with Stochastic Volatilities. Journal of Finance, 42(2), pp. 281-300. https://doi.org/10.1111/j.1540-6261.1987.tb02568.x

Hutchinson, J.M., Lo, A.W., Poggio, T. (1994). A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks. Journal of Finance, 49(3), pp. 851-889. https://doi.org/10.1111/j.1540-6261.1994.tb00081.x

Kaminski, S. (2013). The Pricing of Options on WIG20 Using Garch Models. Saarbrücken: Lambert Academic Publishing.

Latane, H., Rendleman, R. (1976). Standard Deviations of Stock Price Ratios Implied in Option Prices. Journal of Finance, 31(2), pp. 369-382. https://doi.org/10.1111/j.1540-6261.1976.tb01892.x

Liu, B. (2010). Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty. Berlin: Springer.

Lo, A.W., Mackinlay, A.C. (1999). A Non-RandomWalk Down Wall Street. Princeton: Princeton University Press.

Merton, R.C. (1976). Option Pricing when Underlying Stock Returns are Discontinuous. Journal of Financial Economics, 3(1/2), pp. 125-144. https://doi.org/10.1016/0304-405X(76)90022-2

Muth, J.F. (1961). Rational Expectations and the Theory of Price Movements. Econometrica, 29(3), pp. 315-335. https://doi.org/10.2307/1909635

Myszkowski, P.B., Rachwalski, L. (2009). Trading Rule Discovery on Warsaw Stock Exchange Using Coevolutionary Algorithms. In: Ganzha, M. and Paprzycki, M. (eds.) Proceedings of IMCSIT. Katowice: Polskie Towarzystwo Informatyczne, pp. 81-88.

Piontek, K. (2007). Weryfikacja modeli Blacka-Scholesa oraz AR-GARCH dlja opcji na WIG20. In: X. Ogólnopolskie Seminarium Naukowe Dynamiczne Modele Ekonometryczne. Toruń: Copernicus University.

Rubinstein, M. (1994). Implied Binomial Trees. Journal of Finance, 49(3), pp. 771-818. https://doi.org/10.1111/j.1540-6261.1994.tb00079.x

Shimko, D. (1993). Bounds of Probability. Risk, 6, pp. 33-37.

Stádník, B. (2014). The Puzzle of Financial Market Distribution. Ekonomický časopis, 62(7), pp. 709-727.

Strawiňski, P., Ślepaczuk, R. (2008). Analysis of High Frequency Data on the Warsaw Stock Exchange in the Context of Efficient Market Hypothesis. Journal of Applied Economic Sciences, 3(3), pp. 306-319.

Stutzer, M. (1996). A Simple Nonparametric Approach to Derivative Security Valuation. Journal of Finance, 51(5), pp. 1633-1652. https://doi.org/10.1111/j.1540-6261.1996.tb05220.x

Thadewald, T., Büning, H. (2007). Jarque-Bera Test and its Competitors for Testing Normality: A Power Comparison. Journal of Applied Statistics, 34(1), pp. 87-105. https://doi.org/10.1080/02664760600994539

Vlachý, J. (2013). Zdroje a meze opčního obchodování. E+M Ekonomie a management, 13(4), pp. 143-157.

Vlachý, J. (2014). Empirická analýza obchodování s opcemi na akcie Škodových závodů 1928–1938. Politická ekonomie, 62(5), pp. 645-661. https://doi.org/10.18267/j.polek.974

WSE (2014). Information and current data. Retrieved from: http://www.gpw.pl, historical data at http://www.gpwinfostrefa.pl. (Nov. 30, 2014).

https://doi.org/10.5817/FAI2016-1-3

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