Zastosowanie wnioskowania bayesowskiego do wyceny opcji

• Autorzy: Mateusz Pipień

Warianty tytułu

Bayesian Inference: Application to Option Pricing

• Języki publikacji: PL

Abstrakty

Zadaniem opracowania jest zastosowanie jednego z procesów GARCH z asymetriami do modelowania zmienności stóp zmian dolara amerykańskiego i do wyceny europejskiej opcji kupna wystawianej na ten kurs.

EN

In this paper we present the results of application of Bayesian inference in option pricing. Bayesian approach to estimation and forecasting yields natural, probabilistic, and non-asymptotic rule for modelling Statistical uncertainty. The GARCH(1, 1) model with asymmetries was applied for the daily logarithmic growth rates of PLN/DEM exchange rates in order to model and forecast daily volatility and to price the European call option for this currency. We present predictive densities of the volatility parameter as well as predictive densities of the Black and Scholes formula for the price of the option. We also present predictive distributions of payoff functions related to the priced options. The empirical results confirm - presented previously in the literature - usefulness of Bayesian inference in modelling uncertainty about price of an option and payoff function related to it. Bayesian GARCH(1, 1) model with asymmetries yield predictive density of the Black and Scholes formula very dispersed, but the predictive medians if this distributions forecasted very well the true (quote) prices of considered European call options. The predictive distribution of the related payoff function reflects significant uncertainty about future payoff. Very low value of posterior probabilities of realisations of considered options together with very flat density of the Conditional (with respect to the case when the option is realised) predictive density of payoff function show difficulties with alternative option pricing method through the future payoff forecast. (original abstract)

Słowa kluczowe

PL

Wnioskowanie bayesowskie; Wycena opcji; Modelowanie ekonometryczne; Szeregi czasowe

EN

Bayesian inference; Options pricing; Econometric modeling; Time-series

• Czasopismo: Zeszyty Naukowe / Akademia Ekonomiczna w Krakowie
• Rocznik: 2003
• Numer: nr 628
• Strony: 71--85

Twórcy

autor

Mateusz Pipień

Bibliografia

• Andersen T.G., Bollerslev T. [1998], Answering the Sceptics: Yes, Standard Volatility Models do Provide Accurate Forecasts, "International Economic Review", vol. 39.
• Bauwens L., Lubrano M. [1997], Bayesian Option Pricing Using Asymmetric GARCH, CÓRE, Discussion Paper No. 9759, Universite Catholique de Louvain, Louvain-la-Neuve.
• Bauwens L., Lubrano M., Richard J.-F. [1999], Bayesian Inference in Dynamic Econometric Models, Oxford University Press, Oxford.
• Black F., Scholes M. [1973], The Pricing of Options and Corporate Liabilities, "Journal of Political Economy", vol. 81.
• Bollerslev T. [1986], Generalised Autoregressive Conditional Heteroscedasticity, „Journal of Econometrics", vol. 31
• Duan J.-Ch. [1995], The GARCH Option Pricing Model, "Mathematical Finance", vol. 5.
• Engle R.F, Lilien D.M., Robins R.P. [1987], Estimating Time Varying Risk Premia in the Term Structure: the ARCH-M Model, "Econometrica", vol. 55.
• Fernandez C., Osiewalski J., Steel M.F.J. [1995], Modelling and Inference with v-Spherical Distributions, "Journal of the American Statistical Association", vol. 90.
• Fernandez C., Steel M.F.J. [1998], On Bayesian Modelling of Fat Tails and Skewness, "Journal of the American Statistical Association", vol. 93.
• Ghysels E., Harvey A., Renault E. [1995], Stochastic Volatility [w:] Handbook of Statistics, vol 14: Statistical Methods in Finance, eds G.S. Maddali and C.R. Rao, North-Holland Publ. Co., Amsterdam.
• Glosten L.R., Jagannathan R., Runkle D.E. [1993], O/t the Relation Between the Expected Value and the Yolatility of the Nominal Excess Return on Stocks, "Journal of Finance", vol.48.
• Nelson D. [1990], Stationarity and Persistence in GARCH(1, 1) Model, "Econometric Theory", vol. 6.
• Noh J., Engle R.F., Kane A. [994],Forecasting Volatility and Option Prices of the S & P 500 Index, "Journal of Derivatives", vol. 2.
• Osiewalski J., Pipień M. [2003], Bayesian Analysis and Option Pricing in Univariate Models with Asymmetries and GARCH-1N-MEAN Effects, "Przegląd Statystyczny", t. 50.
• Pagan A., Schwert G. [990],Alternative Models for Conditional Stock Volatility, JJournal of Econometrics", vol. 45.