Princing European options on instruments with a constant dividend yield : The randomized discrete-time approach

• Autorzy: Weron R.
• Języki publikacji: EN

Abstrakty

EN

Due to the well-known fact that market returns are not normally distributed, we use generalized hyperbolic distributions for pricing options in a randomized discrete-time setup. The obtained formulas can be used for pricing options on stock indexes, currencies and futures contracts. We test them on options written on the Nikkei 225 index futures and conclude that a proper calibration scheme could give us an advantage in the financial market.

Słowa kluczowe

EN

option pricing; dividends; randomization; alternative models

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2002
• Tom: Vol. 22, Fasc. 2
• Strony: 407--418
• Opis fizyczny: Biblogr. 22 poz.

Twórcy

autor

Weron R.

• Hugo Steinhaus Center, Institute of Mathematics, Wrocław University of Technology 50-370 Wrocław, Poland

Bibliografia

• [1] R. B. D’Agostino and M. A. Stephens, Goodness-of-Fit Techniques, Marcel Dekker, New York 1986.
• [2] L. Bachelier, Theorie de la speculation, Ann. Sei. École Norm. Sup, III-17 (1900), pp. 21-86.
• [3] O. E. Barndorff-Nielsen, Exponentially decreasing distributions for the logarithm of particle size, Proc. Roy. Soc. London A 353 (1977), pp. 401-419.
• [4] O. E. Barndorff-Nielsen, Processes of the normal inverse Gaussian type, Finance & Stochastics 2 (1998), pp. 41-68.
• [5] F. Black, The pricing of commodity contracts, J. Financial Economics 3 (1976), pp. 167-179.
• [6] J. P. Bouchaud and M. Potters, Theory of Financial Risk, Cambridge University Press, 2000.
• [7] J. C. Cox, S. A. Ross and M. Rubinstein, Option pricing: A simplified approach, J. Financial Economics 7 (1979), pp. 229-263.
• [8] E. Eberlein and J. Jacod, On the range of option prices, Finance & Stochastics 1 (1997), pp. 131-140.
• [9] E. Eberlein and U. Keller, Hyperbolic distributions in finance, Bernoulli 1 (1995), pp. 281-299.
• [10] E. Eberlein, U. Keller and K. Prause, New insights into the smile, mispricing and value at risk: The hyperbolic model, J. Business 71 (1998), pp. 371-406.
• [11] H. Geman, D. Madan and M. Yor, Time changes for Levy processes, Mathematical Finance 11 (2001), pp. 79-96.
• [12] B. V. Gnedenko, On limit theorems for a random number of random variables, Lecture Notes in Math. 1021 (1983), pp. 167-176.
• [13] J. M. Harrison and S. R. Pliska, Martingales and stochastic integrals in the theory of continuous trading, Stochastic Process. Appl. 11 (1981), pp. 215-260.
• [14] J. Hull, Options, Futures, and Other Derivatives, Prentice Hall International, London 1997.
• [15] A. Janicki and A. Weron, Simulation and Chaotic Behavior of a-Stable Stochastic Processes, Marcel Dekker, New York 1994.
• [16] U. Küchler, K. Neumann, M. Sorensen and A. Streller, Stock returns and hyperbolic distributions, Math. Comput. Modelling 29 (1999), pp. 1-15.
• [17] B. B. Mandelbrot, The variation of certain speculative prices, J. Business 36 (1963), pp. 394-419.
• [18] A. Misiorek, Alternative option pricing models and the volatility smile, unpublished MSc thesis, Wroclaw University of Technology, 2000.
• [19] S. Rachev and S. Mittnik, Stable Paretian Models in Finance, Wiley, 2000.
• [20] S. T. Rachev and L. Rüschendorf, Models for option prices, Theory Probab. Appl. 39 (1994), pp. 120-152.
• [21] A. Rejman, A. Weron and R. Weron, Option pricing proposals under the generalized hyperbolic model, Comm. Statist. Stochastic Models 13 (1997), pp. 867-885.
• [22] A. Weron and R. Weron, Financial Engineering: Derivatives Pricing, Computer Simulations, Market Statistics (in Polish), WNT, Warsaw 1998.