Finanse, Rynki Finansowe, Ubezpieczenia

Previously: Zeszyty Naukowe Uniwersytetu Szczecińskiego. Finanse, Rynki Finansowe, Ubezpieczenia


ISSN: 2450-7741     eISSN: 2300-4460    OAI    DOI: 10.18276/frfu.2017.89/2-36
CC BY-SA   Open Access 

Issue archive / 5/2017
Wycena asymetrycznych opcji potęgowych – nowe podejście oparte na transformacie Fouriera
(PRICING ASYMMETRIC POWER OPTIONS – NEW METHOD BASED ON THE FOURIER TRANSFORM)

Authors: Arkadiusz Orzechowski
Szkoła Główna Handlowa
Keywords: asymmetric power options Fourier transform Black-Scholes model
Data publikacji całości:2017
Page range:10 (439-448)
Cited-by (Crossref) ?:

Abstract

The purpose of this article is to compare three ways of evaluating asymmetric power options in the Black-Scholes framework: martingale approach and two concepts based on the Fourier transform (including one derived by the author of the article). The methodology of the conducted research is based on comparing computational efficiency of every approach to pricing asymmetric power options. As a part of the subject matter, speed and accuracy of three methods of pricing options is analyzed. Based on the obtained results, it can be concluded that both Fourier-based approaches generate theoretical prices of the options slower than in the martingale method. Moreover, Fourier-based methods are error-prone. In spite of this, they can not be considered to be unequivocally worse than the martingale approach, as they offer possibility of pricing options, including asymmetric power options, in models that best reflect the real market conditions, i.e, the stochastic volatility models. The greatest value of the submitted paper is a possibility of applying the author’s method of pricing asymmetric power options and analysis of its speed and computational accuracy.
Download file

Article file

Bibliography

1.Black, F., Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy 3 (81), 637–654. DOI: 10.1086/260062.
2.Bakshi, G., Madan, D. (2000). Spanning and derivative – security valuation. Journal of Financial Economics 2 (55), 205–238. DOI: 10.1016/S0304-405X(99)00050-1.
3.Cahyani, A.C.P., Sumarti, N. (2015). Implementation of power barrier option valuation. AIP Conference Proceedings, 1 (1677), 1–4. DOI: 10.1063/1.4930640.
4.Chernov, M., Gallant, A., Ghysels, E., Tauchen, G. (2001). Alternative models of stock prices dynamics. Journal of Econometrics 1–2 (116), 225–257. DOI: 10.1016/S0304-4076(03)00108-8.
5.Cont, R. (2001). Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance, 1 (2), 223–236. DOI: 10.1088/1469-7688/1/2/304.
6.Dufrense, P.C., Keirstead, W. Ross, M.P. (1996). Pricing derivatives the martingale way. Retrieved from: www.haas.berkeley.edu/groups/finance/WP/rpf279.pdf.
7.Eraker, B. (2004). Do stock prices and volatility jump? Reconciling evidence from spot and option prices. Journal of Finance 3 (59), 1367–1403. DOI. 10.1111/j.1540-6261.2004.00666.x.
8.Heston, S. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. The Review of Financial Studies, 2 (6), 327–343. DOI: 10.1093/rfs/6.2.327.
9.Kou, S. (2002). Jump-diffusion model for option pricing. Management Science, 8 (48), 1086–1101. DOI: 10.1287/mnsc.48.8.1086.166.
10.Macovschi, S., Quittard-Pinon, F. (2006). On the pricing of power and other polynomial options. Journal of Derivarives, 4 (13), 61–71. DOI: 10.3905/jod.2006.635421.
11.Madan, D., Carr, P., Chang, E. (1998). The variance gamma process and option pricing. European Finance Review 1 (2), 79–105. DOI: https://doi.org/10.1023/A:1009703431535.
12.Pan, J. (2002). The jump-risk premia implicit in options: evidence from an integrated time-series study. Journal of Financial Economics 1 (63), 3–50. DOI: 10.1016/S0304-405X(01)00088-5.
13.Peters, E. (1989). Fractal structure in the capital markets, Financial Analysts Journal, 4 (45), 32–37, DOI: http://dx.doi.org/10.2469/faj.v45.n4.32.
14.Prakasa Rao, B.L.S. (2016). Pricing geometric Asian power options under mixed fractional Brownian motion environment. Physica A. Statistical Mechanics and its Applications, 15 (446), 92–99. DOI: 10.1016/j.physa.2015.11.013.
15.Schröder, M. (2013). On arithmetic-average Asian power options: closed forms and explicit methods for valuation. Quarterly Journal of Mechanics & Applied Mathematics, 1 (66), 1–27. DOI: 10.1093/qjmam/hbs017.
16.Xiao, W.L., Zhang, W.G., Zhang X.L., Wang, Y.L. (2010). Pricing currency options in a fractional Brownian motion with jumps. Economic Modelling, 5 (27), 935–942, DOI: 0.1016/j.econmod.2010.05.010.
17.Zhang, P.G. (1998). Exotic options. A guide to second generation options (2nd ed.). Singapore: World Scientific Publishing.