배당을 고려한 옵션과 바스켓옵션의 유사성에 대한 연구 = Dealing a Discrete Dividend with Basket Option Pricing Models

다국어 초록 (Multilingual Abstract)

For pricing options with discrete dividends, a continuous dividend model, an escrow model, a forward model, and a piecewise lognormal model have been developed. Among the models, the piecewise lognormal model is regarded as the most realistic with consistency. However, the model has no analytic closed form solution and therefore approximation analytic closed form solutions have been studied. Here, we show the similarity between European spread options, which are special cases of European basket options, and European options with a constant dividend. Our numerical study shows that an approximation of Etore and Gobet(2012) is the most accurate among option pricing formulas with the piecewise lognormal model. However, an approximation from spread option pricing formula of Li et al.(2008) is comparable to the approximation of Etore and Gobet(2012). These results show that an option pricing formula with a discrete dividend can be improved when we have an improved spread option pricing formula.

참고문헌 (Reference)

1 Posner, S., "Valuing exotic options by approximating the spd with higher moments" 7-, 1998

2 Merton, R. C., "Theory of rational option pricing" 141-183, 1973

3 Margrabe, W., "The value of an option to exchange one asset for another" 177-186, 1978

4 Black, F., "The pricing of options and corporate liabilities" 81 : 637-654, 1973

5 Bos, R., "Stock options dealing with discrete dividends" 16 : 109-112, 2003

6 Etoré, P., "Stochastic expansion for the pricing of call options with discrete dividends" 19 : 233-264, 2012

7 Levy, E., "Pricing european average rate currency options" 11 : 474-491, 1992

8 Ju, N., "Pricing asian and basket options via taylor expansion" 5 : 79-103, 2002

9 Hull, J. C., "Options, futures, and other derivatives" Pearson Education 2006

10 Lo, C.-L., "Moment-matching approximations for asian options" 21 : 103-122, 2014

11 Sahel, F., "Matching sensitivities to discrete dividends: A new approach for pricing vanillas" 2011 : 80-85, 2011

12 Bos, M., "Finessing fixed dividends" 15 : 157-158, 2002

13 Black, F., "Fact and fantasy in the use of options" 36-72, 1975

14 Vellekoop, M., "Efficient pricing of derivatives on assets with discrete dividends" 13 : 265-284, 2006

15 Kirk, E., "Correlation in the energy markets" 71-78, 1995

16 Li, M., "Closed-form approximations for spread option prices and greeks" 15 : 58-80, 2008

17 Veiga, C., "Closed formula for options with discrete dividends and its derivatives" 16 : 517-531, 2009

18 Bjerksund, P., "Closed form spread option valuation" 14 : 1785-1794, 2014

19 Haug, E.G., "Back to basics: A new approach to the discrete dividend problem" 9 : 37-47, 2003

20 Milevsky, M.A., "Asian options, the sum of lognormals, and the reciprocal gamma distribution" 33 : 409-422, 1998

21 Dai, T.-S., "Accurate approximation formulas for stock options with discrete dividends" 16 : 1657-1663, 2009

22 Milevsky, M.A., "A closed-form approximation for valuing basket options" 5 : 54-61, 1998

23 Borovkova, S., "A closed form approach to the valuation and hedging of basket and spread option" 14 : 8-24, 2007