Browse > Article
http://dx.doi.org/10.14317/jami.2020.439

PRICING STEP-UP OPTIONS USING LAPLACE TRANSFORM  

KIM, JERIM (Department of Mathematics, University of Seoul)
KIM, EYUNGHEE (Finance Insurance Research Institute)
KIM, CHANGKI (Korea University Business School)
Publication Information
Journal of applied mathematics & informatics / v.38, no.5_6, 2020 , pp. 439-461 More about this Journal
Abstract
A step-up option is a newly developed financial instrument that simultaneously provides higher security and profitability. This paper introduces two step-up options: step-up type1 and step-up type2 options, and derives the option pricing formulas using the Laplace transform. We assume that the underlying equity price follows a regime-switching model that reflects the long-term maturity of these options. The option prices are calculated for the two types of funds, a pure stock fund composed of risky assets only and a mixed fund composed of stocks and bonds, to reflect possible variety in the fund underlying asset mix. The impact of changes in the model parameters on the option prices is analyzed. This paper provides information crucial to product developments.
Keywords
barrier option; step-up option; option pricing; Laplace transform; regime switching; multi-barriers;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Cheuk, T., Vorst, T. Complex barrier options, Journal of Derivatives 4 (1996), 8-22.   DOI
2 Cox, J.C., Rubinstein, M. Options markets, Englewood Cliffs, NJ: Prentice-Hall, 1985.
3 Easton, S., Gerlach, R., Graham, M., Tuyl, F., An empirical examination of the pricing of exchange-traded barrier options, Journal of Futures Markets 24 (2004), 1049-1064.   DOI
4 Geman, H., Yor, M., Pricing and hedging double-barrier options: a probabilistic approach, Mathematical Finance 6 (1996), 365-378.   DOI
5 Hong, Y., Valuation bounds on barrier options under model uncertainty, Journal of Futures Markets 33 (2013), 199-234.   DOI
6 Hui, C.H., Time dependent barrier option values, Journal of Futures Markets 17 (1997), 667-688.   DOI
7 Hui, C.H., Lo, C.F., Currency barrier option pricing with mean reversion, Journal of Futures Markets 26 (2006), 939-958.   DOI
8 Karatzas, I., Wang, H., A barrier option of American type, Applied Mathematics Optimization 42 (2000), 259-279.   DOI
9 Kim, J., Kim, J., Yoo, H. J., Kim, B., Pricing external barrier options in a regime-switching model, Journal of Economic Dynamics and Control 53 (2015), 123-143.   DOI
10 Kunitomo, N., Ikeda, M., Pricing options with curved boundaries, Mathematical Finance 2 (1992), 275-298.   DOI
11 Lin, J., Palmer, K., Convergence of barrier option prices in the binomial model, Mathematical Finance 23 (2013), 318-338.   DOI
12 Lindset, S., Persson. S., A note on a barrier exchange option: The world's simplest option formula? Finance Research Letters 3 (2006), 207-211.   DOI
13 Merton, R.C., Theory of rational option pricing, Bell Journal of Economics and Management Science 4 (1973), 141-183.   DOI
14 Rubinstein, M., Reiner, E., Breaking down the barriers, Risk Magazine 8 (1991), 28-35.
15 Pavel, A., Sascha, W., Are structured products fairly priced? An analysis of the German market for equity-linked instruments, Journal of Banking and Finance 29 (2005), 2971-2993.   DOI
16 Pelsser, A., Pricing double barrier options using Laplace transforms, Finance and Stochastics 4 (2000), 95-104.   DOI
17 Petrella, G., An extension of the Euler Laplace transform inversion algorithm with applications in option pricing, Operations Research Letters 32 (2004), 380-389.   DOI
18 Wong, H.Y., Kwok, Y.K., Multi asset barrier options and occupation time derivatives, Applied Mathematical Finance 10 (2003), 245-266.   DOI
19 Rubinstein, M., Reiner, E., Unscrambling the binary code, Risk Magazine 9 (1991), 37-42.
20 Wang, A., Liu, Y.H., Hsiao, Y.L., Barrier option pricing: a hybrid method approach, Quantitative Finance 3 (2009), 341-352.   DOI
21 Boyarchenko, M.A., Levendorskii, S.Z. Prices and sensitivities of barrier and first touch digital options in Levy-driven models, International Journal of Theoretical and Applied Finance 12 (2009), 1125-1170.   DOI
22 Abate, I., Whitt, W. The Fourier-series method for inverting transforms of probability distributions, Queueing Systems 10 (1992), 5-88.   DOI
23 Bin, G., Jing-zhi, H., Marti, S. The valuation of American barrier options using the decomposition technique, Journal of Economic Dynamics Control 24 (2000), 1783-1827.   DOI
24 Boyarchenko, S.I., Levendorskii, S.Z. Barrier options and touch-and-out options under regular Levy processes of exponential type, Annals of Applied Probability 12 (2002), 1261-1298.   DOI
25 Boyarchenko, M.A., Levendorskii, S.Z. Valuation of continuously monitored double barrier options and related securites, Mathematical Finance, 22 (2012), 419-444.   DOI
26 Boyle, P., Lau, S. Bumping up against the barrier with the binomial method, Journal of Derivatives 1 (1994), 6-14.   DOI
27 Brown, C., Handley, J., Palmer, K. A closer look at barrier exchange options, Journal of Futures Markets 33 (2013), 29-43.   DOI
28 Carr, P., Two extensions to barrier option valuation, Applied Mathematical Finance 2 (1995), 173-209.   DOI