- Volume 19 Issue 6
A floating-strike lookback call (or put) option gives the holder the right to buy (or sell) at some percentage of the lowest (or highest) price of the underlying asset. This paper will propose an outside lookback call (or put) option that gives the holder the right to buy (or sell) one underlying asset at its guaranteed floating-strike price that is some percentage times the smaller (or the greater) of a specific guaranteed amount and the lowest (or highest) price of the other underlying asset. In addition, this paper derives explicit pricing formulas for these outside lookback options. Section 3 and Section 4 assume that the underlying assets pay no dividends. In contrast, Section 5 derives explicit pricing formulas for these options when their underlying assets pay dividends continuously at a rate proportional to their prices. Some numerical examples are also discussed.
Floating strike;outside lookback option;Brownian motion
- Baxter, M. and Rennie, A. (1998). Financial Calculus: An Introduction to Derivative Pricing, Cambridge University Press, New York.
- Conze, A. and Viswanathan (1991). Path dependent options: The case of lookback options, Journal of Finance, 46, 1893-1907. https://doi.org/10.1111/j.1540-6261.1991.tb04648.x
- Gerber, H. U. and Shiu, E. S. W. (1994). Option pricing by Esscher transforms, Transactions of the Society of Actuaries, 46, 99-140; Discussions 141-191.
- Gerber, H. U. and Shiu, E. S. W. (1996). Actuarial bridges to dynamic hedging and option pricing, Insurance: Mathematics and Economics, 18, 183-218. https://doi.org/10.1016/0167-6687(96)85007-4
- Goldman, M. B., Sosin, H. B. and Gatto, M. A. (1979). Path dependent options: Buy at the low, sell at the high, Journal of Finance, 34, 1111-1127.
- Heynen, R. C. and Kat, H. M. (1994a). Crossing barriers, Risk, 7, 46-50.
- Heynen, R. C. and Kat, H. M. (1994b). Selective memory, Risk, 7, 73-76.
- Heynen, R. C. and Kat, H. M. (1997). Lookback Options - Pricing and Applications in Exotic Options: The State of the Art, edited by Clewlow, C. and Strickland, C. London: International Thomson.
- Lee, H. (2008). Pricing floating-strike lookback options with flexible monitoring periods, The Korean Journal of Applied Statistics, 21, 485-495. https://doi.org/10.5351/KJAS.2008.21.3.485
- Lee, H. (2009). Pricing outside floating-strike lookback options, The Korean Journal of Applied Statistics, 22, 59-73. https://doi.org/10.5351/KJAS.2009.22.1.059
- Nelken, I. (1996). The Handbook of Exotic Options: Instruments, Analysis, and Applications, McGraw- Hill, New York
- Zhang, P. G. (1998). Exotic Options: A Guide to Second Generation Options, 2nd ed., World Scientific, Singapore.