Full Text:
<2607>
CLC number: O211.63; O29
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 0000-00-00
Cited: 0
Clicked: 5383
A generalization of exotic options pricing formulae
| |||||||||||||
Li Shu-jin, Li Sheng-hong. A generalization of exotic options pricing formulae[J]. Journal of Zhejiang University Science A, 2006, 7(4): 584-590.
@article{title="A generalization of exotic options pricing formulae",
author="Li Shu-jin, Li Sheng-hong",
journal="Journal of Zhejiang University Science A",
volume="7",
number="4",
pages="584-590",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A0584"
}
%0 Journal Article
%T A generalization of exotic options pricing formulae
%A Li Shu-jin
%A Li Sheng-hong
%J Journal of Zhejiang University SCIENCE A
%V 7
%N 4
%P 584-590
%@ 1673-565X
%D 2006
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2006.A0584
TY - JOUR
T1 - A generalization of exotic options pricing formulae
A1 - Li Shu-jin
A1 - Li Sheng-hong
J0 - Journal of Zhejiang University Science A
VL - 7
IS - 4
SP - 584
EP - 590
%@ 1673-565X
Y1 - 2006
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2006.A0584
Abstract: Exotic options, or “path-dependent” options are options whose payoff depends on the behavior of the price of the underlying between 0 and the maturity, rather than merely on the final price of the underlying, such as compound options, reset options and so on. In this paper, a generalization of the Geske formula for compound call options is obtained in the case of time-dependent volatility and time-dependent interest rate by applying martingale methods and the change of numeraire or the change of probability measure. An analytic formula for the reset call options with predetermined dates is also derived in the case by using the same approach. In contrast to partial differential equation (PDE) approach, our approach is simpler.
[1] Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy, 81(3):637-659.
[2] Brealey, R., Myers, S.C., 1991. Principles of Corporate Finance. McGraw-Hill, New York.
[3] Carr, P., 1988. The valuation of sequential exchange opportunities. Journal of Finance, 5:1235-1256.
[4] Cheng, W., Zhang, S., 2000. The analytics of reset options. The Journal of Derivatives, (Fall):59-71.
[5] Elettra, A., Rossella, A., 2003. A generalization of the Geske formula for compound options. Mathematical Social Sciences, 45(1):75-82.
[6] Geman, H., Karoui, N.E.L., Rochet, J.C., 1995. Change of numeraire of probability measure and option pricing. Journal Application Probability, 32:443-458.
[7] Geske, R., 1979. The valuation of compound options. Journal of Financial Economics, 7(1):63-81.
[8] Geske, R., Johnson, H.E., 1984. The valuation of corporate liabilities as compound options: a correction. Journal of Financial and Quantitative Analysis, 19(2):231-232.
[9] Gray, S.F., Whaley, R.E., 1997. Valuing bear market reset warrants with a periodic rest. Journal of Derivatives, 5(1):99-106.
[10] Gray, S., Whaley, R., 1999. Reset put options: valuation, risk characteristics, and an application. Australian Journal of Management, 24:1-20.
[11] Merton, R.C., 1973. Theory of rational option pricing. Bell Journal of Economics, 4:141-183.
[12] Musiela, M., Rutkowski, M., 1997. Martingal Methods in Financial Modeling. Springer-Verlag, Berlin Heidelberg.
[13] Nelken, I., 1998. Reassessing the reset. Risk, (Oct.):36-39.
[14] Pliska, S.R., 1997. Introduction to Mathematical Finance. Blackwell, Oxford.
[15] Trigeogis, L., 1996. Real Options: Managerial Flexibility and Strategy in Resource Allocation. MIT Press, Cambridge, MA.
Open peer comments: Debate/Discuss/Question/Opinion
<1>