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The compound option approach to American options on jump-diffusions. (English) Zbl 1201.91195

Summary: We derive analytical valuation formulas for compound options when the underlying asset follows a jump-diffusion process. We then apply these results to value extendible options, American call options on stocks that pay discrete dividends, and American options on assets that pay continuous proportional dividends. Numerical results are provided.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)
60J75 Jump processes (MSC2010)
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[1] Amin, K. I., Jump diffusion option valuation in discrete time, Journal of Finance, 48, 1833-1863 (1993)
[2] Ananthanarayanan, A. L.; Schwartz, E. S., Retractable and extendible bondsthe Canadian experience, Journal of Finance, 35, 31-47 (1980)
[3] Ball, C.; Torous, W., On jumps in common stock prices and their impact on call option pricing, Journal of Finance, 40, 155-173 (1985)
[4] Barone-Adesi, G.; Whaley, R. E., Efficient analytic approximation of American option values, Journal of Finance, 42, 301-320 (1987)
[5] Bates, D. S., The crash of ’87: was it expected? The evidence from options markets, Journal of Finance, 46, 1009-1044 (1991)
[6] Bates, D. S., Jumps and stochastic volatilityexchange rate processes implicit in deutsche mark options, The Review of Financial Studies, 9, 99-107 (1996)
[7] Black, F.; Scholes, M. S., The pricing of options and corporate liabilities, Journal of Political Economy, 83, 637-659 (1973) · Zbl 1092.91524
[8] Breen, R., The accelerated binomial option pricing model, Journal of Financial and Quantitative Analysis, 26, 153-164 (1991)
[9] Brennan, M. J.; Schwartz, E. S., Savings bonds, retractable bonds, and callable bonds, Journal of Financial Economics, 5, 67-88 (1977)
[10] Bunch, D. S.; Johnson, H., A simple and numerically efficient valuation method for American puts using a modified Geske-Johnson approach, Journal of Finance, 47, 809-816 (1992)
[11] Cox, J. C.; Ross, S., The valuation of options for alternative stochastic processes, Journal of Financial Economics, 3, 145-166 (1976)
[12] Dias, M.A.G., Rocha, K.M.C., 2000. Petroleum concessions with extendible options using mean reversion with jumps to model oil prices. Working paper, IPEA, Brazil.; Dias, M.A.G., Rocha, K.M.C., 2000. Petroleum concessions with extendible options using mean reversion with jumps to model oil prices. Working paper, IPEA, Brazil.
[13] Geske, R., The valuation of corporate liabilities as compound options, Journal of Financial and Quantitative Analysis, 12, 541-552 (1977)
[14] Geske, R., The valuation of compound options, Journal of Financial Economics, 7, 63-81 (1979)
[15] Geske, R., A note on an analytic valuation formula for unprotected American call options on stocks with known dividends, Journal of Financial Economics, 7, 375-380 (1979)
[16] Geske, R.; Johnson, H. E., The American put option valued analytically, Journal of Finance, 39, 1511-1524 (1984)
[17] Gukhal, C.R., 1995. American call options on stocks with discrete dividends. Working Paper, Graduate School of Business, Columbia University.; Gukhal, C.R., 1995. American call options on stocks with discrete dividends. Working Paper, Graduate School of Business, Columbia University.
[18] Harrison, J. M.; Kreps, D. M., Martingales and arbitrage in multiperiod securities markets, Journal of Economic Theory, 20, 381-408 (1979) · Zbl 0431.90019
[19] Ho, T. S.; Stapleton, R. C.; Subrahmanyam, M. G., The valuation of American options with stochastic interest ratesa generalization of the Geske-Johnson technique, Journal of Finance, 52, 827-840 (1997)
[20] Jarrow, R. A.; Rosenfeld, E., Jump risks and the intertemporal capital asset pricing model, Journal of Business, 57, 337-351 (1984)
[21] Jorion, P., On jump processes in the foreign exchange and stock markets, Review of Financial Studies, 1, 427-455 (1988)
[22] Longstaff, F. A., Pricing options with extendible maturitiesanalysis and applications, Journal of Finance, 45, 935-957 (1990)
[23] Merton, R. C., Theory of rational option pricing, Bell Journal of Economics, 4, 141-183 (1973) · Zbl 1257.91043
[24] Merton, R. C., Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics, 3, 125-144 (1976) · Zbl 1131.91344
[25] Naik, V. T.; Lee, M., General equilibrium pricing of options on the market portfolio with discontinuous returns, Review of Financial Studies, 3, 493-521 (1990)
[26] Omberg, E., A note on the convergence of binomial-pricing and compound-option models, Journal of Finance, 42, 463-469 (1987)
[27] Roll, R., An analytical formula for unprotected American call options on stocks with known dividends, Journal of Financial Economics, 5, 251-258 (1977)
[28] Selby, M. J.P; Hodges, S. D., On the evaluation of compound options, Management Science, 33, 347-355 (1987)
[29] Whaley, R. E., On the valuation of American call options on stocks with known dividends, Journal of Financial Economics, 9, 207-211 (1981)
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