A jump-diffusion model for option pricing

Management Science

Volumn 48, Issue 8, 2002, Pages 1086-1101

  Kou, S G ^a  

^a Department of Earth and Environmental Sciences   (United States)

Author keywords

Contingent claims; Heavy tails; High peak; Interest rate models; Overreaction and underreaction; Rational expectations

Indexed keywords

BROWNIAN MOVEMENT; INDUSTRIAL ECONOMICS; INVESTMENTS; MARKETING; MATHEMATICAL MODELS; NORMAL DISTRIBUTION; POISSON DISTRIBUTION; SALES;

CONTINGENT CLAIMS; HEAVY TAILS; HIGH PEAK; INTEREST RATE MODELS; JUMP-DIFFUSION MODEL; OPTION PRICING; RATIONAL EXPECTATIONS;

FINANCE;

EID: 0036698288     PISSN: 00251909     EISSN: None     Source Type: Journal    
DOI: 10.1287/mnsc.48.8.1086.166     Document Type: Article

References (39)

1. Abramowitz, M., I. A. Stegun. 1972. Handbook of Mathematical Function, 10th Printing, U.S. National Bureau of Standards, Washington, D.C.
2. Andersen, L., J. Andreasen. 2000. Volatility skews and extensions of the libor market model. Appl. Math. Finance 7 1-32.
3. Andersen, T., L. Benzoni, J. Lund. 1999. Estimating jump-diffusions for equity returns. Working paper, Northwestern University, Evanston, IL.
4. Barberis, N., A. Shleifer, R. Vishny. 1998. A model of investor sentiment. J. Financial Econom. 49 307-343.
5. Barndorff-Nielsen, O. E., N. Shephard. 2001. Non-Gaussian Ornstein-Uhlenbeck based models and some of their uses in financial economics (with discussion). J. Roy. Statist. Soc., Ser. B. 63 167-241.
6. Björk, T., Y. Kabanov, W. Runggaldier. 1997. Bond market structure in the presence of marked point processes. Math. Finance 7 211-239.
7. Blattberg, R. C., N. J. Gonedes. 1974. A comparison of the stable and student distributions as statistical models for stock prices. J. Bus. 47 244-280.
8. Boyle, P., M. Broadie, P. Glasserman. 1997. Simulation methods for security pricing. J. Econom. Dynam. Control 21 1267-1321.
9. Clark, P.K. 1973. A subordinated stochastic process model with finite variance for speculative prices. Econometrica 41 135-155.
10. Cox, J. C., S. A. Ross. 1976. The valuation of options for alternative stochastic processes. J. Financial Econom. 3 145-166.
11. ____, J. E. Ingersoll, S. A. Ross. 1985. A theory of the term structure of interest rates. Econometrica 53 385-407.
12. Das, S. R., S. Foresi. 1996. Exact solutions for bond and option prices with systematic jump risk. Rev. Derivatives Res. 1 7-24.
13. Davydov, D., V. Linetsky. 2001. The valuation and hedging of path-dependent options under the CEV process. Management Sci. 47 949-965.
14. Derman, E., I. Kani. 1994. Riding on a smile. RISK (Feb) 7 32-39.
15. Duffie, D., J. Pan, K. Singleton 2000. Transform analysis and option pricing for affine jump-diffusions. Econometrica 68 1343-1376.
16. Dupire, B. 1994. Pricing with a smile. RISK (Feb) 7 18-20.
17. Engle, R. 1995. ARCH, Selected Readings. Oxford University Press, Oxford, U.K.
18. Fama, E. 1998. Market efficiency, long-term returns, and behavioral finance. J. Financial Econom. 49 283-306.
19. Fouque, J.-P., G. Papanicolaou, K. R. Sicar, 2000. Derivatives in Financial Markets with Stochastic Volatility. Cambridge University Press, Cambridge, U.K.
20. Geman, H., D. B. Madan, M. Yor. 2001. Time changes for Lévy processes. Math. Finance 11 79-96.
21. Glasserman, P., S. G. Kou. 1999. The term structure of simple interest rates with jump risk. Working paper, Columbia University, New York.
22. Grünewald, B., S. Trautmann. 1996. Option hedging in the presence of jump risk. Preprint, Johannes Gutenberg-Universität Mainz, Germany.
23. Heston, S. 1993. A closed-form solution of options with stochastic volatility with applications to bond and currency options. Rev. Financial Stud. 6 327-343.
24. Heyde, C. C. 2000. A risk asset model with strong dependence through fractal activity time. J. Appl. Probab. 36 1234-1239.
25. Hull, J., A. White. 1987. The pricing of options on assets with stochastic volatilities. J. Finance 42, 281-300.
26. Johnson, N., S. Kotz, N. Balakrishnan. 1995. Continuous Univariate Distribution, Vol. 2, 2nd ed. Wiley, New York.
27. Kou, S. G., H. Wang. 2000. First passage times for a jump diffusion process. Working paper, Columbia University, New York.
28. ____, ____. 2001. Option pricing under a double exponential jump diffusion model. Working paper, Columbia University, New York.
29. Lucas, R. E. 1978. Asset prices in an exchange economy. Econometrica 46 1429-1445.
30. Madan, D. B., E. Seneta. 1990. The variance gamma (V.G.) model for share market returns. J. Bus. 63 511-524.
31. ____, P. Carr, E. C. Chang. 1998. The variance gamma process and option pricing. Eur. Finance Rev. 2 79-105.
32. Mandelbrot, B. 1963. The variation of certain speculative prices. J. Bus. 36 394-419.
33. Merton, R. C. 1976. Option pricing when underlying stock returns are discontinuous. J. Financial Econom. 3 125-144.
34. Naik, V., M. Lee. 1990. General equilibrium pricing of options on the market portfolio with discontinuous returns. Rev. Financial Stud. 3 493-521.
35. Ramezani, C. A., Y. Zeng. 1999. Maximum likelihood estimation of asymmetric jump-diffusion process: Application to security prices. Working paper, Department of Statistics, University of Wisconsin, Madison, WI.
36. Rogers, L. C. G. 1997. Arbitrage from fractional Brownian motion. Math. Finance 7 95-105.
37. Samorodnitsky, G., M. S. Taqqu. 1994. Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. Chapman and Hall, New York.
38. Snanthikumar, J. G. 1985. Bilateral phase-type distributions. Naval Res. Logist. Quart. 32 119-136.
39. Stokey, N. L., R. E. Lucas. 1989. Recursive Methods in Economic Dynamics. Harvard University Press, Cambridge, MA.