Convergence of jump-diffusion models to the Black-Scholes model

Stochastic Analysis and Applications

Volumn 21, Issue 1, 2003, Pages 141-160

  Hong, Dowon ^a   Wee, In Suk ^b  

^a Electronics and Telecommunications Research Institute (ETRI)   (South Korea)

^b Korea University   (South Korea)

Author keywords

Black Scholes model; Jump diffusion; L vy process; Locally risk minimizing hedging strategy; Minimal martingale measure

Indexed keywords

EID: 0037284766     PISSN: 07362994     EISSN: None     Source Type: Journal    
DOI: 10.1081/SAP-120017536     Document Type: Article

References (24)

1. Aase, K.K. Contingent claims valuation when the security price is a combination of an Ito process and a random point process. Stoch. Process. Appl. 1988, 28, 185-220.
2. Barndorff-Nielsen, O.E. Processes of normal inverse Gaussian type. Finance Stoch. 1998, 2, 41-68.
3. Billingsley, P. Convergence of Probability Measures; Wiley: New York, 1968.
4. Black, F.; Scholes, M. The pricing of options and corporate liabilities. J. Polit. Econ. 1973, 81, 637-659.
5. Chan, T. Pricing contingent claims on stocks driven by Lévy processes. Ann. Appl. Probab. 1999, 9, 504-528.
6. Colwell, D.B.; Elliott, R.J. Discontinuous asset prices and non-attainable contingent claims. Math. Finance 1993, 3, 295-308.
7. Duffle, D.; Protter, P. From discrete to continuous time finance: weak convergence of the financial gain process. Math. Finance 1992, 2, 1-15.
8. Eberlein, E.; Jacod, J. On the range of option prices. Finance Stoch. 1997, 1, 131-140.
9. Eberlein, E.; Keller, U. Hyperbolic distributions in finance. Bernoulli 1995, 1, 281-299.
10. Föllmer, H.; Schweizer, M. Hedging of contingent claims under incomplete information. In Applied Stochastic Analysis; Davis, M.H.A., Elliott, R.J., Eds.; Gordon and Breach: New York, 1991; 389-414.
11. Föllmer, H.; Sondermann, D. Hedging of non-redundant contingent claims. In Contributions to Mathematical Economics in Honor of Gerard Debreu; Hildenbrand, W., Mas-Colell, A., Eds.; North-Holland: Amsterdam, 1986; 205-223.
12. Gihman, I.I.; Skorohod, A.V. Stochastic Differential Equations; Springer-Verlag: New York, 1972.
13. Harrison, J.M.; Kreps, D.M. Martingales and arbitrage in multiperiod securities markets. J. Econ. Theory 1979, 20, 381-408.
14. Harrison, J.M.; Pliska, S.R. Martingales and stochastic integrals in the theory of continuous trading. Stoch. Process. Appl. 1981, 11, 215-260.
15. Harrison, J.M.; Pliska, S.R. A stochastic calculus model of continuous trading: complete market. Stoch. Process. Appl. 1983, 15, 313-316.
16. Jacod, J.; Shiryaev, A.N. Limit Theorems for Stochastic Processes; Springer-Verlag: New York, 1987.
17. Madan, D.B.; Milne, F. Option pricing with V.G. Martingale components. Math. Finance 1991, 1, 39-55.
18. Madan, D.B.; Seneta, E. The V.G. model for share market returns. J. Business 1990, 63, 511-524.
19. Mao, X. Exponential Stability of Stochastic Differential Equations; Marcel Dekker: New York, 1994.
20. Merton, R.C. The theory of rational option pricing. Bell J. Econ. Manag. Sci. 1973, 4, 141-183.
21. Merton, R.C. Option pricing when underlying stock returns are discontinuous. J. Financial Econ. 1976, 3, 125-144.
22. Mulinacci, S. An approximation of American option prices in a jump-diffusion model. Stoch. Process. Appl. 1996, 62, 1-17.
23. Protter, P. Stochastic Integration and Differential Equations: A New Approach; Springer-Verlag: New York, 1990.
24. 24. Schweizer, M. Option hedging for semimartingales. Stoch. Process. Appl. 1991, 37, 339-363.