Bounds on European option prices under stochastic volatility

Mathematical Finance

Volumn 9, Issue 2, 1999, Pages 97-116

  Frey, Rüdiger ^a   Sin, Carlos A ^b  

^a ETH ZURICH   (Switzerland)

^b NONE

Author keywords

Incomplete markets; Option pricing; Stochastic volatility; Superreplication

Indexed keywords

EID: 0033455471     PISSN: 09601627     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9965.00064     Document Type: Article

References (28)

1. AVELLANEDA, M., A. LEVY, and A. PARAS (1995): Pricing and Hedging Derivative Securities in Markets with Uncertain Volatilities, Appl. Math. Finance 2, 73-88.
2. BAJEUZ, I., and J. C. ROCHET (1996): Dynamic Spanning: Are Options an Appropriate Instrument?, Math. Finance 6, 1-17.
3. BALL, C., and A. ROMA (1994): Stochastic Volatility Option Pricing, J. Financial Quant. Anal. 29(4), 584-607.
4. BLACK, F. (1976): Studies in Stock Price Volatility Change; in Proceedings of the 1976 Business Meeting of the Business and Economics Statistics Selection, American Statistical Association, pp. 177-181.
5. CVITANIC, J., H. PHAM, and N. TOUZI (1999): Superreplication in Stochastic Volatility Models Under Portfolio Constraints, J. Appl. Probab. 36(2).
6. DELBAEN, F. (1992): Representing Martingale Measures when Asset Prices are Continuous and Bounded, Math. Finance 2, 107-130.
7. DELBAEN, F., and W. SCHACHERMAYER (1995): The No-Arbitrage Property under a Change of Numeraire, Stoch. Stoch. Reports 53, 213-226.
8. DELBAEN, F., and W. SCHACHERMAYER (1997): The Banach Space of Workable Contingent Claims, Ann. Inst. H. Poincaré-Prob. Stat. 33, 113-144.
9. EBERLEIN, E., and J. JACOD (1997): On the Range of Option Prices, Finance Stoch. 1(2), 131-140.
10. EL KAROUI, N., and M. CHALEYAT-MAUREL (1978): Un Problème de Réflexion et ses Applications au Temps Local et aux Equations Differentielles Stochastiques; in Temps Locaux, Astérisque. Paris: Société Mathématique de France, 117-144.
11. EL KAROUI, N., and M. JEANBLANC-PIQUÉ (1990): Sur la robustesse de l'equation de Black-Scholes, International Conference in Finance, HEC Paris.
12. EL KAROUI, N., M. JEANBLANC-PICQUÉ, and S. SHREVE (1998): Robustness of the Black and Scholes Formula, Math. Finance 8, 93-126.
13. EL KAROUI, N., andM.-C. QUENEZ (1995): Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market, SIAM J. Control Optim. 33(1), 27-66.
14. EMANUEL, D., and J. MACBETH (1982): Further Results on the Constant Elasticity of Variance Option Pricing Model, J. Financial Quant. Anal. 17, 533-554.
15. FÖLLMER, H., and M. SCHWEIZER (1991): Hedging of Contingent-Claims under Incomplete Information; in Applied Stochastic Analysis. London: Gordon & Breach, 205-223.
16. FREY, R. (1997): Derivative Asset Analysis in Models with Level-Dependent and Stochastic Volatility, CWI Quart., Amsterdam 10, 1-34.
17. HESTON, S. (1993): A Closed Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options, Rev. Financial Stud. 6, 327-343.
18. HOFMANN, N., E. PLATEN, and M. SCHWEIZER (1992): Option Pricing under Incompleteness and Stochastic Volatility, Math. Finance 2, 153-187.
19. HULL, D., and A. WHITE (1987): The Pricing of Options on Assets with Stochastic Volatilities, J. Finance 42(2), 281-300.
20. KARATZAS, I., and S. SHREVE (1988): Brownian Motion and Stochastic Calculus. Berlin: Springer.
21. KRAMKOV, D. (1996): Optional Decomposition of Supermartingales and Hedging Contingent Claims in Incomplete Security Markets, Prob. Theory and Related Fields 105, 459-479.
22. LYONS, T. (1995): Uncertain Volatility and the Risk-Free Synthesis of Derivatives, Appl. Math. Finance 2, 117-133.
23. NAIK, V. (1993): Option Valuation and Hedging with Jumps in the Volatility of Asset Returns, J. Finance 48, 1969-1984.
24. PHAM, H., and N. TOUZI (1996): Equilibrium State Prices in a Stochastic Volatility Model, Math. Finance 6, 215-236.
25. RENAULT, E., and N. TOUZI (1996): Option Hedging and Implied Volatilities in a Stochastic Volatility Model, Math. Finance 6, 279-302.
26. SIN, C. (1998): Complications with Stochastic Volatility Models, Adv. Appl. Probab. 30, 256-268.
27. SIN, C. (1996): Strictly Local Martingales and Hedge Ratios in Stochastic Volatility Models, Ph.D. thesis, Cornell University.
28. WIGGINS, J. B. (1987): Option Valuation under Stochastic Volatility, Theory and Empirical Estimates, J. Financial Econ. 19, 351-372.