American Options Exercise Boundary When the Volatility Changes Randomly

Applied Mathematics and Optimization

Volumn 39, Issue 2-3, 1999, Pages 411-422

  Touzi, N ^a,b  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b CREST   (France)

Author keywords

Incomplete markets; Optimal stopping; Viscosity solutions

Indexed keywords

BOUNDARY CONDITIONS; FUNCTIONS; MATHEMATICAL MODELS; VISCOSITY;

VISCOSITY SOLUTIONS;

RANDOM PROCESSES;

EID: 0347180402     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002459900112     Document Type: Article

References (26)

1. Alvarez, O., P. L. Lions, and J. M. Lasry (1995). Convex viscosity solutions and state constraints. Preprint CEREMADE.
2. Bajeux, I., and J. C. Rochet (1996). Dynamic spanning: are options an appropriate instrument. Mathematical Finance 6(1): 1-16.
3. Barles, G., J. Burdeau, M. Romano, and N. Samsoen (1992). Critical stock price near expiration. Mathematical Finance 5(2):77-96.
4. Bensoussan, A. (1984). On the theory of option pricing. Acta. Applicandae Mathematicae 2:139-158.
5. Black, F., and M. Scholes (1973). The pricing of options and corporate liabilities. Journal of Political Economy 81:637-659.
6. Crandall, M.G, H. Ishii, and P.L. Lions (1990). User's Guide to Viscosity Solutions of Second Order Partial Differential Equations. Cahiers du CEREMADE, 9039, Universit Paris IX Dauphine.
7. Delbaen, F., and W. Schachermayer (1994). A general version of the fundamental theorem of asset pricing. Mathematische Annalen, 2:463-520.
8. El Karoui, N. (1981). Les Aspects Probabilistes du Contrôle Stochastique. Lecture Notes in Mathematics 876. Springer-Verlag, Berlin, pp. 73-238,
9. Friedman, A. (1975). Stochastic Differertial Equations and Applications, vol. 1. Academic Press, New York.
10. Harrison, J.M., and D.M. Kreps (1979). Martingale and arbitrage in multiperiods securities markets. Journal of Economic Theory 20: 381-408.
11. Harrison, J.M., and S. Pliska (1981). Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and their Applications 11: 215-260.
12. Hull, J., and A. White (1987). The pricing of options on assets with stochastic volatilities. The Journal of Finance 3: 281-300.
13. Karatzas, I. (1989). Optimization problems in the theory of continuous trading. SIAM Journal on Control and Optimization 27: 1221-1259.
14. Karatzas, I., and S.E. Shreve (1988). Brownian Motion and Stochastic Calculus. Springer-Verlag, New York.
15. Ladyzenskaja, O. A, V. A. Solonnikov, and N. N. Ural'ceva (1968). Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs 23. American Mathematical Society, Providence, RI.
16. Lions, P. L. (1983a). Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations, part I: the dynamic programming principle and applications. Communications in Partial Differential Equations 8(9-15):1101-1174.
17. Lions, P. L. (1983b). Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations, part II: viscosity solutions and uniqueness. Communications in Partial Differential Equations 8(9-15): 1229-1276.
18. Lions, P. L. (1983c). Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations, part III: regularity of the optimal cost function. Preprint CEREMADE.
19. McKean, H. P. (1965). A free boundary problem for the heat equation arising from a problem in mathematical economics. Industrial Management Review 6: 32-39.
20. Myneni, R. (1992). The pricing of the American option. Annals of Applied Probability 2: 1-23.
21. Renault, E., and N. Touzi (1996). Option hedging and implied volatility in a stochastic volatility model. Mathematical Finance 6: 279-302.
22. Romano, M., and N. Touzi (1996). Contingent claims and market completeness in a stochastic volatility model. Mathematical Finance 7: 399-412.
23. Scott, L. (1987). Option pricing when the variance changes randomly: theory, estimation and application. Journal of Financial and Quantitative Analysis 22: 419-438.
24. Stricker, C. (1990). Arbitrage et lois de martingale. Annales de l'Institut Henri Poincarré 26: 451-460.
25. Van Moerbeke, P. L. J. (1976). On optimal stopping and free boundary problems. Archive for Rational Mechanics and Analysis 60:101-148.
26. Wiggins, J. (1987). Option values under stochastic volatility. Journal of Financial Economics 19:351-372.