Polynomial chaos for simulating random volatilities

Mathematics and Computers in Simulation

Volumn 80, Issue 2, 2009, Pages 245-255

  Pulch, Roland ^a   van Emmerich, Cathrin ^a  

^a UNIVERSITY OF WUPPERTAL   (Germany)

Author keywords

Method of lines; Option price; Parabolic equation; Polynomial chaos; Volatility

Indexed keywords

METHOD OF LINES; OPTION PRICE; PARABOLIC EQUATION; POLYNOMIAL CHAOS; VOLATILITY;

CHAOS THEORY; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; MONTE CARLO METHODS; POLYNOMIALS; RANDOM PROCESSES; RANDOM VARIABLES; STOCHASTIC MODELS;

COSTS;

EID: 70349774376     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2009.05.008     Document Type: Article

References (19)

1. Augustin F., Gilg A., Paffrath M., Rentrop P., and Wever U. Polynomial chaos for the approximation of uncertainties: chances and limits. Eur. J. Appl. Math. 19 (2008) 149-190
2. Black F., and Scholes M. The pricing of options and corporate liabilities. J. Political Econ. 81 (1973) 637-659
3. Cameron R., and Martin W. The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals. Ann. Math. 48 2 (1947) 385-392
4. Günther M., and Jüngel A. Finanzderivate mit MATLAB (2003), Vieweg, Wiesbaden
5. Hairer E., Nørsett S.P., and Wanner G. Solving Ordinary Differential Equations, vol. 1. Nonstiff Problems. 2nd ed. (1993), Springer, Berlin
6. Hairer E., and Wanner G. Solving Ordinary Differential Equations, vol. 2. Stiff and Differential-Algebraic Equations. 2nd ed. (1996), Springer, Berlin
7. Heston S.L. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Fin. Stud. 6 (1993) 327-343
8. Hull J., and White A. The pricing of options on assets with stochastic volatilities. J. Fin. 42 2 (1987) 281-300
9. Marsaglia G., and Zaman A. A new class of random number generators. Ann. Appl. Prob. 1 3 (1991) 462-480
10. Marsaglia G. The mathematics of random number generators. Proc. Symp. Appl. Math. (1992) 73-90
11. MATLAB. The Language of Technical Computing (2004), The MathWorks, South Natick, MA
12. Merton R.C. Theory of rational option pricing. Bell J. Econ. Manage. Sci. 4 (1973) 141-183
13. Øksendal B. Stochastic Differential Equations. 6th ed. (2003), Springer, Berlin
14. Scott L. Option pricing when the variance changes randomly: theory, estimation and an application. J. Fin. Quant. Anal. 22 (1987) 419-438
15. Stein E.M., and Stein J.C. Stock price distribution with stochastic volatility: an analytic approach. Rev. Fin. Stud. 4 (1991) 727-752
16. Wiener N. The homogeneous chaos. Am. J. Math. 60 (1938) 897-936
17. Wiggings J. Option values under stochastic volatility: theory and empirical estimates. J. Fin. Econ. 19 (1987) 351-372
18. Wilmott P. Paul Wilmott on Quantitative Finance (2000), John Wiley & Sons, Chichester
19. Xiu D., and Karniadakis G.E. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24 2 (2002) 619-644