Structure preserving stochastic integration schemes in interest rate derivative modeling

Applied Numerical Mathematics

Volumn 58, Issue 3, 2008, Pages 284-295

  Kahl, C ^a,b   Gunther M ^a   Rossberg, T ^b  

^a UNIVERSITY OF WUPPERTAL   (Germany)

^b Product Development Group   (United Kingdom)

Author keywords

Constant elasticity of variance; Displaced diffusion; Eternal life span; Forward rate model; Libor market models; Mean reverting; Milstein schemes; Positivity; Stochastic differential equation; Structure preserving

Indexed keywords

BROWNIAN MOVEMENT; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; INTEGRATION; PROBLEM SOLVING;

CONSTANT ELASTICITY; DISPLACED DIFFUSION; ETERNAL LIFE SPAN; FORWARD RATE MODELS; LIBOR MARKET MODELS; MEAN REVERTING; MILSTEIN SCHEMES; STOCHASTIC DIFFERENTIAL EQUATION; STRUCTURE-PRESERVING;

STOCHASTIC MODELS;

EID: 38749099790     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2006.11.013     Document Type: Article

References (11)

1. Andersen L., and Brotherton-Ratcliffe R. Extended Libor market models with stochastic volatility. Working paper, General Re Financial Products (2001). http://ssrn.com/abstract=294853
2. Hairer E., Lubich Ch., and Wanner G. Geometric Numerical Integration, Structure-Preserving Algorithms for Ordinary Differential Equations. second ed. (2004), Springer, Berlin
3. Heston S. A closed-form solution for options with stochastic volatility with application to bond and currency options. Rev. Financ. Stud. 6 (1993) 327-343
4. Hull J., and White A. The pricing of options on assets with stochastic volatilities. J. Finance 42 (1987) 281-300
5. Jamshidian F. LIBOR and swap market models and measures. Finance Stoch. 1 (1997) 293-330
6. Kahl C. Positive numerical integration of stochastic differential equations. Master's thesis, University of Wuppertal (2004). http://www.math.uni-wuppertal.de/~kahl/publications.html
7. Karlin S., and Taylor H.M. A Second Course in Stochastic Processes (1981), Academic Press, New York
8. Kloeden P.E., and Platen E. Numerical Solution of Stochastic Differential Equations (1999), Springer, Berlin
9. Milshtein G.N. Numerical Solution of Stochastic Differential Equations (1995), Kluwer, Dordrecht
10. Milshtein G.N., Platen E., and Schurz H. Balanced implicit methods for stiff stochastic systems. SIAM 38 3 (1998) 1010-1019
11. Schurz H. Numerical regularization for SDE's: Construction of nonnegative solutions. Dyn. Syst. Appl. 5 1 (1996) 323-352