Name
Title | ||
|---|---|---|
Fast resolution of a single factor Heath-Jarrow-Morton model with stochastic volatility |
Abstract | ||
|---|---|---|
This paper considers the single factor Heath-Jarrow-Morton model for the interest rate curve with stochastic volatility. Its natural formulation, described in terms of stochastic differential equations, is solved through Monte Carlo simulations, that usually involve rather large computation time, inefficient from a practical (financial) perspective. This model turns to be Markovian in three dimensions and therefore it can be mapped into a 3D partial differential equations problem. We propose an optimized numerical method to solve the 3D PDE model in both low computation time and reasonable accuracy, a fundamental criterion for practical purposes. The spatial and temporal discretizations are performed using finite-difference and Crank-Nicholson schemes respectively, and the computational efficiency is largely increased performing a scale analysis and using Alternating Direction Implicit schemes. Several numerical considerations such as convergence criteria or computation time are analyzed and discussed. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.cam.2011.09.027 | J. Computational Applied Mathematics |
Keywords | Field | DocType |
stochastic volatility,partial differential equations problem,single factor heath-jarrow-morton model,low computation time,fast resolution,computation time,practical purpose,pde model,optimized numerical method,large computation time,stochastic differential equation,numerical consideration,quantitative finance,computational finance | Alternating direction implicit method,Stochastic volatility,Mathematical optimization,Monte Carlo method,Computational finance,Mathematical finance,Mathematical analysis,Stochastic differential equation,Numerical analysis,Partial differential equation,Mathematics | Journal |
Volume | Issue | ISSN |
236 | 6 | Journal of Computational and Applied Mathematics 236, 6, Pages
1637-1655 (2011) |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Eusebio Valero | 1 | 43 | 6.63 |
| manuel torrealba | 2 | 0 | 0.34 |
| Lucas Lacasa | 3 | 16 | 6.12 |
| francois fraysse | 4 | 0 | 0.34 |