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| Pricing con Crank-Nicolson× | Modello SABR× | |
|---|---|---|
| Campo | Finanza quantitativa | Finanza quantitativa |
| Famiglia≠ | Machine learning | Regression model |
| Anno di origine≠ | 1947 | 2002 |
| Ideatore≠ | John Crank and Phyllis Nicolson | Patrick S. Hagan |
| Tipo≠ | PDE Solver | Interest Rate Model |
| Fonte seminale≠ | Crank, J., & Nicolson, P. (1947). A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Mathematical Proceedings of the Cambridge Philosophical Society, 43(1), 50-67. DOI ↗ | Hagan, P. S., Kumar, D., Lesniewski, A. S., & Woodward, D. E. (2002). Managing smile risk. Wilmott Magazine, 1, 84-108. link ↗ |
| Alias≠ | CN Method, Implicit Finite Difference | Stochastic Volatility Model |
| Correlati≠ | 3 | 4 |
| Sintesi≠ | The Crank-Nicolson method is a widely-used implicit finite difference scheme for solving PDEs in option pricing. It provides second-order accuracy in both space and time, unconditional stability, and can efficiently price derivatives with early exercise features (American options) or complex boundary conditions. | The SABR (Stochastic Alpha-Beta-Rho) model is a stochastic volatility framework introduced by Hagan et al. in 2002 for valuing interest rate derivatives. It captures the smile effect in implied volatility through correlated Brownian motions and has become industry standard for swaption and caplet pricing. |
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