Valuing Early-Exercise Interest-Rate Options With Multi-Factor Affine Models

Abstract

Multi-factor interest-rate models are widely used. Contingent claims with early exercise features are often valued by resorting to trees, finite-difference schemes and Monte Carlo simulations. When jumps are present, however, these methods are less effective. In this work we develop an algorithm based on a sequence of measure changes coupled with Fourier transform solutions of the pricing partial integro-differential equation to solve the pricing problem. The new algorithm, which we call the irFST method, also neatly computes option sensitivities. Furthermore, we are also able to obtain closed-form formulae for accrual swaps and accrual range notes. We demonstrate the versatility and precision of the method through numerical experiments on European, Bermudan and callable bond options, accrual swaps and accrual range notes.

Valuing guaranteed withdrawal benefits with stochastic interest rates and volatility

“…Also, one could imagine introducing jumps and/or regime switching into the linked equity and/or interest rates. The resulting PDE would become a PIDE and/or system of PDEs, but approaches such as those developed in Jackson et al (2008) and Jaimungal and Surkov (2010) can be applied for efficient evaluation. Moreover, multiple indicies and/or currencies could in principle be incorporated by increasing the number of stochastic degrees of freedom, but the resulting PDEs may run into curse of dimensionality issues.…”

A semi‐Lagrangian ε$$ \varepsilon $$‐monotone Fourier method for continuous withdrawal GMWBs under jump‐diffusion with stochastic interest rate

“…The key challenge in solving the PIDE (4.1) is that a closed‐form expression for its Green's function is not known to exist, due to the $$$ {v}_r $$$ term arising from the short rate. (Also see [49] for relevant discussions related to similar difficulties). To handle the above challenge, we consider a combination of a semi‐Lagrangian (SL) method and a Green's function approach.…”