Long-dated foreign exchange interest rate hybrid financial derivatives: modeling,calibration, pricing, and risk-management
The proposed project addresses three major challenges in modeling long-dated (maturities of 30 years or more) foreign exchange (FX) interest rate (IR) hybrid derivatives, namely
(i) the strong sensitivity of the products to the skew of the FX volatility smiles,
(ii) their very long maturities, and
(iii) popular embedded exotic features, which provide possibilities of early termination of the products.
The proposed approach is based on the use of (a) a stochastic process, such as the Heston model, or a regime switching model for the the stochastic volatility of the spot FX rate, (b) multi-factor Gaussian IR models, and (c) L´evy-type jump models. Hybrid numerical methods based on a combination of Monte-Carlo (MC) and partial differential equation (PDE) approaches will be developed for the pricing of these derivatives. The expected benefits of the project to the industrial partner are
(i) flexible modeling frameworks for long-dated FX-IR, which can be easily modified for use for other long-dated hybrids, such as equities and commodities, and associated efficient calibration techniques,
(ii) robust and efficient risk-management techniques for these financial derivatives,
(iii) effective PDE-based variance reduction techniques for multi-dimensional Monte Carlo simulations, and
(iv) highly efficient PDE-based pricing methods for multi-dimensional financial derivatives.