The Swap Market Model with Local Stochastic Volatility

Abstract: Modeling volatility is an intricate part of all financial models and the pricing of derivative contracts. And while local volatility has gained popularity in equity and FX models, it remained neglected in interest rates models. In this thesis, using spot starting swaps, the goal is to build a swap market model with non-parametric local volatility functions and stochastic volatility scaling factors. The local stochastic volatility formula is calibrated through a particle algorithm to match the market’s swaption volatility smile. Numerical experiments are conducted for different currencies to compute the local stochastic volatility at different expiry dates, swap tenors and strike values. The results of the simulation show the high quality calibration of the algorithm and the efficiency of local stochastic volatility in interest rate smile building.