Journal of Computational Finance

A nonparametric local volatility model for swaptions smile

Dariusz Gątarek and Juliusz Jabłecki

  • Despite popularity in equity and FX space, Dupire-style local volatility model has not been applied so far in interest rate space.
  • We fill this gap and derive an equation for the unique state-dependent diffusion coefficient consistent with current swaptions prices.
  • The approach we propose has all the merits of the classic local volatility models as it fits exactly market swaptions prices and allows for fast and accurate calibration while still being realistic and transparent.

We propose a nonparametric local volatility Cheyette model and apply it to pricing interest rate swaptions. Concretely, given market prices of swaptions, we show how to construct a unique diffusion process consistent with these prices. We then link the resulting local volatility to the dynamics of the entire interest rate curve. The model preserves completeness and allows consistent pricing of illiquid, out-of-the-money and exotic interest rate products. The model is relatively straightforward to implement and calibrate and less involved than stochastic volatility approaches.

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