Non-parametric local volatility formula for interest rate swaptions

The volatility smile in the interest rate derivative models has long been an important topic in theory and practice. With a growing divergence of monetary policy cycles between the US and Europe, there is a stronger need for robust smile models that would allow for pricing illiquid, out-of-the-money and exotic interest rate products. Dariusz Gatarek, Juliusz Jabłecki and Dong Qu propose a simple Dupire-like local volatility formula that works for swaptions. Working in a Cheyette-type quasi-Gaussian framework, they link the resulting swap rate local volatility to the dynamics of two state variables parameterising the entire evolution of the interest rate curve, which allows for fast and accurate calibration


Ever since the seminal contributions of Bruno Dupire (1994) and Emanuel Derman and Iraj Kani (1994), who independently developed a discrete-time binomial tree version of the same result, it has been well known that there exists a unique diffusion process consistent with market prices of all available European options with different Black-Scholes implied volatilities for different strikes and expirations. Although the resulting local volatility function has been shown to have rather poor

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