Non-parametric local volatility formula for interest rate swaptions

Gatarek, Jabłecki and Qu introduce a Dupire-like formula for swaptions

gatarek-chart

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 predicti