Implied Remaining Variance in Derivative Pricing

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In this note, the authors give a way to calculate a swaption-implied volatility curve in closed form via the well-known quadratic root formula. The closed-form expression has three free parameters, which parsimoniously govern the assumed dynamics of implied volatility under forward swap measure. Preliminary empirical work suggests the curve fits the swaptions market well (although not perfectly). Unlike previous models of stochastic implied volatility, the current model has no implications for the dynamics of instantaneous volatility.