The SABR forward smile

Thomas Roos presents the expressions for the implied volatilities of European and forward starting options

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In this article, Thomas Roos, using short-time expansion techniques, obtains analytic implied volatilities for European and forward starting options for a SABR-type stochastic volatility model with an arbitrary local volatility component and time-dependent (piecewise-constant) parameters. The formulas can be used to efficiently calibrate the model to European options at two expiries and to calculate the spanning forward starting option price

A forward starting option

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