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Markovian Projection Method for Volatility Calibration

We present the Markovian projection method, a method to obtain closed-form approximations to European option prices on various underlyings that, in principle, is applicable to any (diffusive) model. Successful applications of the method have already appeared in the literature, in particular for interest rate models (short rate and forward Libor models with stochastic volatility), and interest rate/FX hybrid models with FX skew. The purpose of this note is thus not to present other instances where the Markovian projection method is applicable (even though more examples are indeed given) but to distill the essence of the method into a conceptually simple plan of attack, a plan that anyone who wants to obtain European option approximations can follow.