Large Deviation Theory And Computation Of Implied Volatilities

The area of large deviations is a set of asymptotic results on rare events probabilities and a set of methods to derive such results. Large deviations theory is a very active field in applied probability, and finds important applications in finance, where questions related to extremal events play an increasingly major role. The purpose of these lectures is to explain some essential techniques in large deviations theory, and to illustrate how they are applied recently for example in stochastic volatility models to compute implied volatilities near maturities.