We learn from data that volatility is mostly path-dependent: at least 85-90% of the variance of the implied volatility of equity indexes is explained endogenously by past index returns, and around 60% for (noisy estimates of) future daily realized volatility. The path-dependency that we uncover...

Option pricing in a nutshell -- Monte Carlo -- Some excursions in option pricing -- Nonlinear PDEs: a bit of theory -- Examples of nonlinear problems in finance -- Early exercise problems -- Backward stochastic differential equations -- The uncertain lapse and mortality model -- The uncertain...

Given a smooth -valued diffusion starting at point x, we study how fast the Euler scheme with time step 1/n converges in law to the random variable . To be precise, we look for the class of test functions f for which the approximate expectation converges with speed 1/n to . When f is smooth with...