Lookback options are path dependent contingent claims whose payoffs depend on the extrema of a given security's price over a certain period of time. Using probabilistic tools, the authors derive explicit formulas for various European lookback options and provide some results about their American...

French Abstract: Ce cours, destiné à des étudiants de Master 2 en ingénierie mathématiques, statistiques et actuariat, est une introduction à la théorie et la pratique de la finance quantitative et de la valorisation des options

The local volatility model is widely used as this is the unique one-factor Markov model perfectly calibrated to a continuum of vanilla options in strike and expiry. It requires unfortunately an arbitrage-free interpolation of implied volatility in expiry and a time-consuming Euler discretization...

Pricing a contingent claim on a non-tradable asset (e.g. a management warrant package in an LBO) cannot be done with standard hedging based option pricing theory. Common alternatives are utility indifference pricing, suggested by various authors, or risk premium pricing (using the option pricing...

We present an efficient algorithm for computing the Vega KT in the local volatility model based on the calculation of the local Vega through Monte-Carlo simulation and algorithmic differentiation. In comparison with the PDE algorithm presented in [Guennoun], our algorithm is applicable for...

Probabilities of default built for regulatory purposes cannot be applied directly to expected credit losses impairment calculations under the IFRS 9 new standard. This is because the regulatory framework requires stressed through-the-cycle (TTC) probabilities, so as to avoid a procyclical...