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...

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...

We consider the risk neutral valuation of fixed term securities lending in a multi-curve framework, taking into account the forward basis of each component of the transaction relative to the discount curve, including basis between currencies. We show that a convexity adjustment arises from the...

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

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...

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...