In this paper, we show how to calibrate the most usual stochastic processes: arithmetic and geometric Brownian motions,, mean-reverting processes and jump processes. This paper contains also many applications to Canadian financial data. We observe, among other phenomena, that a mean-reverting...

En recourant de plus en plus aux modèles à forme réduite, la théorie de l'évaluation du risque de crédit se distance de plus en plus de l'ingénierie financière traditionnelle qui donne la part belle aux modèles structurels. Bien qu'ils postulent l'absence d'arbitrage, les modèles à...

Plusieurs gestionnaires de portefeuille pensent encore à tort qu’une couverture delta suffit pour protéger leur portefeuille contre les fluctuations des marchés financiers. Mais une augmentation marquée de la volatilité des cours boursiers les décevra dans leurs attentes. Après avoir...

Monte Carlo simulation has an advantage upon the binomial tree as it can take into account the multidimensions of a problem. However it convergence speed is slower. In this article, we show how this method may be improved by various means: antithetic variables, control variates and low...

In this paper, we simulate portfolios which aim to insure the invested capital. The object of our simulations is the duplication of the cashflows of strategies based on options. We initially show how to duplicate the cash-flows of a call by using a leveraged portfolio of stocks. After, we...

Markets makers quote many option categories in terms of implicit volatility. In doing so, they can reactivate the Black and Scholes model which assumes that the volatility of an option underlying is constant while it is highly variable. First of all, this article, whose purpose is very...

The popularity of Kalman filter is increasing in financial studies, notably to estimate diffusion processes. In this article, we show how we can use it to forecast the volatility of returns and the price-earnings ratio of the S&P500. The Kalman filter is consequently very versatile when...

In this paper, we study the following models : Heath-Jarrow-Morton (1992) and Libor-Market- Model, also known as Brace-Gatarek-Musiela model (1997). We survey the extensions of these models and their representation in the Black and Scholes world. Our approach is pedagogical and is based on an...