In the years following the publication of Black and Scholes [7], numerous alternative models have been proposed for pricing and hedging equity derivatives. Prominent examples include stochastic volatility models, jump diffusion models, and models based on Levy processes. These all have their own...

This teaching note shows the relationship between levered and unlevered betas and the general formulation for the cost of equity. It also shows, step by step, the procedure to estimate betas from data found in the stock market.It shows well known procedures for estimating betas: correlation...

Este trabajo muestra la relación entre las betas apalancadas y sin deuda y la formulación general para el costo del capital. También muestra, paso a paso, el procedimiento para calcular las betas a partir de los datos que se encuentran en el mercado de valores. Se muestran procedimientos...

The paper discusses the problem of hedging not perfectly replicable contingent claims by using a benchmark, the numerraire portfolio, as reference unit. The proposed concept of benchmarked risk minimization generalizes classical risk minimization, pioneered by Follmer, Sondermann and Schweizer....

This article explores the behavior of the stock market in Colombia with the information given by the Bolsa de Bogotá Index (Indice de la Bolsa de Bogotá, IBB). The index is analyzed from January, 1930 to December, 1998. The inflation rate covers the same period; the inflation rate as measured...

The paper proposes a financial market model that generates stochastic volatility and stochastic interest rate using a minimal number of factors that characterise the dynamics of the different denominations of the deflator. It models asset prices essentially as functionals of square root and...

This paper describes a financial market modelling framework that exploits the notion of a deflator . The denominations of the deflator measured in units of primary assets form a minimal set of basic financial quantities that completely specify the overall market dynamics, where deflated asset...

This paper introduces a benchmark model for financial markets, which is based on the unique characterization of a benchmark portfolio that is chosen to be the growth optimal portfolio. The general structure of risk premia for asset prices and portfolios is derived. Furthermore, the short rate is...

This paper considers a new class of Monte Carlo methods that are combined with PDE expansions for the pricing and hedging of derivative securities for multidimensional diffusion models. The proposed method combines the advantages of both PDE and Monte Carlo methods and can be directly applied to...

This paper proposes a consistent approach to discrete time valuation in insurance and finance. This approach uses the growth optimal portfolio as references unit or benchmark. When used as benchmark, it is shown that all benchmarked price processes are supermartingales.