The volatility implied by observed market prices as a function of the strike and time to maturity form an Implied Volatility Surface (IVS). Practical applications require reducing the dimension and characterize its dynamics through a small number of factors. Such dimension reduction is...

Modelling portfolio credit risk is one of the crucial challenges faced by financial services industry in the last few years. We propose the valuation model of collateralized debt obligations (CDO) based on copula functions with up to three parameters, with default intensities estimated from...

This paper analyzes empirical market utility functions and pricing kernels derived from the DAX and DAX option data for three market regimes. A consistent parametric framework of stochastic volatility is used. All empirical market utility functions show a region of risk proclivity that is...

Market option prices in last 20 years confirmed deviations from the Black and Scholes (BS) models assumptions, especially on the BS implied volatility. Implied binomial trees (IBT) models capture the variations of the implied volatility known as volatility smile. They provide a discrete...

Traditionally volatility is viewed as a measure of variability, or risk, of an underlying asset. However recently investors began to look at volatility from a different angle. It happened due to emergence of a market for new derivative instruments - variance swaps. In this paper first we...