To evaluate the aggregate risk in a financial or insurance portfolio, a risk analyst has to calculate the distribution function of a sum of random variables. As the individual risk factors are often positively dependent, the classical convolution technique will not be sufficient. On the other...

In this paper we consider the problem of deriving correlation estimates from observed option data. An implied correlation estimate arises when we match the observed index option price with a corresponding model price. The underlying model assumes that stock prices can be described using a...

In this paper we consider the problem of deriving correlation estimates from observed option data. An implied correlation estimate arises when we match the observed index option price with a corresponding model price. The underlying model assumes that stock prices can be described using a...

To evaluate the aggregate risk in a financial or insurance portfolio, a risk analyst has to calculate the distribution function of a sum of random variables. As the individual risk factors are often positively dependent, the classical convolution technique will not be sufficient. On the other...

In this paper we show that under appropriate moment conditions, the supermodular ordered random vectors X = (X1, X2, ... , Xn) and Y = (Y1, Y2, ... ,Yn) with equal expected utilities (or distorted expectations) of the sums X1 + X2 + ... + Xn and Y1 + Y2 + ... + Yn for an appropriate utility (or...

In this paper we show that under appropriate moment conditions, two supermodular ordered random vectors with equal expected utilities (or distorted expectations) of the sums for an appropriate utility (or distortion) function, must necessarily be equal in distribution. The results in this paper...

In order to price multivariate derivatives, there is need for a multivariate stock price model. To keep the simplicity and attractiveness of the one-dimensional Black & Scholes model, one often considers a multivariate model where each individual stock follows a Black & Scholes model, but the...

This paper proposes different diffusion processes to model herd behavior indices such as the Herd Behavior Index (HIX) or the comonotonicity index (CIX). These models arise by combining popular mean-reverting processes with simple algebraic functions mapping the definition domain of the...

For an arbitrage-free market with a single underlying asset, we investigate conditions under which the consecutive price levels are comonotonic. Furthermore, for an arbitrage-free market with n assets we investigate the consequences of assuming comonotonicity of the vector containing the price...