Previous research has shown that for stock indices, the most likely time until a return of a particular size has been observed is longer for gains than for losses. We demonstrate that this so-called gain-loss asymmetry vanishes if the temporal dependence structure is destroyed by scrambling the time series. We also show that an artificial index constructed by a simple average of a number of individual stocks display gain-loss asymmetry-this allows us to explicitly analyze the dependence between the index constituents. We consider mutual information and correlation-based measures and show that the stock returns indeed have a higher degree of dependence in times of market downturns than upturns.

Researchers have studied the first passage time of financial time series and observed that the smallest time interval needed for a stock index to move a given distance is typically shorter for negative than for positive price movements. The same is not observed for the index constituents, the individual stocks. We use the discrete wavelet transform to illustrate that this is a long rather than short time scale phenomenon -if enough low frequency content of the price process is removed, the asymmetry disappears. We also propose a new model, which explain the asymmetry by prolonged, correlated down movements of individual stocks.

Risk-minimization, Static hedge, Barrier option, Bates model, NIG model, Model risk, G13, C61,

JEL classification: G10 G21 C63 C46 Keywords:Value-at-Risk Delta-gamma approximation Fourier inversion Characteristic function Error boundsThe Value-at-Risk of a delta-gamma approximated derivatives portfolio can be computed by numerical integration of the characteristic function. However, while the choice of parameters in any numerical integration scheme is paramount, in practice it often relies on ad hoc procedures of trial and error. For normal and multivariate t-distributed risk factors, we show how to calculate the necessary parameters for one particular integration scheme as a function of the data (the distribution of risk factors, and delta and gamma) in order to satisfy a given error tolerance. This allows for implementation in a fully automated risk management system. We also demonstrate in simulations that the method is significantly faster than the Monte Carlo method, for a given error tolerance.

We study the pricing of barrier options on stocks with lumpy dividends. By extending the European option methodology presented in Haug, Haug, and Lewis (2003), we show that in the Black–Scholes model with a single dividend payment, barrier option prices can be expressed in terms of well‐behaved one‐dimensional integrals that can be evaluated very rapidly. With multiple dividend payments, the price integrals are more involved, but we show that for the down‐and‐out call option a simple approximation method gives accurate results. Copyright © 2009 Wilmott Magazine Ltd