On the basis of transaction data, this paper analyzes the strike proÞle of implied volatilities of German DAX options for a time to expiration of 45 days. Beside the S&P option contract, the DAX option is one of the most heavily traded stock index options in the world. Using WLS spline regressions over the sample period from 1995 to 1999, we estimate a time series of smile characteristics, which we then try to attribute to economic fundamentals. Their choice is motivated by common theoretical explanations of the smile. The strike pattern almost exclusively appears as a "skew" rather than a "smile". We Þnd that the dynamics of the smile proÞle can be accurately modelled by a stationary AR(1) process. Market uncertainty, measured by volatility of volatility, and liquidity effects seem to play an important role in determining the pattern of DAX implied volatilities across exercise prices.

Volatility movements are known to be negatively correlated with stock index returns. Hence, investing in volatility appears to be attractive for investors seeking risk diversification. The most common instruments for investing in pure volatility are variance swaps, which now enjoy an active over-the-counter (OTC) market. This paper investigates the risk-return tradeoff of variance swaps on the Deutscher Aktienindex and Euro STOXX 50 index over the time period from 1995 to 2004. We synthetically derive variance swap rates from the smile in option prices. Using quotes from two large investment banks over two months, we validate that the synthetic values are close to OTC market prices. We find that variance swap returns exhibit an option-like profile compared to returns of the underlying index. Given this pattern, it is crucial to account for the non-normality of returns in measuring the performance of variance swap investments. As in the US, the average returns of selling variance swaps are found to be strongly positive and too large to be compatible with standard equilibrium models. The magnitude of the estimated risk premium is related to variance uncertainty and past index returns. This indicates that the variance swap rate does not seem to incorporate all past information relevant for forecasting future realized variance.Implied volatility, smile, variance swap, volatility risk premium,

Variance swap, Volatility risk premium, Portfolio analysis, Higher moments, Polynomial goal programming, Hedge funds, G10, G12, G13,

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