This paper performs specification analysis on the term structure of variance swap rates on the S&P 500 index and studies the optimal investment decision on the variance swaps and the stock index. The analysis identifies two stochastic variance risk factors, which govern the short and long end of the variance swap term structure variation, respectively. The highly negative estimate for the market price of variance risk makes it optimal for an investor to take short positions in a short-term variance swap contract, long positions in a long-term variance swap contract, and short positions in the stock index.
We introduce new quantile estimators with adaptive importance sampling. The adaptive estimators are based on weighted samples that are neither independent nor identically distributed. Using a new law of iterated logarithm for martingales, we prove the convergence of the adaptive quantile estimators for general distributions with nonunique quantiles, thereby extending the work of Feldman and Tucker. We illustrate the algorithm with an example from credit portfolio risk analysis.
DescriptionThe subprime crisis has shown that the sophisticated risk management models used by banks and insurance companies had serious flaws. Some people even suggest that these models are completely useless. Others claim that the crisis was just an unpredictable accident that was largely amplified by the lack of expertise and even naivety of many investors. This book takes the middle view. It shows that these models have been designed for "tranquil times", when financial markets behave smoothly and efficiently. However, we are living in more and more "turbulent times": large risks materialize much more often than predicted by "normal" models, financial models periodically go through bubbles and crashes. Moreover, financial risks result from the decisions of economic actors who can have incentives to take excessive risks, especially when their remunerations are ill designed. The book provides a clear account of the fundamental hypotheses underlying the most popular models of risk management and show that these hypotheses are flawed. However it shows that simple models can still be useful, provided they are well understood and used with caution.
