When the pricing kernel is U-shaped, then expected returns of claims with payout on the upside are negative for strikes beyond a threshold, determined by the slope of the U-shaped kernel in its increasing region, and have negative partial derivative with respect to strike in the increasing...

This paper studies the structure of stock market crashes, rallies, their jump arrival rates, and extremes. Large market moves are characterized in a pure-jump modeling framework. Based on both raw and devolatized returns, it is shown empirically that crashes are more severe in intensity than...

The Bachelier Society for Mathematical Finance, founded in 1996, held its 1st World Congress in Paris on June 28 to July 1, 2000, thus coinciding in time with the centenary of the thesis defence of Louis Bachelier. In his thesis Bachelier introduced Brownian motion as a tool for the analysis of...

The current volume is a compendium of chapters, each of which consists of discursive review and recent research on the topic of exotic option pricing and advanced markets, written by leading scientists in this field.

A local volatility model is enhanced by the possibility of a single jump to default. The jump has a hazard rate that is the product of the stock price raised to a prespecified negative power and a deterministic function of time. The empirical work uses a power of -1.5. It is shown how one may...

Optimal portfolios of variance swaps are constructed taking account of both autocorrelation and cross asset dependencies. Market prices of variance swaps are extracted from option surface calibrations. The methods developed permit simulation of cash flows to arbitrary portfolios of variance...

The theory of pricing to acceptability developed for incomplete markets by Cherny and Madan (2009b) is applied to marking ones own default risk. It is observed in agreement with Heckman (2004), that assets and liabilities are not to be priced under fair value accounting principles at the same...

Longer horizon returns are constructed from data on daily returns. Observed drawbacks of a Lévy process are a sharp decrease in skewness and excess kurtosis. Drawbacks to scaling are a flat term structure of skewness and excess kurtosis. A strategy that combines some exposure to independent...

The concept of stress levels embedded in S&P 500 options are defined and illustrated with explicit constructions. The particular example of a stress function used is MINMAXVAR. Seven joint laws for the top 50 stocks in the index are considered. The first time changes a Gaussian one factor...

When firms access unbounded liability exposures and are granted limited liability, then an all equity firm holds a call option, whereby it receives a free option to put losses back to the taxpayers. We call this option the taxpayer put, where the strike is the negative of the level of reserve...