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...

Distortions introduced by limited liability towards higher volatility and kurtosis, increased liability skewness, reduced asset skewness and an incentive to decorrelate assets from liabilities are demonstrated in the context of a stylized model. The concept of acceptable risks operationalized by...

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...

Models of dependence in asset returns with non-Gaussian marginals are investigated on ETF daily return data. The first is a full rank Gaussian copula. The second is a linear mixture of independent Lévy processes. The third correlates Gaussian components in a variance gamma representation. On a...

Index option pricing on world market indices are investigated using Lévy processes with no positive jumps. Economically this is motivated by the possible absence of longer horizon short positions while mathematically we are able to evaluate for such processes the probability of a Rally Before a...

Asset price dynamics are taken to be accumulations of surprise jumps in the logarithm of prices. A Markov pure jump model is formulated on making variance gamma parameters deterministic functions of the price level. Estimation is done by matrix exponentiation of the transition rate matrix for a...

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...

Loan spreads are analysed for two types of loans. The first takes losses at maturity only; the second one follows the formulation of CFOs (Collateralized Fund Obligations), with losses registered over the lifetime of the contract. In both cases, the implementation requires the choice of a...

Realized variance option and options on quadratic variation normalized to unit expectation are analyzed for the property of monotonicity in maturity for call options at a fixed strike. When this condition holds the risk neutral densities are said to be increasing in the convex order. For Lévy...