The Sato process model for option prices is expanded to accomodate credit considerations by incorporating a single jump to default occuring at an independent random time with a Weibull distribution. Explicit formulas for bid and ask prices are derived. Liquidity considerations are captured 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...

A bank's stock price is modeled as a call option on the spread of random assets over random liabilities. The logarithm of assets and liabilities are jointly modeled as driven by four variance gamma processes and this model is estimated by calibrating to quoted equity options seen as compound...

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...

Risk premia are related to price probability ratios or for continuous time pure jump processes the ratios of jump arrival rates under the pricing and physical measures. The variance gamma model is employed to synthesize densities with risk premia seen as the ratio of the three parameters. The...

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...

At each maturity a discrete return distribution is inferred from option prices. Option pricing models imply a comparable theoretical distribution. As both the transformed data and the option pricing model deliver points on a simplex, the data is statistically modeled by a Dirichlet distribution...

It is argued that the growth in the breadth of option strikes traded after the financial crisis of 2008 poses difficulties for the use of Fourier inversion methodologies in volatility surface calibration. Continuous time Markov chain approximations are proposed as an alternative. They are shown...

For mean reverting base probabilities option pricing models are developed using an explicit measure change induced by the selection of a terminal time and a terminal random variable. The models employed are the square root process and an OU equation driven by centered variance gamma shocks. VIX...

Summarizing option surfaces using parametric representations, their movements are decomposed into a number of effects. Arguments are presented for treating traditional sensitivity attribution terms as regression factors leading to significant attribution improvements