Exponentials of squared returns in Gaussian densities, with their consequently thin tails, are replaced by the absolute return to form Laplacian and exponentially tilted Laplacian densities at unit time. Scaling provides densities at other maturities. Stochastic processes with these marginals...

Conic pricing (or bid and ask pricing) of credit risk shows how counterparty credit risk when conservatively valued at the bid price results in larger CVA than would occur under risk neutral pricing. On the other hand when it comes to the debt valuation adjustment, since it is a liability, it...

Options paying the product of put and/or call option payouts at different strikes on two underlying assets are observed to synthesize joint densities and replicate differentiable functions of two underlying asset prices. The pricing of such options is undertaken from three perspectives. The...

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...

Minimal discounted distorted expectations across a range of stress levels are employed to model risk acceptability in markets. Interactions between discounting and stress levels used in measure changes are accommodated by lowering discount rates for the higher stress levels. Acceptability...

A Markov chain with an expanding non-uniform grid matching risk neutral marginal distributions is constructed. Conditional distributions of the chain are in the variance gamma class with prespecified skewness and excess kurtosis. Time change and space scale volatilities are calibrated from...

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...

No arbitrage for two price economies with no locally risk free asset implies that suitably deflated prices are nonlinear martingales. However, both the deflating process and the measure change depend on the process being deflated. Further assumptions allow the nonlinear martingales in discrete...

Learning the pre limited liability value process of equity claims and its relationship to the stock price is an answer to the financial jeorpardy question when observed option prices are the answer being given by the market. Constant dollar equity holder values, prior to the imposition of...

Allowing for correlated squared returns across two consecutive periods, portfolio theory for two periods is developed. This correlation makes it necessary to work with non-Gaussian models. The two period conic portfolio problem is formulated and implemented. This development leads to a mean ask...