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...

Comparisons are made of the CBOE skew index with those derived from parametric skews of bilateral gamma models and from the differentiation of option implied characteristic exponents. Discrepancies may be attributed to strike discretization in evaluating prices of powered returns. The remedy...

The problem studied is the pricing of options on the CBOE Skew index. The option pricing theory developed seeks to hedge the risk using positions in the market for options on a related asset and the option is then priced at the cost of this hedge. The theory is applied to pricing VIX options...

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...

Nonlinear martingale theory is used to form lower and upper price processes straddling a martingale. The martingale return is then modeled in terms of risk charges associated with the returns on the straddling lower and upper processes. The move to physically expected returns is made via 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...

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...

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...