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...

The logarithm of SPX is modeled as a Sato process running at a speed proportional to the current level of the VIX. When the logarithm of the VIX is an exponential compound Poisson process with drift one may obtain exact expressions for the prices of equity options taken at an independent...

The theory of two price markets of Cherny and Madan (2010) yields closed forms for bid and ask prices. Defining profits as the difference between the mid quote and the risk neutral expectation and capital as difference between the ask and the bid price one obtains precise expressions for these...

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...

We develop a dynamic model in which traders have differential information about the payoff of the risky asset and trade the risky asset with proportional transaction costs. Firstly, trading volume provides useful information on the asset fundamental value which cannot be inferred from the...

The study of tail events has become a central preoccupation for academics, investors and policy makers, given the recent financial turmoil. However, what differentiates a crash from a tail event? This article answers this question by taking a risk management perspective that is based on an...