Motivated by the Kyle-Back model of “insider trading”, we consider certain classes of linear transformations of two independent Brownian motions and study their canonical decomposition as semimartingales in their own filtration. In particular we characterize those transformations which...

We show the existence, for any k E N, of processes which have the same k-marginals as Brownian motion, although they are not Brownian motions. For k = 4, this proves a conjecture of Stoyanov. The law P' of such a "weak Brownian motion of order k" can be constructed to be equivalent to Wiener...

Realized variance option and options on quadratic variation normalized to unit expectation are analysed 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...

For longer horizons, assuming no dividend distributions, equilibrium models for discounted stock prices are formulated as conditional expectations of nontrivial terminal random variables defined at infinity. Observing that extant models fail to have this property, new models are proposed. The...

Probability distortions for constructing nonlinear G-expectations for the bid and ask or lower and upper prices in continuous time are here extended to the direct use of measure distortions. Fairly generally measure distortions can be constructed as probability distortions applied to an...

Static and discrete time pricing operators for two price economies are reviewed and then generalized to the continuous time setting of an underlying Hunt process. The continuous time operators define nonlinear partial integro-differential equations that are solved numerically for the three...

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...

We introduce a class of stochastic processes, which we refer to as Lyrebirds. These extend a class of stochastic processes, which have recently been coined as Peacocks, but are more commonly known as processes which are increasing in the convex order. We show how these processes arise naturally...

A positive spot rate model driven by a gamma process and correlated to equity is introduced and calibrated via closed forms for the joint characteristic function for the rate r, its integral y and the logarithm of the stock price s under the T-forward measure. The law of the triple (r,y,s) is...