We consider an option c which is contingent on an underlying (tilde S) that is not a traded asset. This situation typically arises in the context of real options. We investigate the situation when there is a "surrogate" traded asset S whose price process is highly correlated with that of (tilde...

We introduce a variant of the Barndorff-Nielsen and Shephard stochastic volatility model where the non Gaussian Ornstein-Uhlenbeck process describes some measure of trading intensity like trading volume or number of trades instead of unobservable instantaneous variance. We develop an explicit...

We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as backward recursion or backward stochastic differential equation,...

We compute and discuss the Esscher martingale transform for exponential processes, the Esscher martingale transform for linear processes, the minimal martingale measure, the class of structure preserving martingale measures, and the minimum entropy martingale measure for stochastic volatility...

We introduce a variant of the Barndorff-Nielsen and Shephard stochastic volatility model where the non-Gaussian Ornstein-Uhlenbeck process describes some measure of trading intensity like trading volume or number of trades instead of unobservable instantaneous variance. We develop an explicit...