The concept of stress levels embedded in S&P 500 options are defined and illustrated with explicit constructions. The particular example of a stress function used is MINMAXVAR. Seven joint laws for the top 50 stocks in the index are considered. The first time changes a Gaussian one factor...

This paper develops a valuation model of European options incorporating a stochastic default barrier, which extends a constant default barrier proposed in the Hull-White model. The default barrier is considered as an option writer's liability. Closed-form solutions of vulnerable European option...

We study a modification of an American option such that the option holder can exercise the option early before the expiration, and he or she can revert later this decision to exercise a number of times. This feature gives additional flexibility and risk protection for the option holder. We found...

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...