The replication of any European contingent claim by a static portfolio of calls and puts with strikes forming a continuum, formally proven by Carr and Madan (1998), extends to "standard dispersion" options written on the Euclidean norm of a vector of n asset performances. With the help of...

We consider risk-neutral valuation of a contingent claim under bilateral counterparty risk in a reduced-form setting similar to that of Duffie and Huang [1996] and Duffie and Singleton [1999]. The probabilistic valuation formulas derived under this framework cannot be usually used for practical...

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...

We develop a new option pricing framework that tightly integrates with how institutional investors manage options positions. The framework starts with the near-term dynamics of the implied volatility surface and derives no-arbitrage constraints on its current shape. Within this framework, we...

Complex insurance risks typically have multiple exposures. Options on multiple underliers with a short maturity are employed to hedge this exposure. Hedges are illustrated for GMWBVA accounts invested in the nine sector ETF's of the US economy. The underliers are simulated risk neutrally by...

We generalize the Kelly criterion and the growth-optimal portfolio (GOP) concept beyond log-wealth maximization. We show that models of speculative price dynamics with time change require different compounding algebras leading to GOPs that do not coincide with log-wealth maximization. In...

In option pricing it is customary to specify first a stochastic underlying model and then extract from it valuation equations. Still, it is possible to reverse this paradigm: starting from an arbitrage-free valuation formula, one could derive a family of risk-neutral probabilities and a...

The replication of any European contingent claim by a static portfolio of calls and puts with strikes forming a continuum, formally proven by Carr and Madan (1998), is part of the more general theory of integral equations. We apply spectral decomposition techniques to show that replication may...

We show that under the Black Scholes assumption the price of an arithmetic average Asian call option with fixed strike increases with the level of volatility. This statement is not trivial to prove and for other models in general wrong. In fact we demonstrate that in a simple binomial model no...