Very exotic derivatives

Pricing Exotic Derivatives Using Regret Minimization

We price various financial instruments, which are classified as exotic options, using the regret bounds of an online algorithm. In addition, we derive a general result, which upper bounds the price of any derivative whose payoff is a convex function of the final asset price. The market model used is adversarial, making our price bounds robust. Our results extend the work of [9], which used regr...

Moment Methods for Exotic Volatility Derivatives

The latest generation of volatility derivatives goes beyond variance and volatility swaps and probes our ability to price realized variance and sojourn times along bridges for the underlying stock price process. In this paper, we give an operator algebraic treatment of this problem based on Dyson expansions and moment methods and discuss applications to exotic volatility derivatives. The method...

Exotic derivatives under stochastic volatility models with jumps

In equity and foreign exchange markets the risk-neutral dynamics of the underlying asset are commonly represented by stochastic volatility models with jumps. In this paper we consider a dense subclass of such models and develop analytically tractable formulae for the prices of a range of first-generation exotic derivatives. We provide closed form formulae for the Fourier transforms of vanilla a...

Ecological invasion in competition-diffusion systems when the exotic species is either very strong or very weak

Reaction-diffusion systems with a Lotka-Volterra-type reaction term, also known as competition-diffusion systems, have been used to investigate the dynamics of the competition among m ecological species for a limited resource necessary to their survival and growth. Notwithstanding their rather simple mathematical structure, such systems may display quite interesting behaviours. In particular, w...

Exotic Atoms and Exotic Nuclei