Exotic options are popular financial derivatives that play essential roles in financial markets. How to price them efficiently and accurately is very important both in theory and practice. The lattice model is usually used to price them. The prices computed by the lattice converge to the theoretical value under the continuous-time model. But the lattice model may produce quite slow convergence;...

Optimal decision-making often requires an assessment of the costs and benefits associated with each available course of action. Previous studies have shown that lesions to the anterior cingulate cortex (ACC) impair cost-benefit decision-making in laboratory animals, but the neural mechanisms underlying the deficit are not well understood. We recorded from ACC neurons in freely moving rats as th...

We have derived the analytical kernels of the pricing formulae of the CEV knockout options with time-dependent parameters for a parametric class of moving barriers. By a series of similarity transformations and changing variables, we are able to reduce the pricing equation to one which is reducible to the Bessel equation with constant parameters. These results enable us to develop a simple and ...

of time the underlying asset price spends outside of a pre-specified price range (occupation time). Proportional and simple double-barrier step options are gradual knockout options with the principal amortized based on the occupation time outside of the range. Delayed double-barrier options are extinguished when the occupation time outside of the range exceeds a prespecified knock-out window (d...

In this note we value and hedge European options on assets paying discrete stochastic dividends. Our hedging strategy is based only on the underlying asset, risk-free bonds and dividend strips. Our simple strategy is easily seen to be compatible with early results based, among other things, on the existence of a dividend forward contract. Such contracts, however, are not traded in the market pl...

The central part of pricing agricultural commodity futures options is to find appropriate stochastic process of the underlying assets. The Black’s (1976) futures option pricing model laid the foundation for a new era of futures option valuation theory. The geometric Brownian motion assumption girding the Black’s model, however, has been regarded as unrealistic in numerous empirical studies. Opt...