Previous option pricing research typically assumes that the risk-free rate or the short rate is constant during the life of the option. In this study, we incorporate the stochastic nature of the short rate in our option valuation model and derive explicit formulas for European call and put options on a stock when the short rate follows the Merton model. Using our option model as a benchmark, ou...

When the underlying asset is a continuous martingale, call option prices solve the Dupire equation, a forward parabolic PDE in the maturity and strike variables. By contrast, when the underlying asset is described by a discontinuous semimartingale, call prices solve a partial integro-differential equation (PIDE), containing a non-local integral term. We show that the two classes of equations sh...

We revisit the American put and call option valuation problems. We derive analytical formulas for the option prices and approximate ordinary differential equations for the optimal exercise boundaries. Numerical simulations yield accurate option prices and comparable computational speeds when benchmarked against the binomial method for calculating option prices. Our approach is based on the Mell...

Closed form option pricing formulae explaining skew and smile are obtained within a parsimonious non-Gaussian framework. We extend the non-Gaussian option pricing model of L. Borland (Quantitative Finance, 2, 415-431, 2002) to include volatility-stock correlations consistent with the leverage effect. A generalized Black-Scholes partial differential equation for this model is obtained, together ...

In a competitive electricity market traditional demand side management options offering customers curtailable service at reduced rates are replaced by voluntary customer responses to electricity spot prices. In this new environment, customers wishing to ensure a fixed electricity price while taking advantage of their flexibility to curtail loads can do so by purchasing a forward electricity con...

We present new families of lower bounds for the price of the American put option on a dividend paying stock when the stock follows a log normal process and the option can be exercised continuously to a finite horizon . By put call parity, these bounds can be easily converted to bounds on the price of the Ameican call option on a dividend paying stock. By numerically optimizing these bounds, we ...

Consider the European call option written on a zero-coupon bond. Suppose the call option has maturity T and strike price K while the bond has maturity S>T. We propose a numerical method for evaluating the call option price under the Chan, Karolyi, Longstaff and Sanders (CKLS) model in which the increment of the short rate over a time interval of length dt, apart from being independent and stati...