We develop an asymptotic expansion technique for pricing timer options under general stochastic volatility models around small volatility of variance. Closed-form approximation formulas have been obtained for the Heston model and the 3/2-model. The approximation has an easy-to-understand...

We introduce a simple extension of a shifted geometric Brownian motion for modelling forward LIBOR rates under their canonical measures. The extension is based on a parameter uncertainty modelled through a random variable whose value is drawn at an in¯nitesimal time after zero. The shift in...

In the present paper we construct stock-price processes with the same marginal lognormal law as that of a geometric Brownian motion and also with the same transition density (and returns' distributions) between any two instants in a given discrete-time grid. <p>We then illustrate how option prices...</p>

Recent empirical studies on interest rate derivatives have shown that the volatility structure of interest rates is frequently humped. Several researchers have modelled interest rate dynamics in such a way that humped volatility structures are possible and yet analytical formulas for European...