An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and accurate predictions for the value of a large class of...

In this paper we are interested in Monte Carlo pricing of American options via the Longstaff–Schwartz algorithm. In particular, we show that it is possible to obtain a variance reduction technique based on importance sampling by means of Girsanov theorem. The almost sure convergence of the...

For a long time interest-rate models were built on a single yield curve used both for discounting and forwarding. However, the crisis that has affected financial markets in the last years led market players to revise this assumption and accommodate basis-swap spreads, whose remarkable widening...

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...

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...

<section xml:id="fut21659-sec-0001"> We develop an approximation technique for pricing finite‐maturity timer options under Heston‐like stochastic volatility models. By approximating the distributions of the accumulated variance and the random variance budget exceeding time, we obtain analytic expressions for timer option...</section>

We develop an asymptotic expansion technique for pricing timer options in stochastic volatility models when the effect of volatility of variance is small. Based on the pricing PDE, closed-form approximation formulas have been obtained. The approximation has an easy-to-understand...