An exchange option, also called “Margrabe option”, gives the right, but not the obligation to exchange an asset for another asset. In a recent paper in the Encyclopedia of Quantitative Finance (2010), Professor Rolf Poulsen writes that “[t]he Margrabe formula is still valid with stochastic...

Lions and Musiela (2007) give sufficient conditions to verify when a stochastic exponential of a continuous local martingale is a martingale or a uniformly integrable martingale. Blei and Engelbert (2009) and Mijatovi c and Urusov (2012c) give necessary and sufficient conditions in the case of...

In stochastic volatility models based on time-homogeneous diff usions, we provide a simple necessary and suffi cient condition for the discretely sampled fair strike of a variance swap to converge to the continuously sampled fair strike. It extends Theorem 3.8 of Jarrow, Kchia, Larsson and...

This paper presents a new approach to perform a nearly unbiased simulation using inversion of the characteristic function. As an application we are able to give unbiased estimates of the price of forward starting options in the Heston model and of continuously monitored Parisian options in the...

The purpose of this article is to value some life insurance contracts in a stochastic interest rate environment taking into account the default risk of the underlying insurance company. The participating life insurance contracts considered here can be expressed as portfolios of barrier options...

There is considerable interest in finding numerical methods to price Asian options. Tse and Mok (2009) have proposed a new very simple closed-form expression for the price of a fixed-strike Asian option. Unfortunately their formula is not correct. This note shows that it is incorrect and...

Reformulating the results of del Baño Rollin, Ferreiro-Castilla, and Utzet (2010), we are able to give necessary and sufficient conditions for the moments of the stock price to exist and extend Theorem 2.1 of Forde and Jacquier (2011). Precisely Forde and Jacquier (2011) provide necessary...

In this paper, we discuss a newly introduced exotic derivative called the “Timer Option”. Instead of being exercised at a fixed maturity date as a vanilla option, it has a random date of exercise linked to the accumulated variance of the underlying stock. Unlike common...

The paper develops an efficient Monte Carlo method to price discretely monitored Parisian options based on a control variate approach. The paper also modifies the Parisian option design by assuming the option is exercised when the barrier condition is met rather than at maturity. We obtain...