The aim of the paper is to develop pricing formulas for European type Asian options written on the exchange rate in a two currency economy. The exchange rate as well as the foreign and domestic zero coupon bond prices are assumed to follow geometric Brownian motions. As a special case of a discrete Asian option we analyse the delayed payment currency option and develop closed form pricing and h...

In this paper, two analytic solutions for the valuation of European-style Parisian and Par. asian options under the Black-Scholes framework are, respectively, presented. A key feature of our solution procedure is the reduction of a three-dimensional problem to a two-dimensional problem through a coordinate transform designed to combine the two time derivatives into one. Compared with some previ...

 Commodity markets: overview, description and structure  Commodity spot price models, their performance and calibration  Forward curve modeling for commodities  Modeling commodity price volatility  Correlations/dependencies in commodity portfolios  Modeling risk of a commodity portfolio  Typical commodity derivatives (quanto, Asian, spread and basket options, volumetric and swing options...

We prove a symmetry relationship between floating-strike and fixed-strike Asian options for assets driven by general Lévy processes using a change of numéraire and the characteristic triplet of the dual process. We apply the same technique to prove a similar relationship between floating-strike and fixed-strike lookback options.

We give a complete and self-contained proof of the existence of a strong solution to the free boundary and optimal stopping problems for pricing American path-dependent options. The framework is sufficiently general to include geometric Asian options with nonconstant volatility and recent path-dependent volatility models.