The mainstream model of option pricing is based on an exogenously given process of price movements. The implication of this assumption is that price movements are not affected by actions of market participants. However, if we assume that there are indeed impacts on the price movements it no...

We explain the valuation and correlation hedging of Foreign Exchange Basket Options in a multi-dimensional Black-Scholes model that allows including the smile. The technique presented is a fast analytic approximation to an accurate solution of the valuation problem.

We focus on closed-form option pricing in Heston's stochastic volatility model, in which closed-form formulas exist only for few option types. Most of these closed-form solutions are constructed from characteristic functions. We follow this approach and derive multivariate characteristic...

This paper aims to unify exotic option closed formulas by generalizing a large class of existing formulas and by setting a framework that allows for further generalizations. The formula presented covers options from the plain vanilla to most, if not all, mountain range exotic options and is...

We present a closed pricing formula for European options under the Black-Scholes model and formulas for its partial derivatives. The formulas are developed making use of Taylor series expansions and by expressing the spatial derivatives as expectations under special measures, as in Carr,...

In Foreign Exchange Markets vanilla and barrier options are traded frequently. The market standard is a cutoff time of 10:00 a.m. in New York for the strike of vanillas and a knock-out event based on a continuously observed barrier in the inter bank market. However, many clients, particularly...

We derive a semi-analytical formula for pricing forward-start options in the Barndorff-Nielsen- Shephard model. In terms of computational time, this formula is equivalent to one-dimensional integration.

When pricing the convexity effect in irregular interest rate derivatives such as, e.g., Libor-in-arrears or CMS, one often ignores the volatility smile, which is quite pronounced in the interest rate options market. This note solves the problem of convexity by replicating the irregular interest...

No front-office software can survive without providing derivatives of option prices with respect to underlying market or model parameters, the so called Greeks. If a closed form solution for an option exists, Greeks can be computed analytically and they are numerically stable. However, for...