Bei der Altersvorsorge von Privatanlegern boomt in der derzeitigen Marktsituation die Vermarktung von Riesterverträgen. Verschiedene Anbieter versuchen, sich diesen Markt zu erschließen. Neben den Versicherungen haben auch Banken und Investmentgesellschaften Angebote auf den Markt gebracht. In...

The vanna-volga method, also called the traders' rule of thumb is an empirical procedure that can be used to infer an implied-volatility smile from three available quotes for a given maturity. It is based on the construction of locally replicating portfolios whose associated hedging costs are...

A quanto option can be any cash-settled option, whose payoff is converted into a third currency at maturity at a pre-specified rate, called the quanto factor. There can be quanto plain vanilla, quanto barriers, quanto forward starts, quanto corridors, etc. The valuation theory is covered for...

The Heston model stands out from the class of stochastic volatility (SV) models mainly for two reasons. Firstly, the process for the volatility is nonnegative and mean-reverting, which is what we observe in the markets. Secondly, there exists a fast and easily implemented semi-analytical...

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,...

The foreign exchange options market is one of the largest and most liquid OTC derivative markets in the world. Surprisingly, very little is known in the academic literature about the construction of the most important object in this market: The implied volatility smile. The smile construction...

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...

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 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...