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...

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 BlackScholes 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, together...

This paper analyzes the evolution of the structured products market focusing on the tools available for private investors, on which they rely for the selection process. The selection process is extremely difficult because there is a myriad of products, because of the dynamic nature of the market...

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,...

This paper analyzes the evolution of the structured products market focusing on the tools available for private investors, on which they rely for the selection process. The selection process is extremely difficult because there is a myriad of products, because of the dynamic nature of the market...

We investigate the characteristic functions of multi-factor Cheyette Models and the application to the valuation of interest rate derivatives. The model dynamic can be classiffied as an affine-diffusion process implying an exponential structure of the characteristic function. The characteristic...

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 Zeiten stark schwankender Finanzmarkte liegt der Fokus von Investoren insbesondere auf dem mit einer Anlage verbundenen Risiko. Gerade in diesen Marktphasen suchen Investoren nach Moglichkeiten, ihr bestehendes Portfolio weiter zu diversifizieren. Volatilitätsinvestments bieten durch ihre...

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...