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 document widespread violations of stochastic dominance in the one-month S&P 500 index options market over the period 1986-2002. These violations imply that a trader can improve her expected utility by engaging in a zero-net-cost trade. We allow the market to be incomplete and also imperfect...

In Foreign Exchange Markets Compound options (options on options) are traded frequently. Instalment options generalize the concept of Compound options as they allow the holder to prolong a Vanilla Call or Put option by paying instalments of a discrete payment plan. We derive a closed-form...

Security prices contain valuable information that can be used to make a wide variety of economic decisions. To extract this information, a model is required that relates market prices to the desired information, and that ideally can be implemented using timely and low-cost methods. The authors...

Turbo-Certificates are one of the most popular structured equity products for private investors in Germany. They can be regarded as special forms of barrier options. The relation between the barrier level and the strike price is especially important for the design of these products. By using a...

Nonparametric methods for estimating the implied volatility surface or the implied volatility smile are very popular, since they do not impose a specific functional form on the estimate. Traditionally, these methods are two-step estimators. The first step requires to extract implied volatility...

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...