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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 example in [3] and [1]. --
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 added to corresponding Black-Scholes prices to produce smile-consistent values. Besides being intuitive and easy to implement, this procedure has a clear financial interpretation, which further supports its use in practice.
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 example in [3] and [1].
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 added to corresponding Black-Scholes prices to produce smile-consistent values. Besides being intuitive and easy to implement, this procedure has a clear financial interpretation, which further supports its use in practice. --
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 American style options, there is no closed-form solution. The price is computed by binomial trees, finite difference methods or an analytic approximation. Taking derivatives of these prices leads to instable numerics or misleading results, specially for Greeks of higher order. We compare the computation of the Greeks in various pricing methods and conclude with the recommendation to use Leisen-Reimer trees.
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 procedure and the volatility quoting mechanisms are FX specific and differ significantly from other markets. We give a detailed overview of these quoting mechanisms and introduce the resulting smile construction problem. Furthermore, we provide a new formula which can be used for an efficient and robust FX smile construction.
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 functions depending on at least two spot values for different points in time. The derived characteristic functions are used as building blocks to set up (semi-) analytical pricing formulas for exotic options with payoffs depending on finitely many spot values such as fader options and discretely monitored barrier options. We compare our result with different numerical methods and examine accuracy and computational times.
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 der vorliegenden Arbeit untersuchen wir vier repräsentative Anlagekonzepte bei Riester- Rentenverträgen unter Auslassung der Gebührenstrukturen: DWS Riesterrente Premium, AXA Twin- Star Rente Invest, Nürnberger Fondsgebundene Zulagen-Rente Doppel-Invest und Allianz Riesterrente mit Fonds und Garantie. Wir simulieren über einen Anlagehorizont von 35 Jahren die Verteilungen des bei Renteneintritt zur Verfügung stehenden Kapitals. Den Verlauf eines internationalen Aktienportfolios simulieren wir mit einer Displaced-Double-Exponential Sprungdiffusion...
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