132 research outputs found
Esscher transform and the duality principle for multidimensional semimartingales
The duality principle in option pricing aims at simplifying valuation
problems that depend on several variables by associating them to the
corresponding dual option pricing problem. Here, we analyze the duality
principle for options that depend on several assets. The asset price processes
are driven by general semimartingales, and the dual measures are constructed
via an Esscher transformation. As an application, we can relate swap and quanto
options to standard call and put options. Explicit calculations for jump models
are also provided.Comment: Published in at http://dx.doi.org/10.1214/09-AAP600 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Analysis of Fourier transform valuation formulas and applications
The aim of this article is to provide a systematic analysis of the conditions
such that Fourier transform valuation formulas are valid in a general
framework; i.e. when the option has an arbitrary payoff function and depends on
the path of the asset price process. An interplay between the conditions on the
payoff function and the process arises naturally. We also extend these results
to the multi-dimensional case, and discuss the calculation of Greeks by Fourier
transform methods. As an application, we price options on the minimum of two
assets in L\'evy and stochastic volatility models.Comment: 26 pages, 3 figures, to appear in Appl. Math. Financ
Risk Management Based on Stochastic Volatility
Risk management approaches that do not incorporate randomly changing volatility
tend to under- or overestimate the risk depending on current market conditions. We show how some popular stochastic volatility models in combination with the hyperbolic model introduced in Eberlein and Keller (1995) can be applied quite easily for risk management purposes. Moreover, we compare their relative performance on the basis of German stock index data
State modelling of the land mobilepropagation channel for dual-satellite systems
The quality of service of mobile satellite reception can be improved by using multi-satellite diversity (angle diversity). The recently finalised MiLADY project targeted therefore on the evaluation and modelling of the multi-satellite propagation channel for land mobile users with focus on broadcasting applications. The narrowband model combines the parameters from two measurement campaigns: In the U.S. the power levels of the Satellite Digital Audio Radio Services were recorded with a high sample rate to analyse fast and slow fading effects in great detail. In a complementary campaign signals of Global Navigation Satellite Systems (GNSS) were analysed to obtain information about the slow fading correlation for almost any satellite constellation. The new channel model can be used to generate time series for various satellite constellations in different environments. This article focuses on realistic state sequence modelling for angle diversity, confining on two satellites. For this purpose, different state modelling methods providing a joint generation of the states ‘good good’, ‘good bad’, ‘bad good’ and ‘bad bad’ are compared. Measurements and re-simulated data are analysed for various elevation combinations and azimuth separations in terms of the state probabilities, state duration statistics, and correlation coefficients. The finally proposed state model is based on semi-Markov chains assuming a log-normal state duration distribution
State modelling of the land mobile propagation channel with multiple satellites
We evaluate a new approach for multisatellite state modelling: the Master-Slave approach. By this concept slave satellites are modelled according to an existing master, whereas the correlation between multiple slaves is omitted. Master-Slave is therefore a generic name for a state modelling concept, for which different realisations are possible. As a possible realisation we present the Conditional Assembling Method. For modelling of only two satellites (one master and one slave), the Conditional Assembling Method enables an accurate resimulation of the correlation coefficient between the satellites and the probabilities of single and combined states. Based on this condition, the performance of Master-Slave for three, four, and five satellites is evaluated in terms of state probability modelling. Therefore, the correlation coefficients and the all bad-state probabilities with Master-Slave are compared with the measurements for different elevation angles and azimuth angle separations of the multisatellite system. Master-Slave has a high modelling error in case of small azimuth separation between the slave satellites (except that one slave has a small azimuth separation to the master). Furthermore, a master satellite with a high elevation provides a lower probability error compared to a master with low elevation
State Modelling of the Land Mobile Propagation Channel with Multiple Satellites
We evaluate a new approach for multisatellite state modelling: the Master-Slave approach. By this concept slave satellites are modelled according to an existing master, whereas the correlation between multiple slaves is omitted. Master-Slave is therefore a generic name for a state modelling concept, for which different realisations are possible. As a possible realisation we present the Conditional Assembling Method. For modelling of only two satellites (one master and one slave), the Conditional Assembling Method enables an accurate resimulation of the correlation coefficient between the satellites and the probabilities of single and combined states. Based on this condition, the performance of Master-Slave for three, four, and five satellites is evaluated in terms of state probability modelling. Therefore, the correlation coefficients and the all bad-state probabilities with Master-Slave are compared with the measurements for different elevation angles and azimuth angle separations of the multisatellite system. Master-Slave has a high modelling error in case of small azimuth separation between the slave satellites (except that one slave has a small azimuth separation to the master). Furthermore, a master satellite with a high elevation provides a lower probability error compared to a master with low elevation
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