78 research outputs found
Option pricing in affine generalized Merton models
In this article we consider affine generalizations of the Merton jump
diffusion model [Merton, J. Fin. Econ., 1976] and the respective pricing of
European options. On the one hand, the Brownian motion part in the Merton model
may be generalized to a log-Heston model, and on the other hand, the jump part
may be generalized to an affine process with possibly state dependent jumps.
While the characteristic function of the log-Heston component is known in
closed form, the characteristic function of the second component may be unknown
explicitly. For the latter component we propose an approximation procedure
based on the method introduced in [Belomestny et al., J. Func. Anal., 2009]. We
conclude with some numerical examples
Nonparametric Bayesian volatility estimation for gamma-driven stochastic differential equations
Regression Methods in Pricing American and Bermudan Options Using Consumption Processes
Numerical algorithms for the efficient pricing of multidimensional discrete-time American and Bermudan options are constructed using regression methods and a new approach for computing upper bounds of the options' price. Using the sample space with payoffs at optimal stopping times, we propose sequential estimates for continuation values, values of the consumption process, and stopping times on the sample paths. The approach allows the constructing of both lower and upper bounds for the price by Monte Carlo simulations. The algorithms are tested by pricing Bermudan max-calls and swaptions in the Libor market model.D.B. gratefully acknowledges the partial support of DFG through SFB 649. This work was completed while G.M. was a visitor at the Weierstrass-Institute für Angewandte Analysis und Stochastik (WIAS), Berlin, thanks to financial support from this institute and DFG (grant No. 436 RUS 17/137/05 and 436 RUS 17/24/07), which are gratefully acknowledged
Holomorphic transforms with application to affine processes
In a rather general setting of It\^o-L\'evy processes we study a class of
transforms (Fourier for example) of the state variable of a process which are
holomorphic in some disc around time zero in the complex plane. We show that
such transforms are related to a system of analytic vectors for the generator
of the process, and we state conditions which allow for holomorphic extension
of these transforms into a strip which contains the positive real axis. Based
on these extensions we develop a functional series expansion of these
transforms in terms of the constituents of the generator. As application, we
show that for multidimensional affine It\^o-L\'evy processes with state
dependent jump part the Fourier transform is holomorphic in a time strip under
some stationarity conditions, and give log-affine series representations for
the transform.Comment: 30 page
Sensitivities for Bermudan Options by Regression Methods
In this article, we propose several pathwise and finite difference-based methods for calculating sensitivities of Bermudan options using regression methods and Monte Carlo simulation. These methods rely on conditional probabilistic representations that allow, in combination with a regression approach, for efficient simultaneous computation of sensitivities at many initial positions. Assuming that the price of a Bermudan option can be evaluated sufficiently accurate, we develop a method for constructing deltas based on least squares. We finally propose a testing procedure for assessing the performance of the developed methods and give a numerical illustration. © 2009 Springer-Verlag.Partially supported by the Deutsche Forschungsgemeinschaft through SFB 649 “Economic Risk” and DFG Research Center Matheon “Mathematics for Key Technologies” in Berlin
Traffic optimization in transport networks based on local routing
Congestion in transport networks is a topic of theoretical interest and
practical importance. In this paper we study the flow of vehicles in urban
street networks. In particular, we use a cellular automata model to simulate
the motion of vehicles along streets, coupled with a congestion-aware routing
at street crossings. Such routing makes use of the knowledge of agents about
traffic in nearby roads and allows the vehicles to dynamically update the
routes towards their destinations. By implementing the model in real urban
street patterns of various cities, we show that it is possible to achieve a
global traffic optimization based on local agent decisions.Comment: 4 pages, 5 figure
Optimal Dual Martingales, Their Analysis and Application to New Algorithms for Bermudan Products
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