Monte Carlo methods in finance

Monte Carlo methods are used in corporate finance and mathematical finance to value and analyze (complex) instruments, portfolios and investments by simulating the various sources of uncertainty affecting their value, and then determining the distribution of their value over the range of resultant outcomes. This is usually done by help of stochastic asset models. The advantage of Monte Carlo methods over other techniques increases as the dimensions (sources of uncertainty) of the problem increase. Monte Carlo methods were first introduced to finance in 1964 by David B. Hertz through his Harvard Business Review article, discussing their application in Corporate Finance. In 1977, Phelim Boyle pioneered the use of simulation in derivative valuation in his seminal Journal of Financial Economics paper. This article discusses typical financial problems in which Monte Carlo methods are used. It also touches on the use of so-called "quasi-random" methods such as the use of Sobol sequences.

Effect of intelligent antennas on radio system planning and on mitigation

Juliane Iten Chaves Simoes

Smart antennas have been recently applied to improve the capacity and the performance of second generation wireless mobile communication systems. In general, smart antennas reduce the effects of multipath fading and improve the signal-to-noise-plus-interference ratio (SNIR). Additional advantages such as channel capacity increase in urban areas, coverage extension in urban areas and spectrum efficiency in general can be obtained with the aid of smart antennas at the base station. Drawbacks are the cost, and both hardware and software complexity. Smart antennas promise a clear advantage in multi-service traffic scenario in comparison with non-adaptive antenna techniques. It is generally accepted that the adaptive antennas technique will be a key enable for the success of the European third generation mobile communication system known as Universal Mobile Telecommunication System (UMTS). The first part of this thesis presents two types of smart antenna systems: switched beam antennas and adaptive arrays. It introduces statistical models for them and investigates the performance measures of cellular radio systems with and without smart antennas deployed at base stations. Employing Monte-Carlo methodology, a tool has been developed to analyze the interference between two different systems that share the same geographical area and have neighboring frequency channels. The statistical smart antennas model has been used to verify the mitigation of the interference compared with others antennas used at the base station. These simulations have been done for TDMA, FDMA and CDMA systems. Wireless communication operating at different frequencies on the non-ionizing radiation (NIR) region of the electromagnetic spectrum has greatly increased in the last few decades, with important benefits for the population. These include mobile communication, such as cellular telephone systems. However, the radiated electromagnetic field levels increased substantially in areas where people may stay during long periods each day. This may result in long-term exposure to the population. International guidelines and standards were developed aiming at protecting the population, and limiting the maximum radiation produced. The methods used by regulation authorities to evaluate the field levels at places of sensitive use yield very conservative results. They need thus to be refined prior to the introduction of adaptive antennas. In the second part of the thesis, a 3D ray tracing tool is developed to predict the propagation for real scenarios using UMTS systems. This tool takes into account 3D radiation diagrams and multipath propagation. It was used in real scenarios to compare the real field levels with the levels obtained by the approximate methods defined by the regulation standards. Finally, this tool was used to predict the field levels in a scenario containing smart antennas. Scenario not foreseen in the method described in the standards.

EPFL2008

The Scrambled Net Filter

Thomas Gsponer

The standard Kalman filter is a powerful and widely used tool to perform prediction, filtering and smoothing in the fields of linear Gaussian state-space models. In its standard setting it has a simple recursive form which implies high computational efficiency. As the latter is essentially a least squares procedure optimality properties can be derived easily. These characteristics of the standard Kalman filter depend strongly on distributional and linearity assumptions of the model. If we consider nonlinear non-Gaussian state-space models all these properties and characteristics are no longer valid. Consequently there are different approaches on the robustification of the Kalman filter. One is based on the the ideas of minimax problems and influence curves. Others use numerical integration and Monte Carlo methods. Herein we propose a new filter by implementing a method of numerical integration, called scrambled net quadrature, which consists of a mixture of Monte Carlo methods and quasi-Monte Carlo methods, providing an integration error of order of magnitude

N^{-3/2}\log(N)^{(r-1)/2}

in probability, where

r

denotes dimension. We show that the point-wise bias of the posterior density estimate is of order of magnitude

N^{-3}\log(N)^{r-1}

but grows linearly with time.

2002