This Master thesis investigates the use of Artificial Neural Networks (ANNs)for calculating present values, Value-at-Risk and Expected Shortfall of options, both European call options and more complex rainbow options. The performance of the ANN is evaluated by comparing it to a second-order Taylor polynomial using pre-calculated sensitivities to certain risk-factors. A multilayer perceptron approach is chosen based on previous literature and applied to both types of options. The data is generated from a financial risk-management software for both call options and rainbow options along with the related Taylor approximations. The study shows that while the ANN outperforms the Taylor approximation in calculating present values and risk measures for certain movements in the underlying risk-factors, the general conclusion is that an ANN trained and evaluated in accordance with the method in this study does not outperform a Taylor approximation even if it is theoretically possible for the ANN to do so. The important conclusion of the study is that the ANN seems to be able to learn to calculate present values that otherwise require Monte Carlo simulation. Thus, the study is a proof of concept that requires further development for implementation.
A short presentation on the basic building blocks of creating forward curves after the credit crisis. We look at curve blending, extrapolation and interpolation issues, as well as modeling tools. An example of multi-tenor EUR-swap curve is presented. This is a non-technical presentation. For more information please contact Magnus Nyström.
This thesis consists of two parts, one concerning implied volatility and one concerning local volatility. The SABR model and SVI model are investigated to model implied volatility. The performance of the two models were tested on the Eurcap market in March 2008. Two ways of extracting local volatility are reviewed by a test performed on data from European options based on the S&P 500 index. The first method is a way of solving regularized Dupire’s equation and the other one is based on finding the most likely path.
The so-called Hodrick-Prescott filter was first introduced in actuarial science to estimate trends from claims data and now is widely used in economics and finance to estimate and predict e.g. business cycles and trends in financial data series. This filter depends on a smoothing parameter. The authors propose new consistent estimators of this smoothing parameter and construct corresponding non-asymptotic confidence intervals with a precise confidence level. Link to Prof. Boualem Djehiche at the Royal Institute of Technology.
Master Thesis researching the possibilty to create a general monte carlo simulation framework using low discrepancy sequences. Standard Monte Carlo requires a large number of trials and is therefore slow. To speed up the process there exist different variance reduction techniques and also Quasi Monte Carlo simulation, where deterministic numbers (low discrepancy sequences) is used instead of random. The thesis investigated the variance reduction techniques; control variate technique, antithetic variate technique, and the low discrepancy sequences; Sobol, Faure and Halton.
The focus of this thesis is on the risk neutral valuation of Bermudan swaptions and its application to pricing situations where observed market data used for calibration is limited. By exploring the properties of the solution to the optimal stopping problem that specifies the price process of these instruments, a general valuation method suited for practical computations is suggested. The valuation method is based on restricting the evolution of the short rate process to that of a recombining binomial tree and is able to produce fast price estimates of Bermudan swaptions based on limited input data when specifying the dynamics of the short rate process to the Ho-Lee model.