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.
This thesis proposes a way to design software for Monte Carlo simulation that facilitates the simulation of many different kinds of stochastic processes. Monte Carlo simulation is a powerful tool that has applications in many financial contexts. One important application is the pricing of complex financial derivatives. A software for Monte Carlo simulation that is adaptable to price different derivatives could potentially save money, time and effort. The thesis provides an introduction to Monte Carlo simulation in the financial markets. An analysis of the problem considered in the thesis project is given and a design of a Monte Carlo simulation engine is given. Finally, examples illustrating the use of the software are given.