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.
Reflections on choosing development tools for applied financial engineering. We present a brut force code comparison on creating and plotting the extended Nelson-Siegel yield curve using both Quantlab and Matlab. This example is simplistic – but choosing platform for financial engineering is not. On which level do you want your financial analytics projects to start on?
This paper studies the practical pricing of Bermudan swap options, attempting to find both lower and upper bounds for the option price. It uses the BGM model with three driving factors and Monte Carlo simulation for determining the evolution of forward interest rates. A discretisation proposed by Glasserman is used, as an alternative to direct discretisation of the forward rates. Two suboptimal exercise strategies using exercise boundaries proposed by Andersen are evaluated for finding the lower bound for the option price. A perfect foresight strategy is evaluated for finding an upper bound. This paper also studies the systematic errors in the forward rate evolution and discusses simple measures for reducing their impact on the option pricing.
The main objective of this work is to find a pricing model for weather derivatives with payouts depending on temperature. We use historical data to first suggest a stochastic process that describes the evolution of the temperature. Since temperature is a non-tradable quantity, we obtain unique prices of contracts in an incomplete market, using the market price of risk. Numerical examples of prices of some contracts are presented, using an approximation formula as well as Monte Carlo simulations.
Paper done in collaboration with Prof. Boualem Djehiche, at the Royal Institute of Technology in Stockholm, and presented at the Nordic Symposium on Contingent Claims, May 2001, at Stockholm School of Economics. Published in Applied Mathematical Finance, volume 9, Number 1/March 01, 2002.
In this thesis we survey GARCH modelling with special focus on the fitting of GARCH models to financial return series. The robustness of the estimation of the parameters in the model is examined with three different distributional assumptions for the innovations; Gaussian distribution, Student-t distribution and GED (Generalised Error Distribution). Both the Student-t distribution and the GED have fat tails. The maximum-likelihood approach is used for the parameter estimation. Using backtesting, the related residuals under the three different distributional assumptions are examined.
This master’s thesis explores pricing of callables. These are special bonds that allow the issuer at a number of certain times to buy back the bond. Three different models for the short-term interest rate; Hull and Whites model, Black, Derman and Toys model as well as Black and Karsinsikis model have been adjusted for pricing callables. The models have been implemented in Quantlab, a program for quantitative analysis, and pricing is done according to real-time data.