Calibration of the Volatility Surface by Erik Nilsson
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.
[PDF
report in English]
Consistent estimators of the smoothing parameter in the Hodrick-Prescott filter by Boualem Djehiche et al
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.
[PDF
report in English]
Calibration of Bermudan Swaptions using limited data by Mattias Jansson
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.
[PDF
report in English]
A Monte Carlo solver for financial problems by Stefan Thoren
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.
[PDF
report in English]
A biased comparison between Quantlab and Matlab
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?
[Download - Quantlab vs Matlab]
On Modelling and Pricing Weather Derivatives
Paper on modelling weather derivatives, done in collaboration with 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, see
[external link]
Pricing Bermudan Swaptions by Henrik Alpsten
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.
[PDF report in English]
GARCH modeling by Lars Karlsson
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.
[PDF report in English]
Valuation of Callable Bonds by Erik Sjöberg
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. [PDF report in Swedish]
A note on maximum-smoothness approximation
Research by Anders Forsgren, Department of Mathematics, Royal Institute of Technology, March 1998.
Abstract: Maximum smoothness approximation of forward interest rate is considered.
The smoothness is measured as the integral of the square of the secondderivative
of the forward interest rate. Wellknown results on natural splines are utilized
in order to characterize the optimal solution.
[Recommended visit to Anders Forsgren's site]
[Download pdf]
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