Essays in Quantitative Finance
(2016) Abstract
 This thesis contributes to the quantitative finance literature and consists of four research papers.
Paper 1. This paper constructs a hybrid commodity interest rate market model with a stochastic local volatility function that allows the model to simultaneously fit the implied volatility of commodity and interest rate options. Because liquid market prices are only available for options on commodity futures (not forwards), a convexity correction formula is derived to account for the difference between forward and futures prices. A procedure for efficiently calibrating the model to interest rate and commodity volatility smiles is constructed. Finally, the model is fitted to an exogenously given crosscorrelation structure between... (More)  This thesis contributes to the quantitative finance literature and consists of four research papers.
Paper 1. This paper constructs a hybrid commodity interest rate market model with a stochastic local volatility function that allows the model to simultaneously fit the implied volatility of commodity and interest rate options. Because liquid market prices are only available for options on commodity futures (not forwards), a convexity correction formula is derived to account for the difference between forward and futures prices. A procedure for efficiently calibrating the model to interest rate and commodity volatility smiles is constructed. Finally, the model is fitted to an exogenously given crosscorrelation structure between forward interest rates and commodity prices. When calibrating to options on forwards (rather than futures), the fitting of crosscorrelation preserves the (separate) calibration in the two markets (interest rate and commodity options), whereas in the case of futures, a (rapidly converging) iterative fitting procedure is presented. The crosscorrelation fitting is reduced to finding an optimal rotation of volatility vectors, which is shown to be an appropriately modified version of the “orthonormal Procrustes” problem. The calibration approach is demonstrated on market data for oil futures.
Paper 2. This paper describes an efficient American Monte Carlo approach for pricing Bermudan swaptions in the LIBOR market model using the Stochastic Grid Bundling Method (SGBM) which is a regressionbased Monte Carlo method in which the continuation value is projected onto a space in which the distribution is known. We demonstrate an algorithm to obtain accurate and tight lower–upper bound values without the need for the nested Monte Carlo simulations that are generally required for regressionbased methods.
Paper 3. The credit valuation adjustment (CVA) for overthecounter derivatives are computed using the portfolio’s exposure over its lifetime. Usually, future exposure is approximated by Monte Carlo simulations. For derivatives that lack an analytical approximation for their marktomarket (MtM) value, such as Bermudan swaptions, the standard practice is to use the regression functions from the least squares Monte Carlo method to approximate their simulated MtMs. However, such approximations have significant bias and noise, resulting in an inaccurate CVA charge. This paper extend the SGBM to efficiently compute expected exposure, potential future exposure, and CVA for Bermudan swaptions. A novel contribution of the paper is that it demonstrates how different measures, such as spot and terminal measures, can simultaneously be employed in the SGBM framework to significantly reduce the variance and bias.
Paper 4. This paper presents an algorithm for simulation of options on Lévy driven assets. The simulation is performed on the inverse transition matrix of a discretised partial differential equation. We demonstrate how one can obtain accurate option prices and deltas on the variance gamma (VG) and CGMY model through finite elementbased Monte Carlo simulations. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/4b2fc76c4e1e408aa7158d147dcb37d9
 author
 Karlsson, Patrik ^{LU}
 supervisor

 Birger Nilsson ^{LU}
 opponent

 Professor Miltersen, Kristian, Copenhagen Business School
 organization
 publishing date
 20161219
 type
 Thesis
 publication status
 published
 subject
 keywords
 credit valuation adjustment (CVA), derivative pricing, interest rate derivatives, Monte Carlo simulation
 pages
 150 pages
 defense location
 Faculty of Engineering, MA3
 defense date
 20170223 14:15
 ISBN
 9789177530602
 9789177530619
 language
 English
 LU publication?
 yes
 id
 4b2fc76c4e1e408aa7158d147dcb37d9
 date added to LUP
 20161219 15:58:56
 date last changed
 20170206 13:32:16
@phdthesis{4b2fc76c4e1e408aa7158d147dcb37d9, abstract = {This thesis contributes to the quantitative finance literature and consists of four research papers.<br/><br/>Paper 1. This paper constructs a hybrid commodity interest rate market model with a stochastic local volatility function that allows the model to simultaneously fit the implied volatility of commodity and interest rate options. Because liquid market prices are only available for options on commodity futures (not forwards), a convexity correction formula is derived to account for the difference between forward and futures prices. A procedure for efficiently calibrating the model to interest rate and commodity volatility smiles is constructed. Finally, the model is fitted to an exogenously given crosscorrelation structure between forward interest rates and commodity prices. When calibrating to options on forwards (rather than futures), the fitting of crosscorrelation preserves the (separate) calibration in the two markets (interest rate and commodity options), whereas in the case of futures, a (rapidly converging) iterative fitting procedure is presented. The crosscorrelation fitting is reduced to finding an optimal rotation of volatility vectors, which is shown to be an appropriately modified version of the “orthonormal Procrustes” problem. The calibration approach is demonstrated on market data for oil futures.<br/><br/>Paper 2. This paper describes an efficient American Monte Carlo approach for pricing Bermudan swaptions in the LIBOR market model using the Stochastic Grid Bundling Method (SGBM) which is a regressionbased Monte Carlo method in which the continuation value is projected onto a space in which the distribution is known. We demonstrate an algorithm to obtain accurate and tight lower–upper bound values without the need for the nested Monte Carlo simulations that are generally required for regressionbased methods.<br/><br/>Paper 3. The credit valuation adjustment (CVA) for overthecounter derivatives are computed using the portfolio’s exposure over its lifetime. Usually, future exposure is approximated by Monte Carlo simulations. For derivatives that lack an analytical approximation for their marktomarket (MtM) value, such as Bermudan swaptions, the standard practice is to use the regression functions from the least squares Monte Carlo method to approximate their simulated MtMs. However, such approximations have significant bias and noise, resulting in an inaccurate CVA charge. This paper extend the SGBM to efficiently compute expected exposure, potential future exposure, and CVA for Bermudan swaptions. A novel contribution of the paper is that it demonstrates how different measures, such as spot and terminal measures, can simultaneously be employed in the SGBM framework to significantly reduce the variance and bias.<br/><br/>Paper 4. This paper presents an algorithm for simulation of options on Lévy driven assets. The simulation is performed on the inverse transition matrix of a discretised partial differential equation. We demonstrate how one can obtain accurate option prices and deltas on the variance gamma (VG) and CGMY model through finite elementbased Monte Carlo simulations.}, author = {Karlsson, Patrik}, isbn = {9789177530602}, keyword = {credit valuation adjustment (CVA),derivative pricing,interest rate derivatives,Monte Carlo simulation}, language = {eng}, month = {12}, pages = {150}, school = {Lund University}, title = {Essays in Quantitative Finance}, year = {2016}, }