Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Risk measurement, management and option pricing via a new log-normal sum approximation method
Download
index.pdf
Date
2012
Author
Zeytun, Serkan
Metadata
Show full item record
Item Usage Stats
93
views
37
downloads
Cite This
In this thesis we mainly focused on the usage of the Conditional Value-at-Risk (CVaR) in risk management and on the pricing of the arithmetic average basket and Asian options in the Black-Scholes framework via a new log-normal sum approximation method. Firstly, we worked on the linearization procedure of the CVaR proposed by Rockafellar and Uryasev. We constructed an optimization problem with the objective of maximizing the expected return under a CVaR constraint. Due to possible intermediate payments we assumed, we had to deal with a re-investment problem which turned the originally one-period problem into a multiperiod one. For solving this multi-period problem, we used the linearization procedure of CVaR and developed an iterative scheme based on linear optimization. Our numerical results obtained from the solution of this problem uncovered some surprising weaknesses of the use of Value-at-Risk (VaR) and CVaR as a risk measure. In the next step, we extended the problem by including the liabilities and the quantile hedging to obtain a reasonable problem construction for managing the liquidity risk. In this problem construction the objective of the investor was assumed to be the maximization of the probability of liquid assets minus liabilities bigger than a threshold level, which is a type of quantile hedging. Since the quantile hedging is not a perfect hedge, a non-zero probability of having a liability value higher than the asset value exists. To control the amount of the probable deficient amount we used a CVaR constraint. In the Black-Scholes framework, the solution of this problem necessitates to deal with the sum of the log-normal distributions. It is known that sum of the log-normal distributions has no closed-form representation. We introduced a new, simple and highly efficient method to approximate the sum of the log-normal distributions using shifted log-normal distributions. The method is based on a limiting approximation of the arithmetic mean by the geometric mean. Using our new approximation method we reduced the quantile hedging problem to a simpler optimization problem. Our new log-normal sum approximation method could also be used to price some options in the Black-Scholes model. With the help of our approximation method we derived closed-form approximation formulas for the prices of the basket and Asian options based on the arithmetic averages. Using our approximation methodology combined with the new analytical pricing formulas for the arithmetic average options, we obtained a very efficient performance for Monte Carlo pricing in a control variate setting. Our numerical results show that our control variate method outperforms the well-known methods from the literature in some cases.
Subject Keywords
Risk assessment.
,
Risk management.
,
Risk-return relationships.
,
Investment analysis.
,
Value investing.
,
Hedge funds.
,
Pricing.
URI
http://etd.lib.metu.edu.tr/upload/12615148/index.pdf
https://hdl.handle.net/11511/22115
Collections
Graduate School of Applied Mathematics, Thesis
Suggestions
OpenMETU
Core
Stability advances in robust portfolio optimization under parallelepiped uncertainty
Kara, Guray; Ozmen, Ayse; Weber, Gerhard Wilhelm (2019-03-01)
In financial markets with high uncertainties, the trade-off between maximizing expected return and minimizing the risk is one of the main challenges in modeling and decision making. Since investors mostly shape their invested amounts towards certain assets and their risk aversion level according to their returns, scientists and practitioners have done studies on that subject since the beginning of the stock markets' establishment. In this study, we model a Robust Optimization problem based on data. We found...
Optimal portfolio strategies under various risk measures
Meral, Alev; Uğur, Ömür; Department of Financial Mathematics (2013)
In this thesis, we search for optimal portfolio strategies in the presence of various risk measure that are common in financial applications. Particularly, we deal with the static optimization problem with respect to Value at Risk, Expected Loss and Expected Utility Loss measures. To do so, under the Black-Scholes model for the financial market, Martingale method is applied to give closed-form solutions for the optimal terminal wealths, then via representation problem the optimal portfolio strategies are ac...
Robust conditional value–at–risk under parallelpipe uncertainty: an application to portfolio optimization
Kara, Güray; Weber, Gerhard Wilhelm; Department of Financial Mathematics (2016)
In markets with high uncertainties, the trade–off between maximizing expected return and minimizing the risk is one of the main challenges in modeling and decision making. Since investors mostly shape their invested amounts towards certain assets and their risk version level according to their returns; scientists and practitioners has done studies on this subject since the beginning of the stock markets’ establishment. Developments and inventions in the mathematical optimization provide a wide range of solu...
Credit default swap valuation: an application via stochastic intensity models
Namuslu, Merve; Danışoğlu, Seza; Ayaydın Hacıömeroğlu, Hande; Department of Financial Mathematics (2016)
The objective of this thesis is to study the pricing of a single-name credit default swap (CDS) contract via the discounted cash flow method with reduced-form survival probability functions depending on stochastic intensity. The ability of the model in predicting the market-observed spreads is tested as well by using bond and CDS data from the US market. In credit risk modeling, the CIR (Cox-Ingersoll-Ross) model is used. The main reason for using a reduced-form model in pricing the CDS contracts is the adv...
Margin call risk management with furures and options
Alıravcı, Murat; Duran, Sever; Tanrısever, Fehmi; Department of Industrial Engineering (2013)
This study examines dynamic hedge policy of a company in a multi-period framework. The company begins to operate a project for a customer and it also has a subcontractor which completes an important part of the project by using an economic commodity. The customer will pay a fixed price to the company at the end of the project. Meanwhile, the company needs to pay the debt to the subcontractor and the amount of the debt depends on the spot price of the commodity at that time. The company is allowed to hedge f...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
S. Zeytun, “Risk measurement, management and option pricing via a new log-normal sum approximation method,” Ph.D. - Doctoral Program, Middle East Technical University, 2012.