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Counterparty Credit Risk and Interest Rate Derivatives Pricing
Černý, Jakub
Counterparty Credit Risk and Interest Rate Derivatives Pricing Jakub Černý Abstract: This thesis deals with the pricing of OTC financial derivatives including the coun- terparty credit risk (CCR). It focuses on the interest rate derivatives for which the interest rate must be modeled as random. This is where they differ from the pricing of other derivatives. The credit valuation adjustment (CVA) concept is used to calculate CCR which is in line with current banking regulation Basel III. When we assume the independence of the underlying asset and the credit quality of the counterparty, we obtain an analytical expression of CVA. However, if the independence is violated, the CVA calculation becomes quite complicated. Specifically, the CVA of the inter- est rate swap (IRS) is calculated mainly using the simulation approach which is time and computationally consuming. Therefore, we bring two new methods for IRS CVA calculation where the CVA is expressed in a semi-analytical form. These methods use copula functions, particularly the Gaussian copula and the upper Fréchet bound, and we compare them numerically with a complex simulation study. Furthermore, we pro- pose a method of calibration of the correlation coefficient and we determine the impact of changes in the intensity of default on the final CVA with four...
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Counterparty Credit Risk and Interest Rate Derivatives Pricing
Černý, Jakub ; Witzany, Jiří (advisor) ; Hurt, Jan (referee) ; Málek, Jiří (referee)
Counterparty Credit Risk and Interest Rate Derivatives Pricing Jakub Černý Abstract: This thesis deals with the pricing of OTC financial derivatives including the coun- terparty credit risk (CCR). It focuses on the interest rate derivatives for which the interest rate must be modeled as random. This is where they differ from the pricing of other derivatives. The credit valuation adjustment (CVA) concept is used to calculate CCR which is in line with current banking regulation Basel III. When we assume the independence of the underlying asset and the credit quality of the counterparty, we obtain an analytical expression of CVA. However, if the independence is violated, the CVA calculation becomes quite complicated. Specifically, the CVA of the inter- est rate swap (IRS) is calculated mainly using the simulation approach which is time and computationally consuming. Therefore, we bring two new methods for IRS CVA calculation where the CVA is expressed in a semi-analytical form. These methods use copula functions, particularly the Gaussian copula and the upper Fréchet bound, and we compare them numerically with a complex simulation study. Furthermore, we pro- pose a method of calibration of the correlation coefficient and we determine the impact of changes in the intensity of default on the final CVA with four...
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Counterparty Credit Risk and Interest Rate Derivatives Pricing
Černý, Jakub
Counterparty Credit Risk and Interest Rate Derivatives Pricing Jakub Černý Abstract: This thesis deals with the pricing of OTC financial derivatives including the coun- terparty credit risk (CCR). It focuses on the interest rate derivatives for which the interest rate must be modeled as random. This is where they differ from the pricing of other derivatives. The credit valuation adjustment (CVA) concept is used to calculate CCR which is in line with current banking regulation Basel III. When we assume the independence of the underlying asset and the credit quality of the counterparty, we obtain an analytical expression of CVA. However, if the independence is violated, the CVA calculation becomes quite complicated. Specifically, the CVA of the inter- est rate swap (IRS) is calculated mainly using the simulation approach which is time and computationally consuming. Therefore, we bring two new methods for IRS CVA calculation where the CVA is expressed in a semi-analytical form. These methods use copula functions, particularly the Gaussian copula and the upper Fréchet bound, and we compare them numerically with a complex simulation study. Furthermore, we pro- pose a method of calibration of the correlation coefficient and we determine the impact of changes in the intensity of default on the final CVA with four...
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The Switch from LIBOR to OIS Discounting
Kotálová, Magdalena ; Stádník, Bohumil (advisor) ; Staniek, Dušan (referee)
The main contribution of the diploma thesis is to give a comprehensive picture of the switch from LIBOR to OIS discounting. Prior to the global financial crisis, LIBOR (London Interbank Offered Rate) represented an approximation of the risk-free rate in the valuation of interest rate derivatives. The collapse of Lehman Brothers in 2008 resulted in sharp widening of the LIBOR-OIS spread, an indicator of the interbank market stress. Many derivative practitioners have become concerned about the choice of an appropriate risk-free rate. Traditional valuation approaches using LIBOR discounting have been reviewed. Meanwhile, the OIS (Overnight Indexed Swap) rate has become a better proxy for the risk-free rate, at least for collateralized or centrally cleared transactions. Firstly, the research aims to discover the divergences between LIBOR rates, popular pre-crisis proxies for the riskfree rate, and OIS rates, their post-crisis alternatives. Secondly, it covers the interbank lending market, and analyzes individual LIBOR-OIS spreads for the USD, EUR, GBP and CZK currency. Thirdly, it explores the transition to OIS discounting in connection with an influence on a wide spectrum of interest rate derivatives. Therefore, any potential effects are demonstrated on numerical valuation examples of interest rate swaps in the USD, EUR, and GBP currency. Finally, the diploma thesis addresses a topic of collateral management and clarifies different approaches using LIBOR or OIS rates for collateralized or non-collateralized transactions.
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