none

Yes / Following the global financial crisis, the measurement of counterparty credit risk has become an essential part of the Basel III accord with credit value adjustment being one of the most prominent components of this concept. In this study, we extend the Merton structural credit risk model for counterparty credit risk calculation in the context of calculating the credit value adjustment mainly by estimating the probability of default. We improve the Merton model in a variance-convoluted-gamma environment to include default dependence between counterparties through a linear factor decomposition framework. This allows one to tackle dependence through a systematic common component. Our set-up allows for easier, faster and more accurate fitting for the credit spread. Results confirm that use of the variance-gamma-convolution clearly solves the vanishing credit spread problem for short time-to-maturity or low leverage cases compared to a Brownian motion environment and its modifications. / Ahmet Sensoy gratefully acknowledges support from Turkish Academy of Sciences under its Outstanding Young Scientist Award Programme (TUBA-GEBIP). Frank J. Fabozzi acknowledges the financial support from EDHEC Business School.

This thesis focuses on the parameter stability of additive normal tempered stable processes when calibrating a volatility surface. The studied processes arise as a generalization of Lévy normal tempered stable processes, and their main characteristic are their time-dependent parameters. The theoretical background of the subject is presented, where its construction is discussed taking as a starting point the definition of Lévy processes. The implementation of an option valuation model using Fourier techniques and the calibration process of the model are described. The thesis analyzes the parameter stability of the model when it calibrates the volatility surface of a market index (EURO STOXX 50) during three time spans. The time spans consist of the periods from Dec 2016 to Dec 2017 (after the Brexit and the US presidential elections), from Nov 2019 to Nov 2020 (during the pandemic caused by COVID-19) and a more recent time period, April 2023. The findings contribute to the understanding of the model itself and the behavior of the parameters under particular economic conditions.

本研究透過聯合系統與獨特風險綜合評估違約的強度，假設市場上經濟變數或資訊影響系統之違約強度，然若直接考慮所有經濟變數到模型中將可能會有共線性或維度過高之疑慮，因此透過狀態空間模型來設定狀態變數以及經濟變數之關係並將萃取三大狀態變數分別用以描述市場實質活動面、通貨膨脹以及信用環境。另外，將透過結構式模型來計算獨特性風險大小，當個別潛在的變數低於一定數值將導致個別的違約事件發生。而因布朗運動可能無法描述或校準市場上違約之鋒態以及偏態，將進一步考慮Variance Gamma過程用以更準確描述真實違約狀況。最後透過結合以上兩個風險綜合評估下，考慮一個聯合違約模型來評價信用違約交換之信用價差。 / Systematic and idiosyncratic risks are supposed to jointly trigger the default events. This paper identifies three fundamental risks to capture the systematic movement: real activity, inflation, and credit environment. Since most macroeconomic variables fluctuate together, the state-space model is imposed to extract the three variables from macroeconomic data series. In the idiosyncratic part, the structural model is applied. That is, idiosyncratic default is triggered by the crossing of a barrier. For improvement of the underlying lognormal distribution, we assume the process for the potential variable of the firm follows a Variance Gamma process, sufficient dimensions of which can fit the skewed and leptokurtic distributions. Under the specific setting of combinations of the two risks (the so-called joint default model), we price credit default swaps.

違約事件受到系統性風險與獨特性風險的綜合影響。本研究建構一狀態相依公司信用模型，該模型能反映出系統環境對市場造成的影響與個別公司獨特因子帶來的個別衝擊。 本模型透過從總體環境中萃取出的狀態變數來捕捉系統性變化，另外透過Variance Gamma過程來描繪個別公司的獨特因子帶來的影響。Variance Gamma過程可藉由調整分配的鋒態及偏態來調整布朗運動無法反映出的分配，以更貼近真實的市場訊息。 與縮減試模型相較之下，本模型無需參考信評機構的信用評等資訊，僅依賴市場上公開且透明的資訊，並且與結構式模型相同的是其富有經濟意涵。我們可以透過本模型來同時生成公司流動性危機發生機率與預期流動性危機造成的損失，進而利用本模型評價出個別公司信用違約交換的價格。 關鍵字：信用違約交換；系統風險；獨特性風險；狀態空間模型；Variance Gamma 過程 / Systematic and idiosyncratic risks are thought to affect the default events. This study develops a state-dependent corporate credit model that reflects both systematic movement and idiosyncratic shocks. To capture the systematic movement, the model extracts state factors from macroeconomics data. For the idiosyncratic part, the model applied Variance Gamma Process in depicting the potential variable of the firm by altering the distribution’s skewness and kurtosis. The model contains abundant economic significance as structural-form model does. Comparing to the reduced-form model, it does not rely on the information provided by rating agency but use information that is transparent and public. One can generate a firm’s probabilities of liquidity crisis and expected liquidity shortfalls endogenously and concurrently by employing the model. Credit derivative such as Single-name CDS can be priced under the model.

In this thesis, the structural model in credit risk and the credit derivatives is studied under both Black-Scholes setting and Variance Gamma (VG) setting. Using a Variance Gamma process, the distribution of the firm value process becomes asymmetric and leptokurtic. Also, the jump structure of VG processes allows random default times of the reference entities. Among structural models, the most emphasis is made on the Black-Cox model by building a relation between the survival probabilities of the Black-Cox model and the value of a binary down and out barrier option. The survival probabilities under VG setting are calculated via a Partial Integro Differential Equation (PIDE). Some applications of binary down and out barrier options, default probabilities and Credit Default Swap par spreads are also illustrated in this study.

The submitted work deals with option pricing. Mathematical approach is immediately followed by an economic interpretation. The main problem is to model the underlying uncertainities driving the stock price. Using two well-known valuation models, binomial model and Black-Scholes model, we explain basic principles, especially risk neutral pricing. Due to the empirical biases new models have been developped, based on pure jump process. Variance gamma process and its special symmetric case are presented.