1 Introduction
1.1 Background
For the past twenty years, the credit derivatives market has experienced meteoric growth with a variety of new products being introduced to the market. These new products was essential to the emergence of innovative hedging and investment strategies, but their leverage functions can also significantly increase existing risks, raising the difficulty for market participants and rating agencies to capture their risk characteristics and to price these products. In recent years, the complexity of the new products had caused worldwide financial crisis, not to mention the 2008 subprime crisis. Therefore, studies of the properties of credit derivatives are now attracting a great deal of interests for both market practitioners and academics.
Fast growing new credit derivatives include standard credit default swaps (CDSs) of asset-backed securities and loan-only credit default swaps (LCDSs) of secured bank loans. These credit derivatives initially played roles in insurance, but later turn into credit instruments for investors or speculators, spreading the risk from large financial institutions to individuals. An LCDS is similar to a standard CDS, but with some differences. The main difference between a standard CDS and an LCDS is that the reference obligation for an LCDS is a syndicated secured bank loan, as opposed to a unsecured bond. On 8 June 2006, the International Swaps and Derivatives Association (ISDA) published an LCDS template for the US market, a watershed event expected to boost LCDS demand.
Subsequently, the index product of the LCDS, Markit LCDX North American index was launched in May 2007. This increases transaction liquidity due to the convenience of standardized terms and execution. However, by the end of July 2007, concerns of the global housing bubble started to drag down asset prices and liquidity diminished. Besides, the early termination feature for LCDS also made the product challenging to value. According to statistics from DTCC, the gross notional for Markit LCDX has decreased from 250,000 million to 150,000 between October 2008 and February 2010. As a result, a new bullet version of the U.S. LCDS product, so called Bullet LCDS was launched on April 5, 2010 by publishing revised transaction documentation and announcing market practice changes to the LCDS market. The key change of new Bullet LCDS was the migration to a ―bullet maturity‖ product through the removal of the early termination feature. By doing so, the International Swaps and Derivatives Association (ISDA) harmonized the contracts and conventions of the LCDS with the standard CDS for the purpose to enhance liquidity of LCDS market.
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Despite the change of the LCDS contracts, still a great proportion is traded on the LCDS with early termination, known as the Legacy LCDS. In fact, market practitioners today still use the CDS pricing model to price loan CDSs without considering the cancellation nature of the loans, which causes inaccuracy in the spread prices for loan credit derivatives. Therefore, pricing difficulties of the early termination remain unsolved, and still awaits for further study on the cancellation topic.
In pricing loan credit derivatives, the main idea is to determine the default probability and the cancellation probability. The two primary types of credit risk models are the structural-form models and reduced-form (or intensity-based) models.
Structural-form models are based on the Merton model, in which company equity can be regarded as European call options. Reduced-form models are not determined by the value of the firm, but by the first jump of an exogenous jump process. The parameters (intensities) governing the default hazard rate or the loan cancellation rate can be inferred from market data. Under the reduced-form framework, we can incorporate correlations between default time and cancellation time by allowing stochastic process of the intensities are correlated.
In this paper, we develop the pricing formulas for Legacy LCDS (with cancellation feature) and also extend to its index product the LCDX tranche swap, which is introduced in the latter part of this paper. Then, an sensitivity analysis is presented to point out the importance of the role for the correlation between default and cancellation. Furthermore, a comparison of pricing and hedging between Legacy LCDS and Bullet LCDS as well as Legacy LCDX tranche swap and Bullet LCDX tranche swap is demonstrated. The pricing of the new Bullet LCDS and LCDX tranche swap can be done by simply taking out the cancellation features from the models.
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1.2 Research targets
From the paragraph above, we state that market today has developed the bullet LCDS to remove the cancellation feature from syndicated loan derivatives considering the liquidity of the products; however, still a great proportion is traded on the Legacy LCDS with early termination. Besides, market practitioners today still use the CDS pricing model to price loan CDSs without considering the cancellation nature of the loans, which causes inaccuracy in the spread prices for loan credit derivatives.
In this paper, we introduce two different models to handle the cancellation feature, which is presented in the LCDS and LCDX tranche contracts. First, for the LCDS, we followed a industry standard model and introduced the general intensity-based model. Closed-form solutions for this model can be obtained under Affine Jump Diffusion specifications through a set of Riccati equations. In this thesis, explicit formulas are derived under the CIR parameterization. Second, for the LCDX tranche swap, we introduce the one factor Gaussian copula framework which closely follow the Merton structural framework, where dynamic of both default and cancellation are determined by the underlying firm value model. Here, we extend the single factor Gaussian copula model with a new variable to include the cancellation risk for loan products.
As the first target of this thesis, we try to focus on the role of correlations ρ and υ, where correlation parameter ρ stands for the correlation between the underlying asset value and the macro factor M, while the correlation parameter υ stands for the correlation between default and cancellation. Thus, we conduct a sensitivity analysis for LCDS and the LCDX tranche swap in order to find out what happens when the two correlations comes to work. For the second target of the thesis, we look into the risk characteristics of the loan credit derivatives. Apart from examining the risk characteristics for the LCDS and LCDX tranche swap alone, we are also interested in the change in risk characteristics between Legacy LCDS and Bullet LCDS (with and without cancellation). Therefore, in our result we show a comparison of the cancellable and non-cancellable LCDSs including the risk measurements for expected loss and unexpected loss. Last, following the previous target, we go even further to consider the hedging issue for loan credit derivatives to give concluding remarks for market practitioners. We compute the Greeks and hedge positions for the LCDX tranche swap, and again compare the numerical results with the Bullet version (without cancellation) of the products.
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1.3 Organization
The rest of the thesis is organized as follows. In Chapter 2, we review previous works on the pricing and hedging issues of the LCDS and LCDX. Chapter 3 describes the structure of a LCDS product and its valuation techniques as well as the LCDX tranche swap. Following the introduction of the products, we elaborate on the settings of the intensity-based model proposed by Wei (2007). Next, we move on to a extended one factor Gaussian copula model for pricing LCDX tranche swap. Furthermore, in Chapter 4 we introduce the credit risk measurements and hedging technique for the loan credit derivatives. The pricing and hedging results on LCDS and LCDX tranche swap are presented in Chapter 5. We show the results from our sensitivity analysis in terms of different correlations ρ and υ. Moreover, we examine the risk characteristics and hedging costs for LCDS and LCDX tranche swap compared to their bullet version.
Finally, we conclude our findings and observations in the last chapter.
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