Financial Research
Pricing Collateralization
To circumvent this difficulty, this article uses an indirect empirical approach. We define a swap premium spread as the premium difference between two swap contracts that have exactly the same terms and conditions but are traded with different CSA counterparties. We reasonably believe that if two contracts are identical except counterparties, the swap premium spread should reflect counterparty credit risk only, as all other risks/costs are identical.
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CVS
The earlier works on CVA are mainly focused on unilateral CVA that assumes that only one counterparty is defaultable and the other one is default-free. The unilateral treatment neglects the fact that both counterparties may default, i.e., counterparty risk can be bilateral. A trend that has become increasingly relevant and popular has been to consider the bilateral nature of counterparty credit risk. Although most institutions view bilateral considerations as important in order to agree on new transactions, Hull and White (2013) argue that bilateral CVA is more controversial than unilateral CVA as the possibility that a dealer might default is in theory a benefit to the dealer.
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Convertible Bond
Because of their hybrid nature, convertible bonds attract different type of investors. Especially, convertible arbitrage hedge funds play a dominant role in primary issues of convertible debt. In fact, it is believed that hedge funds purchase 70% to 80% of the convertible debt offered in primary markets. A prevailing belief in the market is that convertible arbitrage is mainly due to convertible underpricing (i.e., the model prices are on average higher than the observed trading prices) (see Ammann et al (2003), Calamos (2011), Choi et al (2009), Loncarski et al (2009), etc.). However, Agarwal et al (2007) and Batta et al (2007) argue that the excess returns from convertible arbitrage strategies are not mainly due to underpricing, but rather partly due to illiquid. Calamos (2011) believes that arbitrageurs in general take advantage of volatility. A higher volatility in the underlying equity translates into a higher value of the equity option and a lower conversion premium. Multiple views reveal the complexity of convertible arbitrage, involving taking positions in the convertible bond and the underlying asset that hedges certain risks but leaves managers exposed to other risks for which they reap a reward.
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Libor Market Model
We introduce a shifted forward measure that uses a variable substitution to shift the center of a forward rate distribution to zero. This ensures that the distribution is symmetric and can be represented by a relatively small number of discrete points. The shift transformation is the key to achieve high accuracy in relatively few discrete finite nodes. In addition, we present several fast and novel drift approximation approaches. Other concepts used in the model are probability distribution structure exploitation, numerical integration and the long jump technique
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Jump Diffusion for Convertible
Although both the structural jump-diffusion model and the reduced-form model contain jumps, these jumps have different meanings: A jump in the structural jump-diffusion model corresponds to a sudden change in the asset value that may or may not cause the firm to default, whereas a jump in the reduced-form model represents the default event itself.
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Examination
Financial derivatives can be categorized into three types. The first category is over-the-counter (OTC) derivatives, which are customized bilateral agreements. The second group is cleared derivatives, which are negotiated bilaterally but booked with a clearinghouse. Finally, the third type is exchange-traded/listed derivatives, which are executed over an exchange. The differences between the three types are described in detail on the International Swap Dealers Association
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Credit Risk Dependency
IRSs and CDSs are two of the largest segments of the OTC derivatives market, collectively accounting for around two-thirds of both the notional amount and market value of all outstanding derivatives. Given this framework, we are able to analyze the value of IRSs with bilateral credit risk and look at how swap rates are affected by correlated default risk. Our study shows that counterparty default correlations have a relatively small impact on swap rates. Furthermore, we find that the value of a fully collateralized IRS is equal to the risk-free value. This conclusion is consistent with the current market practice in which market participants commonly assume fully collateralized swaps are risk-free.
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IRC Calculation
The IRC encompasses all positions subject to a capital charge for specific interest rate risk according to the internal models with exception of securitization and nth-to-default credit derivatives. Equity is optional. For IRC-covered positions, the IRC captures default risk and credit migration risk only.
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Multi-Lateral Credit Risk
A CDS is normally used to transfer the credit risk of a reference entity between two counterparties. The contract reduces the credit risk of the reference entity but gives rise to another form of risk: counterparty risk. Since the dealers are highly concentrated within a small group, any of them may be too big to fail. The interconnected nature, with dealers being tied to each other through chains of OTC derivatives, results in increased contagion risk. Due to its concentration and interconnectedness, the CDS market seems to pose a systemic risk to financial market stability. In fact, the CDS is blamed for playing a pivotal role in the collapse of Lehman Brothers and the disintegration of AIG.
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Bilateral Default Risk
IRS is a typical bilateral contingent contract that can be either an asset or a liability to each party during the life of the contract. Unlike the unilateral defaultable claim valuation problems that have been studied extensively by many authors, the valuation of bilateral contingent claims is still lacking convincing mechanism. The problem is mainly caused by the asymmetric credit qualities and the asymmetric default settlement rules.
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Defaultable Swap
The first study on asymmetric defaultable IRS is conducted by Duffie and Huang (1996). They use a short rate interest rate model combined with a reduced-form default model and lead to numerical approximations by solving a recursive integral. Even the authors admit that it is a substantial complexity solution. Hubner (2001) extends the work carried out by Duffie and Huang (1996) and gets a closed-form solution by introducing a one-dimensional state variable X that can be thought of as a ratio of the market value of the firm’s assets. The author, however, does not show how to calibrate the state variable and not even provide a simple example. In general, these proposed models are not practical enough to use.
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CDS Risk
The standard CDS pricing model in the market assumes that there is no counterparty risk. Although this oversimplified model may be accepted in normal market conditions, its reliability in times of distress has recently been questioned. In fact, counterparty risk has become one of the most dangerous threats to the CDS market. For some time now it has been realized that, in order to value a CDS properly, counterparty effects have to be taken into account
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