Credit spreads options

Credit spread options are options whose payout is linked to the credit spread of the reference credit. This product can be used to manage the credit risk on corporate bond and corporate bond option positions. It isolates credit spread risk, which is an important factor in the underling... 

Various credit derivatives may be priced using this model for example, credit default swaps, total return swaps, and credit spread options. The pricing of these products requires the generation of the appropriate credit dependent cash flows at each node on a lattice of possible outcomes. The fair value may be determined by discounting the probability-weighted cash flows. The probability of the outcomes would be determined by reference to the risk neutral transition matrix. 

First generation pricing models for credit spread options may use models as described in the section on spread models. The key market parameters in a spread option model include the forward credit spread and the volatility of the credit spread. 

A key issue with credit spread options is ensuring that the pricing models used will calibrate to the market prices of credit risky reference assets. The recovery of forward prices of the reference asset would be a constraint to the evolution of the credit spread. More complex spread models may allow for the correlation between the level of the credit... 

As shown in previous sections, the credit spread on a corporate bond takes into account its expected default loss. Structural approaches are based on the option pricing theory of Black Scholes and the value of debt depends on the value of the underlying asset. The determination of yield spread is based on the firm value in which the default risk is found as an option to the shareholders. Other models proposed by Black and Cox (1976), Longstaff and Schwartz (1995) and others try to overcome the limitation of the Merton s model, like the default event at maturity only and the inclusion of a default threshold. This class of models is also known as first passage models . 

Craisider a hypothetical situation. Assume that an option-free bond paying a semi-annual coupon 5.5% on par value, with a maturity of 5 years and discount rate of 8.04% (EUR 5-year swap rate of 1.04% plus credit spread of 700 basis points). Therefore, the valuation of a conventional bond is performed as follows (Figure 9.4). 

The reason to use implied volatility is that market anticipates mean reversion and uses the implied volatility to gauge the volatility of individual assets relative to the market. Implied volatility represents a market option about the underlying asset and therefore is forward looking. However, the estimate of implied volatility is conditioned by the choice of other inputs in particular, the credit spread applied in the option-free bond and the conversion premium of the tmderlying asset (Example 9.2). 

The risk-free rate affects both elements, option-free bond and embedded option. Conversely, the credit spread is applied to the risk-free rate in order to find the price of the option-free bond. If the credit spread is also included into the option pricing model, the option value rises. For instance, consider the scenario in which the risk-free rate is 1.04% and the option value is 0.46. If the risk-free rate is 7.04%, then the option value increases to 0.66. Figure 9.16 shows the effect of a different interest rate level. 

Following the risk neutral theory, the credit spread is not included into option valuation because it is independent from the default risk of the underlying asset. The inclusion of credit spread overvalues the option. 

Interest rates and credit spread A greater level of interest rates decreases the value of the option-free bond or bond floor. Because the credit spread is applied only into the bond floor valuation, a greater credit quality decreases the credit spread and interest rate, and increases the value of the option-free bond. Conversely, higher is the interest rates and credit spread, lower is the value of an option-free bond. 

Consider the following example. We assume to have two hypothetical bonds, a treasury bond and a callable bond. Both bonds have the same maturity of 5 years and pay semiannual coupons, respectively, of 2.4% and 5.5%. We perform a valuation in which we assume a credit spread of 300 basis points and an OAS spread of 400 basis points above the yield curve. Table 11.1 illustrates the prices of a treasury bond, conventional bond and callable bond. In particular, considering only the credit spread we find the price of a conventional bond or option-free bond. Its price is 106.81. To pricing a callable bond, we add the OAS spread over the risk-free yield curve. The price of this last bond is 99.02. We can now see that the OAS spread underlines the embedded call option of the callable bond. It is equal to 106.81-99.02, or 7.79. In Section 11.2.3, we will explain the pricing of a callable bond with the OAS methodology adopting a binomial tree. 

The default risk component of a swap spread will be smaller than for a comparable bond credit spread. The reasons are straightforward. First, since only net interest payments are exchanged rather than both principal and coupon interest payments, the total cash flow at risk is lower. Second, the probability of default depends jointly on the probability of the counterparty defaulting and whether or not the swap has a positive value. See John C. Hull, Introduction to Futures and Options Markets, Third Edition (Upper Saddle River, NJ Prentice Hall, 1998). 

Credit spread derivatives are forwards and options that reflect views on the credit spread movements of underlying credit assets. Therefore,... 

The buyer has the right to buy the spread and benefits from the spread decreasing in value. The payoff has the form max (strike - spread, 0). This option pays out if the spread tightens below the strike level, a tightening spread would result in an increasing bond price. Therefore the credit spread call option provides a payout should the underlying bond position increase in value. 

In this case let us assume that the premium for a credit spread put option is 30 bp. The credit spread put option will be sold by the investor to the counterparty (for example a bank) with a strike level of 370 bp. The option will provide the following payout ... 

The payoffs may be multiplied by a leverage or duration factor to relate the spread changes to price changes of the underlying instrument. However, in our examples, we have ignored this factor. Exhibit 21.10 illustrates how an investor may use a credit spread put option as part of... 

The pricing of a European spread option requires the distribution of the credit spread at the maturity (T) of the option. The choice of model affects the probability assigned to each outcome. The mean reversion factor reflects the historic economic features overtime of credit spreads, to revert to the average spreads after larger than expected movements away from the average spread. 

Bond investors can use credit options to hedge against rating downgrades and similar events that would depress the value of their holdings. To ensure that any loss resulting from such events will be offset by a profit on their options, they purchase contracts whose payoff profiles refiect their bonds credit quality. The options also enable banks and other institutions to take positions on credit spread movements without taking ownership of the related loans or bonds. The writer of credit options earns fee income. 

Credit options allow market participants to express their views on credit alone, without reference to other factors, such as interest rates, with no cost beyond the premium. For example, investors who believe that the credit spread associated with an individual entity or a sector (such as all AA-rated sterling corporates) will widen over the next six months can buy six-month call options on the relevant spread. If the spread widens beyond the strike during the six months, the options will be in the money, and the investors will gain. If not, the investors loss will be limited to the premium paid. 

The models analyze spreads as wholes, rather than splitting them into default risk and recovery risk. Das (1999), for example, notes that equation (10.1) can be used to model credit spreads. Credit options can thus be analyzed in the same way as other types of options, modeling the credit spread rather than, say, the interest rate. 

The price of a corporate bond is a yield spread for conventional bonds or on an OAS basis for callable or other option-embedded bonds. If an OAS calculation is undertaken in a consistent framework, price changes that result in credit events will result in changes in the OAS. Therefore, we can speak in terms of a sensitivity measure for the change in value of a bond or portfolio in terms of changes to a... 

A Z-spread can be calculated relative to any benchmark spot rate curve in the same manner. The question arises what does the Z-spread mean when the benchmark is not the euro benchmark spot rate curve (i.e., default-free spot rate curve) This is especially true in Europe where swaps curves are commonly used as a benchmark for pricing. When the government spot rate curve is the benchmark, we indicated that the Z-spread for nongovernment issues captured credit risk, liquidity risk, and any option risks. When the benchmark is the spot rate curve for the issuer, for example, the Z-spread reflects the spread attributable to the issue s liquidity risk and any option risks. Accordingly, when a Z-spread is cited, it must be cited relative to some benchmark spot rate curve. This is essential because it indicates the credit and sector risks that are being considered when the Z-spread is calculated. Vendors of analytical systems such Bloomberg commonly allow the user to select a benchmark. 

On the asset side, the flexibility of CDS assets instead of bonds means that a wider range of credits can be included. Regulatory, geographic, liquidity, and other limitations on particular assets are often made irrelev-ent by the use of CDSs referencing desired credits. More choices are available. For this reason, a greater spread can usually be achieved for a comparable amount of desired risk through name substitution. In a 100-name portfolio, for example, if 10 names with similar risks could be substituted with an incremental spread of 20 bps per name, this option would be worth 2 bps to the average spread of the portfolio. 

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