# Credit default option

It can be seen as an extension of a CDS on a single entity to a portfolio of entities. The optional second and third entries are, respectively, the lower and upper bounds of the implied volatility to be searched. CDS spread of entity 2. The no-armageddon pricing measure and the role of correlation after the subprime crisis".

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The theta of a CD index swaption is the change in the fair value of the swaption per one day increase of the valuation date. The BPV basis point value on a risk free curve is the change in the fair value of the CD index swaption when the risk-free discount factor curve is shifted up one basis point. To shift up a discount factor curve simply add one basis point to every point of the corresponding spot rate curve of the discount factor curve.

CD index swaption at the recovery rate. Calculates the fair value and risk statistics of a standardized credit default index swap option. Given an option price, a displacement parameter and a correlation calculates the implied volatility of a credit default index swaption. It is the contract dates table of the underlying credit default index swap.

It can have 2 to 7 entries. The first four entries hold in sequence the terminating date, effective date, odd first coupon date and next-to-terminating coupon date for premium payments. The last three entries hold switch values in sequence the effective date adjustment, terminating date adjustment and date generation method for premium payments.

Only the terminating date is required. The third and fourth entries default to 0 and the last three entries default to 1. Accumulated loss of the pool. If it has a value of 0, it will be calculated from the number of defaulted entities.

Otherwise this number is used as the accumulated loss of the reference pool and the number of defaulted entities is ignored for this purpose. This parameter can be user specified or calculated. If it is positive, it will be recognized as a user-specified notional. If it is 0, it will be calculated as the total notional of the initial reference pool.

A negative value is not allowed. Fixed premium coupon rate of the underlying credit default index swap. If it is a single-entity default curve, all entities in the reference pool are assumed to have the same default curve.

If it is a multi-entity default curve, the number of columns of CDS spreads or default probability values must equal the number of the outstanding survived reference entities. For descriptions of an m-entity default curve see the following: If it is a default probability curve or a time-based CDS spread curve, the first column has time in years or dates. If it is a date-based CDS spread curve, the first two columns have the effective and terminating dates of the CDS spreads. These columns must be ordered in the same way as in the reference data table.

Times and dates the terminating dates for a CDS spread curve must be increasing. CDS spreads must be nonnegative. For a date-based default probability curve, the probabilities in the first row must be 0 and the first date must be the valuation date if there is one. Excel users may pass term strings to represent time intervals. A default curve parameter table. The first entry has the default probability curve interpolation method.

The third entry stores the time accrual day counting method if the default curve is time-based. If the default curve is not time based, this entry will be ignored.

The fourth to sixth entries store the effective and terminating date adjustment methods and the date generation method of a CDS curve, respectively. Their default values are 1.

It can be a 2- or 3-entry table. The first two entries are the volatility and the correlation parameters, respectively. The third entry is optional.

It is the displacement parameter of the displacement diffusion model, i. Its default value is 1, which indicates that the CDS spread follows a lognormal distribution. If input as a single rate, there are three format choices: A 2-column flat-rate discount factor curve is constructed internally using the rate, basis, and accrual method. A calculation parameter table.

It can have 1 or 2 entries. The second entry is optional. Note that negative values or very large positive values of the second entry can cause the function to fail. There are four accuracy levels, corresponding to the convergence tolerance levels 0. The optional second entry is defaulted to 1 when missing. Correlation and displacement parameter table.

An option price table. It can have one to three entries. The first entry is the price of the option. The optional second and third entries are, respectively, the lower and upper bounds of the implied volatility to be searched. They are not required, but their inclusion can help reduce the calculation time of the function. Note also that for any set of parameters, there is a limited range of possible and reasonable prices.

Inputting a price outside of this range will lead to an error being returned by the function. The optional second and third entries are any estimates of the lower and upper bounds of the implied volatility that is to be searched, respectively. Including a proper bound or both bounds in the input list can significantly reduce the calculation time, but a solution found may not necessarily stay within the given bounds. Inputting a price outside of this range will lead to an error or an inaccurate result being returned by the function.

Value of defaulted entities. This is the present value of the historical loss of the reference pool. Rho of recovery rate. In finance , a default option , credit default swaption or credit default option is an option to buy protection payer option or sell protection receiver option as a credit default swap on a specific reference credit with a specific maturity. The option is usually European , exercisable only at one date in the future at a specific strike price defined as a coupon on the credit default swap.

Credit default options on single credits are extinguished upon default without any cashflows, other than the upfront premium paid by the buyer of the option. Therefore, buying a payer option is not a good protection against an actual default, only against a rise in the credit spread. This may explain why such options are very illiquid.

They may also feature quite high implied volatilities, as shown by Damiano Brigo However options on credit indices such as iTraxx and CDX include any defaulted entities in the intrinsic value of the option when exercised.

This is expressed at times by stating that the options offer "front-end protection". Proper inclusion of front end protection complicates index options valuation, see for example Claus M. Pedersen , or Brigo and Morini From Wikipedia, the free encyclopedia. Lehman Brothers Quantitative Credit Research.

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