## Abstract

This master’s thesis focuses on the pricing and analysis of options on Credit Default Swap indices, CDS indices. As the name suggests, the underlying is not one credit as well known, but a portfolio contained of many credits. This product gives the inves - tor the option to enter a CDS index at a future date at a prespecified strike. The in - terest and liquidity for this credit derivative has grown increasingly since the Finan cial Crisis 2007 -2009. The liquidity of the underlying CDS index has made index op - tions an easier product for dealers to hedge and diversify their credit risk. This thesis’ pricing framework is based on the article Options(on(Credit(Default(Index( Swaps(written by Jäckel & Liu [2005]. The model is developed to be able to price payer swaptions and receiver swaptions as the values of these swaptions obey the put -call parity. In the theoretical part we derive a pricing model from the known CDS pricing model. With knowledge of the mechanisms of a CDS contract and its two legs, we are able to understand the setup in a CDS index contract. With the basis of calculation of the CDS contract we derive the pricing of the CDS index using the intensity models where the survival probability is described by the default intensity. Beside the knowledge of the CDS contract, we also use assumptions, definitions and derivations known from mathematical theorems. In the applicational part we choose to price a payer swaption that matures in three months. The underlying asset is an on -the -run CDS index. To estimate the volatility of the index spreads, we use observable daily spreads. We estimate this parameter by using Maximum Likelihood Estimation. We maximize the log likelihood function with a fixed ! -parameter. We have calculated the unconditional default probability that calculate the distribution of the number of defaults in the reference pool at the options expiry date. Further than this we have calculated the total risky premium payment, which the option holder is required to pay if he chooses to exercise the option. These calculations and the calculation of the expected call prices made it possible for us to price the payer swaption. We have priced the payer swaption for different strikes and different values of the correlation between defaults in the ref - erence pool to examine the effect on the prices. We find that the prices decrease when the strike increase and that the prices are not effected by a change in the cor - relation parameter when the payer swaption is in -the -money. This is not the case when the payer swaption is out -of -the money as we see that the prices increase when the correlation is high. Since the options on CDS indices are traded over -the -counter, we are not able to compare our calculated prices with market prices. With our financial background we cannot reject our calculated prices as we see that the prices follow known tendencies and tendencies obtained in the article by Jäckel & Liu. At last we discuss the most important assumptions in the pricing model and we con - clude according to the problem statement.

Educations | MSc in Mathematics , (Graduate Programme) Final Thesis |
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Language | Danish |

Publication date | 2015 |

Number of pages | 177 |