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Randor
Topic Author
Posts: 48
Joined: October 8th, 2005, 8:33 am

### Ftd 1st to default: assumption of all names having same risk

I read in hull that in the standard model for ftd, all names are assumed to have the same credit risk.

I am valuing a ftd where basket is just 2 names. So i am thinking that assumption is going to be very bad if the 2 names have very different cds...?

bearish
Posts: 2737
Joined: February 3rd, 2011, 2:19 pm

### Re: Ftd 1st to default: assumption of all names having same risk

Very bad, indeed. It should be trivial to keep track of each name’s risk neutral default probability. The hard part is to account for the dependency (loosely speaking, default correlation). Even in the case of a 100+ name portfolio, you really want to keep track of individual CDS curves.

Randor
Topic Author
Posts: 48
Joined: October 8th, 2005, 8:33 am

### Re: Ftd 1st to default: assumption of all names having same risk

so what is a more appropriate model?  i guess there may be a way to do a simple adjustment to do my case of FTD out of 2 names.
i think there should be a way to do a copula to get the joint distrubtion for survival time, given the 2 marginal distributions and their correlation, what is the algorithm to do this?

and in the case of 100+ name portfolio (ie the standard case), why does the market use such a simple model - surely there must be some better practical alternative?

bearish
Posts: 2737
Joined: February 3rd, 2011, 2:19 pm

### Re: Ftd 1st to default: assumption of all names having same risk

There are hundreds of papers and many books written on this topic, mostly between 1999 and 2008. Then, for some reason, the activity level dwindled. To get a flavor of the sorts of models people used you can look up the 2003 Risk article by Andersen, Sidenius and Basu (it’s freely available).

Randor
Topic Author
Posts: 48
Joined: October 8th, 2005, 8:33 am

### Re: Ftd 1st to default: assumption of all names having same risk

so for my case, can you show me a simple way to do it?
i have implemented the hull method, so i just want to adjust that

bearish
Posts: 2737
Joined: February 3rd, 2011, 2:19 pm

### Re: Ftd 1st to default: assumption of all names having same risk

Not knowing what particular Hull model you have implemented, it's a bit tricky. But if you are looking to use a standard Gaussian default time copula, you have three random variables: the common factor and an idiosyncratic factor for each name. Denoting the default time of name $i$ with $\tau_i$, then $\tau_i = F^{-1}_i (\Phi^{-1} (\sqrt{\rho} X_0 + \sqrt{1-\rho^2} X_i))$. Here $F_i$ denotes the risk neutral survival probability function of time for name $i$, and the $X_i$ are iid standard normal random variables. $\rho$ is the pairwise correlation between the two names, given by exposure to a common factor. The easiest way to do the valuation is to perform a Monte Carlo simulation, but one reasonable alternative is a quadrature scheme. The point is that, given the two default times, the cash flows on your contract are deterministic and can be valued by simply adding up discounted cash flows.

gbelford
Posts: 13
Joined: July 14th, 2002, 3:00 am

### Re: Ftd 1st to default: assumption of all names having same risk

fyi. found Geoff Chaplin's Credit derivatives book & the excel spreadsheets that came with it helpful to understand various copula approaches for FTDs

Randor
Topic Author
Posts: 48
Joined: October 8th, 2005, 8:33 am

### Re: Ftd 1st to default: assumption of all names having same risk

many thanks bearish and gbelford, i will look into this!