Derivative Pricing with Credit Risk

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我现在论文是关于一种citibank发行的衍生品的定价，根据公式我已经算出来它的theoretical price，但是与导师谈过后，他建议我再算出derivative price with credit risk,并给我相对应公式：
W(0)=EXP(-xT)*V(0)
W(0):price with credit risk
V(0): price without credit risk
x为credit spread,接近credit default swap rate
我的问题是：
1. 按照我的理解，credit default swap是为了防止出现亏损，不能支付的情况才购买的，类似保险合同。那么在此是Citibank购买Credit Default Swap么，是从谁那儿购买的呢？
2. 此公式里的Credit Default Swap Rate是citibank的么？和credit spread的区别是什么呢？
问题有点多，因为这个真心不理解，望高人能清楚解释其中的关系

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关键词：credit risk Derivative Pricing Credit Pricin default without credit 衍生品 price

1. CDS spread has some relationship with credit spread, but they are not the same thing

2. What your advisor says, in my opinion is something like pricing derivative with counter-party default risk, not credit derivative. For example, Citi buys an option from other financial institution, at last, the option ends in the money so Citi want to exercise, but the counter-party may default (e.g. do not have enough stock to make the delivery). In this case, this options price should also consider the default risk, which of course will make it cheaper.

If the default risk is from the counter-party, the credit spread you should use is from the counter-party not Citi. If the conter-party has some bonds in the market, you can use its yield minus the yield of the T-bond, to get the spread. I think Hull's book has some discussion and questions on this. Probablely Chapter 23 or 24 of the 8ed.

Of course, Citi can hedge the defualt risk with CDS, but that is probably not a direct hedge.

best,

Thank u for your help again.
In this case, the citibank has issued the bonus certificate. I think, the price of the certificate without credit risk is the theoretical price, which i have got it with the pricing formula. And for the investors or buyers of the bonus certificate, the counterparty is citibank. So, what i neeed to put in the the formula for the price with credit risk is the credit spread of citibank,right?
p.s.: what is T-bond?

我去，不要告诉我刚才发的一堆话没有发出去！！whats wrong

好吧，再来一遍。。。。
首先，先谢谢你的再次帮助，真是热心的好同志啊。。。
我现在研究的是Citibank发行的一种衍生品，叫bonus certificate,它的理论定价我已经通过公式得到了，以我的理解，这就是上面公式里需要的price without credit risk。对于购买它的人来说，counterparty 是citibank,price with credit risk是需要在考虑Citibank的credit spread的基础下算出来的，我理解的对吗？
还有请问，你上面提到的T bond是什么捏？？不能在某个网页直接找到citibank的credit spread么？？
万分感谢

如果是考虑这个衍生品的违约调整价值的话，其实从强度模型出发就能得到它的价值等于无违约的价值乘上一个违约调整项，这个调整项取决于违约概率和违约损失率，一般来讲cds的报价利差能够作为这两项乘积的近似。
对于这个问题我感觉如果这个衍生品的违约概率可以近似看做citi的违约概率的话那么它的违约价值调整可以近似看做cds市场上关于citi的报价利差x，也就是直接W(0)=EXP(-xT)*V(0)。你也可以理解为投资者要买这个产品的话肯定也担心citi会违约，那么定价的时候要把citi本身违约的可能给调整下，而citi自身违约的概率以及损失率基本上可以用cds spread来代替。

seconded~

what the upper floor said is also a good way to deal with this.

Approximately, there is a relationship between default intensity and the CDS spread. lambda=spread/(1-recovery rate),if you assume zero recovery,then lambda=CDS spread which is suggested by the upper floor. After you get the default intensity you can calculate the survival probability which is the so-called risky discount factor exp(-lambda*T) so that you can get the derivative's price with default:
V_risky=exp(-lambda*T)*V_riskfree

best,

冰沁午后 发表于 2013-4-27 19:48
如果是考虑这个衍生品的违约调整价值的话，其实从强度模型出发就能得到它的价值等于无违约的价值乘上一个违 ...

谢谢回复哈，我之前也打了一堆话给另一位热心同学，但是好像网速不给力，被吞了。。。
看来我的理解差不多是正确的，根据教授的推荐，他说我可以在deutsche derivate verband(german derivative union)里找到相应的credit spread,可是我觉得数据很奇怪啊，怎么会那么高都115,75了？？
这是网址，可以选择用英语看http://www.derivateverband.de/ENG/Transparency/CreditSpreads
我觉得应该是百分数，也就是1,11575，我理解的对么
不好意思，问的问题都有弱爆了。。。。

sushuiasushui 发表于 2013-4-27 20:45
谢谢回复哈，我之前也打了一堆话给另一位热心同学，但是好像网速不给力，被吞了。。。
看来我的理解差不 ...

那个是基点，basis point, (pb) 100bp=1%

Bank of America

114.75

means 1.1475%

sushuiasushui 发表于 2013-4-27 20:45
谢谢回复哈，我之前也打了一堆话给另一位热心同学，但是好像网速不给力，被吞了。。。
看来我的理解差不 ...

楼上说的对哈，这是bp，cds报出来的是相对于无风险利率的bp spread