hello, i am working on CDS.I am looking for a way to calculate sensitivity to credit spread move and convexity.On "The Quantitative Finance FAQs Project " there si a topic "What is convexity?" that gives a formula for bonds:mathematically:duration = (t1.PVCF1+t2.PVCF2+..+tn.PVCFn)/(k.PVTCF)where:PVCF= the present value of the cash flow in the period t discounted at the yield to maturityPVTCF= total present value of the cash flow of the security determinated by the yield to maturityk= number of payments per yearand convexity=(t1.(t1+1).PVCF1+t2.(t2+1).PVCF2+tn.(tn+1).PVCFn)/((1+yield/k).(1+yield/k).k.k.PVTCF)Well i'm not quite sure how to apply it to CDS.what is the yield to maturity for CDS then?Other formulas welcome !Does anyone can help me please ?Also if you have any tips on how to best use these two variables for analysis, i'm pretty interested,thank you

Hey.Best thing you can do is try to derive a closed form formula for the CDS price (not too hard, some reasonable simplifying assumptions would be constant default intensity and coupon paid continuously), and take its first and second derivatives wrt the spread and voilà you have your sensitivity to spread move and convexity.

Sounds good. thanks for replying,Considering the formula of the price of a CDS:for a seller of protection we receive the coupons and we pay the recovery which gives a price of:with:Each i is a coupon date.DFi: Discount Factor between t=0 and t=iqi: default probability between t=0 and t=iS: spread of the CDSdi: time between t=i-1 and t=i as a fraction of year i.e (nbr of days)/360R: Recovery ratehow can i translate the hypothesis of constant coupondingBecause if I keep everything constant here, when deriving wrt the spread S, i have a constant for the sensitivity and a null value for the second derivative (the convexity then) wrt S.i am wrong somewhere right ?

there are two different things here: the spread S at which you traded at T0 your CDS, which reflects default probability at T0and the market spread of the CDS at any other time T, which reflects the default probability at T.When computing sensitivities, S is kept constant, since you're actually keeping the same product and therefore have the same cash flows. What you want to compute is what happens to your CDS receiving S when the market spread changes, and that will be reflected in a change of q_i, using your notations.You'll get something like this for the protectin seller: PV=(S0-S)*RiskyDuration where S0 is the traded contractual spread and S=default intensity*(1-Recovery) is the market spread of the CDS. Edited for typo

ok thanks, you're right.i'll have a look at it this way