Desparately seeking for assistance.....How do I use Monte Carlo simulation to calcuate the credit default swap spread (CDS spread) ?Or anyone can refer me to some articles so I can have some idea to get started with the Monte Carlo approach?Thanks....

why would you ever use MC??? It can be solved analytically.

Hi, i am reading the paper by Hull & White: Valuing Credit Default Swaps II: Modelling Default Correlations"In this paper, the authors used Monte Carlo simluation to solve the credit default swap spread. I have no idea on how the authors used MCS to solve this part... and how they generate the MCS. Hope someone can give me a better idea on how MCS is used to solve CDS spread.thanks.

Ahhh. This paper is talking about valuation of a CDS when the protection seller is credit-risky. So you need to look at the joint probability of default (the reference entity and the CDS seller both defaulting...or the likelyhood of the CDS seller defaulting when the swap is ITM)This is not how CDS are priced in practice. They are priced as if the seller is riskless...so no need to use MC.

Hi thanks for your reply..I am trying to replicate the results obtained by the authors in the calculation of credit default swap spreads (counterparty default risk) using Monte Carlo simulation (control variate approach & antithetic sampling) as seen in Table 4 of the paper..So I was wondering if anyone tried to replicate the paper given the CDS formula.... and if anyone can explain the approach to use Monte Carlo and maybe briefly explain the control variate approach.....Thanks..

It's a nice paper, but nobody really uses it to price baskets, gaussian copula to get default times is preferable and generally requires many fewer iterations.However, if you want to do this then the first thing you need to do is calculate the default barrier. I'd use an arrow-debreu method to approximate the barrier, but you could use quadrature, and i expect somebody's found a much better method. You then just evolve the default process for the basket using correlated MC, and check for default at each step.I did this a long time ago and was able to reproduce the figures in the paper. I didn't implement control variates, but I imagine you'd price a single cds with the generated paths and compare with the analytical solution.

Hi, thanks for your reply.....I have been trying to solve the CDS spread over a few weeks already, but still unable to obtain the correct answer of 0.01944 as stated in the textbook....Valuing Credit default swap 1: No Counterparty Default Risk(Also in John Hull's textbook: Chapter 27: Credit Risk Page 640 Example 27.2)CDS Spread Formula:where q(t) = risk neutral probability of default assumed to be constant within a year. A(t) = accrued interest, u(t) = PV of payments at rate of $1 per year btw t=0 and t e(t) = PV of payments at time t = t-t* where t* is the payment date immediately preceding time t pi = 1 - Probability that credit event will occur.. T = life of credit default swap in years = 5 years R = expected recovery rate = 0.3I tried to use both Trapezoid Rule & Simpsons Rule to solve the integral, but failed to obtain the exact solution....... Anyone who tried this can help me spot my mistake??..... I have attached my spreadsheet with calculations, pls advise me on my errors in the spreadsheet........Really appreciate that cos this part is crucial in my analysis of CDS..Thanks.

you don't need anything that complicated, here's a sheet that has the calcs in it

I also want to know how CDS are valued and marked-to-market given the original and the current CDS spreads. (No need for monte carlo).

------------------------------------------------------------------------------------------------------------John Hull & Alan White : Valuing Credit Default Swaps (II) paper I am still trying to get the big picture about CDs valuation with counterparty default risk (Plain vanilla CDS for the time being)Pls correct me if I'm wrong for my approach below:---------------------------------------------------------------------------------------------------------StepsStep 1 : Compute the default barrier for the reference entity and counterparty based on the default probability... One main problem here is that the formulas to calculate the default barrier in the paper are rather misleading..... Are we supposed to use default probabilities to calculate default barrier Kij or the other way round..... i am totally confused by these formulas..pls advise... Qij = default probability of company j at time tiKij = default barrier of company j at time tiTaken from the article: “Standard numerical procedures can be used to evaluate this equation for a given Kij. An iterative procedure can then be used to find the value of Kij that solves this equation” --- > Aren’t these two statements contradicting each other?.... --->What is the unknown? Is it Kij or qij??--------------------------------------------------------------------------------------------------------Step 2 : : Compute the default correlations between reference entity and counterparty using copula approach --------------------------------------------------------------------------------------------------------Step 3 : Once the default correlation is obtained, we are able to get the correlated Wiener process for the credit index of reference entity and counterparty respectively?.... Credit indexes follow an Ito process…. i am not sure how to incorporate default correlations in correlated Wiener process to simulate the credit indexes... pls advise? ---------------------------------------------------------------------------------------------------------Step 4 : Perform simulation to get an average value of CDS spread. Eg. for a 5 year credit default swap: for each step of the simulation: (i) Simulate Xi and Xj credit indexes : i = reference entity, j = counterparty Makes use of correlated Wiener process? - But which method do i use to simulate the credit indexes? (ii) If the Credit index Xi or Xj hits the default barrier, we can compute the credit default spread using the formula given based on the payments and payoffs. end--------------------------------------------------------------------------------------------------------Hi, if anyone who attempted the paper before, kindly advise me if the approach above is correct to replicate the results in John Hull&Alan White : Valuing Credit Default Swaps (II) paper. Thanks a lot!

QuoteWhat is the unknown? Is it Kij or qij??In the calibration phase you have to find the default barrier values Kij wich make the model consistent with the 'observed' default probabilities Qij (computed using bond market prices in their paper), so the unknown is Kij at this step.QuoteCompute the default correlations between reference entity and counterparty using copula approachYou don't need default correlation. This is an output from the model, not an input! You just have tofind instantaneous correlations between the credit indeces. In that article they suggest the use of equity return correlation and other proxies.Quotei am not sure how to incorporate default correlations in correlated Wiener process to simulate the credit indexes... pls advise? At each step of the simulation you have to draw two random variates from a bivariate normal distribution with correlation equal toyour estimated instantaneous correlation. There are standard methods to implement this step. Try a google search or one of the famous books about Monte Carlo methods in finance:Peter Jaeckel's 'Monte Carlo methods in finance' or Paul Glasserman's 'Monte Carlo methods in financial engineering'.Take a look also at Numerical Recipes.Hope it helps.

Thanks for your advice....

Hi, hope that someone can clear my doubts.....I wrote a program for the valuation of credit default swap spread according to the formula below:Some problems:-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------(i) the two random numbers (credit indices) X1, X2 which are correlated variates never seem to hit the barrier which is around -3 or -4 ..... why is this so?..Here's how i generated the random numbers:1) Generate u1 & u2 = random numbers follow normal distribution N(0,1)2) Correlation matrix: input credit index correlation3) Covariance matrix: Var(u1)= Var(u2) =1, Cov(u1,u2) =0 Assume the variance is one? covariance btw uncorrelated u1, u2 = 0?..4) Perform Cholesky factorization to find the correlated normal variates (credit indices) X1 and X2-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------(ii) How to use the formula above the calculate the cds spread using monte carlo simulation? Here's my approach, pls correct me if i'm wrong - Let's say the reference entity defaults first at time a, OR counterparty defaults first at time a, the CDS Spread will be evaluated using this formula, substituting T with a: Juz wondering if this is the right approach to calculate CDS spread by simulating the credit indices?.. --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Anyone who has tried the monte carlo simulation, pls kindly advise. Thanks a lot in advance......

Nobody takes into account their counterparty risk at this level. If the price of a credit is 60 bps it's 60 bps, the counterparty credit is dealt with separately.If you want to do this, the hull-white method is inefficeint because it's a barrier that you have to check for breaching at each different time step. The copula approach gives you default times directly with each scenario and you'll get convergence much faster than with HW. Mark Joshi has a paper on importance sampling to improve upon this as well.