Conditional Monte Carlo ?

silverside · March 15th, 2004, 10:30 pm

can someone please explain what it is and give a simple example?I have some notes on it but they're not that clear, even though I don't think the concept is that complicated.Thanks.

ScilabGuru · March 17th, 2004, 9:30 pm

I suspect that this just means that you simulate conditional distribution. For instance, if you have time series from the model x_{i+1}= f(x_i,y_i, eps_i) - then you have to simulate distribution for X_{i+1} having x_i, y_i fixed

Aaron · March 17th, 2004, 10:55 pm

Conditional Monte Carlo is usually used to estimate derivatives. For example, suppose you wanted to estimate the optimal hedge ratio of an exotic option, too exotic for differentiable closed form solution. You could use Monte Carlo to simulate a price at various underlying prices, then take differences to estimate the hedge ratio. This example is too trivial to justify the name CMC, typical applications are more sophisticated.

sceptic · September 11th, 2005, 2:42 am

Was wondering:I'm looking at a (5%-6%)-CDO tranche that changes subordination level up by 1% after 1, 2, 3 years etc... In case loss exceeds att point A by amount L, next shift is applied to A-L, tranche thickness is reduced by L.Is this something I would need conditional Monte Carlo for:- simulating n paths for the 1rst year- dividing them into n/k path in the second year, calculating expected Att/Det point for each- ...Or is there an easier way to cope with this....

Aaron · September 13th, 2005, 11:55 am

Let me see if I understand. The tranche is 5%-6% the first year. If losses are less than 5%, it becomes 6%-7% (of the original portfolio) next year; and increases by 1% every year as long as it does not get hit. If losses the first year are greater than 6%, it of course is wiped out. If losses are 5.2%, the first year, then the second year it will be 6.2%-7%. Is that correct?In that case, you don't need conditional monte carlo. The shift is not conditional (except in the case that the security gets wiped out, but that just makes it a knock-out).If the shift depended on the losses, you might consider conditional monte carlo.

sceptic · September 13th, 2005, 7:24 pm

You understood 100% correctly, many tks!What I was wondering about is: this is a tranche on the CDX.IG.S4. I do have a base correlation surface. Each MC drawing for a given correlation delivers me a set of default times for the underlyings. I calculate my payoff for this path and do the next drawing. What I did not figure out is: How can I use use base correlations? Or should I just settle for some average compound correlation I deem appropriate for this portfolio?

Aaron · September 14th, 2005, 7:10 pm

I don't think you can use the base correlations. The problem is they are not consistent. My first idea would be to compute a base correlation for something like a 5%/10% tranche, and assume it for the full analysis.

sceptic · September 15th, 2005, 10:19 am

Not sure if I understand what you mean or how to do this. Do you mean the correlations for a [0-5] and a [0-10] tranche, how would my simulation look like?Tried one other thing: if I setup a portfolio of independent tranches (premium legs start paying at forward start dates) - in year one 5%-6% and in year two 6%-7% no matter what happened in year one - then I could use the base correlation curve. Would it be fair to assume that the average price of this portfolio is the maximum value my real deal could be worth and the min of this portfolio is a lower bound? This leaves me with an possible price from 97.7 to 100.1 with the spread the IB offered us... (than I would understand why they don't seem to worry too much about pricing method...)

Aaron · September 15th, 2005, 1:01 pm

No, I mean to use the correlation for a tranche with a 5% attachment point at 10% detachment point.I would not trust a price given by your approach. It's important that your model be based on tradeable market prices, not theoretical correlations. Assuming that default spreads and implied correlations are independent of actual defaults seriously distorts the economics of credit derivatives.