Dear all,Suppose a commodity trader has it's credit rating BBB, and it goes to a bank to get a loan suppose $1,000 to fund it's future activities. The bank's interest rate is 10%, and the tenure of that loan is one year. Therefore after one year it have to pay USD 1,100. To get that loan it need to put some security deposite to that bank, and it put some asset that it own. Bank has transition matrix that shows the probability of default. Due to price volatility in that asset, if after one year it's price is below USD1,100 then it is very natural it would not pay the due amount to bank and hence default. Therefore the problem to that bank is to device a policy for that trader on how much amount should the bank keep as a security deposit. That is how to link trader's transition matrix with the volatility of underlying commodity.Can anyone tell me how most banks handle this type of problem? Your help will be highly appreciable.Thanks

If I was a bank, I would never structure a loan that way. The loan would be full recourse against the commodity firms assets. The collateral value would have to be maintained at say 100 + X% of theloan amount. If the collateral value dropped, I would ask for more collateral. So, I wouldn't bother withmodelling the collateral volatility (unless it was to develop some rules of thumb for the X%),as it is the total (net) assets of the borrower that should be important. Presumably the latter is reflected in theBBB rating. Am I missing something?regards,

Dear Alan,Thank you for your suggestion. However my boss instructed me to find some way to link transition matrix with underlying commodity prices. Any other idea?Regards,

Well, if it was my boss, I would first try to understand from him/her where this loan structure comes from.Is it real or a fantasy?If it's real, why don't you post some sample loan doc language which makes it clear that if the collateral drops below the loan amount and the borrower defaults, then the bank will not expect the borrower to make up the difference. If you're borrowingto buy a house, I would believe it. A non-recourse loan for commodity speculation, though?

Assuming a 100% chance of default if the collateral drops below the loan value, then you want the probability that the commodity's value drops below the required level during the term of the loan. You can model this using techniques in stochastic calculus, models from options theory, or Monte Carlo sims of random walks. (you may need to resort to simulations if you need to model changes in the default level of collateral in response to payments on the loan.)But for simple situations in which: 1) you're willing to ignore the time-value-of-money for the collateral (i.e., that the amount of required collateral needs to grow during the life of the loan), 2) have a low chance of default and 3) involve commodities that you are willing to assume follow a normal distribution for price changes, you get a good first approximation by using volatility on the loan duration as your sigma and looking at the probability of the distribution being below the required level on the maturity date of the loan. This will slightly underestimate the probability of default because it will miss events in which the value of the commodities dropped below the default threshold but then rebounded. (Of course, one could say that this model overestimates chance of default because you wouldn't necessary expect 100% of borrows to default the instant the security deposit drops a penny below the required level -- some percentage of borrowers would make their margin calls.)