FRM handbook Example 22.17: FRM EXAM 2008 - Question 73

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Consider the following information. You have purchased 10,000 barrels of oil for delivery in one year at a price of $25/barrel. The rate of change of the price of oil is assumed to be normally distributed with zero mean and annual volatility of 30%. Margin is to be paid within two days if the credit exposure becomes greater than $50,000. There are 252 business days in the years. Assuming enforceability of the margin agreement, which of the following is the closest number to the 95% one-year credit risk of this deal governed under the margining agreement?

Here is the solution: The WCE is the $50,000 plus the worst move over two days at the 95% level. The worst potential move is 1.645 x 30% x sqrt(2/252) = 4.40%. Applied to the position worth $250,000, this gives a worst move of ,991. Adding this to $50,000 gives $60,991.


Actually, I totally don't understanding the solution. Please help!

Thanks!

 

[RM1]

Default means that the 50000 limit has been reached but no more margin has been posted. There is a window of 2 days in which to post this margin. So you will not know for two days after the limit has been hit that the margin has not been posted. In this two days, the current credit exposure could have moved further.

The amount of further movement is determined by the volatility which is 30% annualized. Volatility moves at the square root of time so for one day the volatility would be 30* sqrt(1/252) and for two days it would be 30*sqrt(2/252).

volatility is the standard deviation. So assuming a standard normal, 95% of all points are above the point z = (-1.645 * sigma). (A one tailed test). So you can be 95% confident that the extra loss over the next two days will be less than 30 * sqrt(2/252) * 1.645

 

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I had the same question for this problem. Very clear explanation above. Thank you a lot!