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## Saturday, March 26, 2011

### daily margin call - simplest futures illustration

Simplest and best-known margin calc is in commodity futures, say a Dec oil contract. Let me use it to describe daily margin calc in my own language.

Clearing house computes and issues daily margin calls. Therefore the formula/algo is crafted from the clearing house's standpoint. Goal is to protect the clearing house from
1) any "reasonable volatility" i.e. a daily price swing smaller than the extreme 0.05% cases. (More extreme cases would show Larger swings.)
Here, let's assume house estimates 1% maximum daily move.
2) any reasonable/unreasonable member default.

relevant -- EOD best bid/ask
irrelevant -- Current spot price -- irrelevant.
irrelevant -- Last transaction price for the same Fut contract -- irrelevant.

Suppose current mid-day fut price = {89.99/90.01} ie {best bid/offer}

Suppose I BUY a contract mid-day at the market i.e. \$90.01. Clearing house locks up an amount \$x as collateral in my margin account to protect house against my default. If I default, on delivery date house still [1] need to BUY from the contract seller @ \$90.01 the agreement/transaction price, but how does the house get the cash to BUY? To answer that, let me first Introducing the basic long margin call formula

EOD-liquidation-value [my long position]  - 1% + x = \$90.01 // Soon We will solve the margin requirement \$x of a long, using agreement price and best BID at EndOfDay.

Here the clearing house is assuming market moves at most 1% against me by end of Day2. So if I declare bankruptcy on Day2, house liquidates my long position at most 1% below Day1's EOD mv.

We will denote "current liquidation value of some position" as mv[that pos]

Now, mv [my long pos] is simply the best SELLING price of that asset (the oil contract) when house must liquidate my position. Think hard -- That's actually the end-of-day best BID. That's \$89.99 in our case, assuming no market move.

x = \$90.01 - \$89.99 * 99%, roughly \$0.02, which translates to \$0.02k = \$20. Here we assume each full contract is \$90k when price = \$90

-- Now suppose market collapses drastically and moves against me to (\$88/\$88.02)

mv [my long position] - 1% + x = \$90.01 // \$90.01 is the me-counterparty agreement price

x = \$90.01 - \$88 * 99%, roughly \$2.01k

A 2.2% Fut price change (89.99 to 88) causes a large margin call. I would say the margin call roughly matches the physical contract valuation drop from \$89.990K to \$88K

[1] so my default doesn't cause a chain reaction taking down the seller.

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## About Me

New York (Time Square), NY, United States
http://www.linkedin.com/in/tanbin