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# Which interest rate to use when calculating greeks?

Discussion in 'Options' started by sync, Feb 8, 2009.

1. ### sync

I'm creating a spreadsheet using the Hoadley add-in to help me manage my positions. What is a good source to use for the current risk-free interest?

Ideally what I would like is an interest rate symbol that can be use to download the latest rate so I don't have to maintain it manually.

2. ### dmo

The correct interest rate to use is YOUR interest rate. If you're a net buyer of options, what would you have made risk-free with the money you used? If you're a net seller of options, how much are you earning on the funds you received? Those are the correct rates for you to use. It's subjective to you, not absolute.

That said, as a practical matter you can use the short-term T-bill rate. I believe they trade 13-week T-bill futures at the CME. The interest rate is 100 minus the front-month futures contract price. So if the futures contract is 98.50, that represents a rate of 100-98.50=1.5% You could set up your spreadsheet to download that automatically and use it in your calculations.

FWIW, in calculating risk for margin purposes in the SPAN system, the CME currently uses an interest rate of zero - and has for some time.

3. ### sync

I'm not getting how my subjective interest rate fits in with calculating the delta of an option.

4. ### Sniemiec

(100-98.5)/98.5 * (365/91) * 100 = 6.11%

5. ### dmo

Sync, if you're talking about options on stock, the risk-free interest rate is used both to calculate the forward price of the stock, and also the cost of carry of the option itself. In both cases, the answer depends on YOUR rate of interest.

As for the forward price, look at it this way. If you bought IBM for a total of \$10,000 and held it for a year and sold it for the same price you paid, you still lost money - the amount of money you DIDN'T earn by putting that \$10,000 in T-bills. If you could have earned 10% risk-free on that \$10,000, then the amount you "lost" was \$1,000, making the forward price \$11,000. So the underlying price used by your BS model is \$11,000.

If you only could have earned 5% risk-free, then the amount you "lost" would have been \$500, making your forward price \$10,500. In that case the BS model uses an underlying price of \$10,500.

If, at the same time, I had an uncle who wanted to borrow money from me at 20% and was willing to put up his house as collateral, then my risk-free rate is truly 20%. If I decide to take the money and instead buy IBM and hold it for a year and it doesn't move, how much have I lost? Answer: \$2,000 - the money I could have made by lending to my uncle. So my forward price is \$12,000, and that's what BS will use as the underlying price for any options that expire in a year.

Is there a difference in the delta of an option depending on whether the underlying price is \$10,500, \$11,000 or \$12,000? Of course.

Also a factor is the cost of carry of the options themselves - which again is subjective to the person buying them.

6. ### dtan1e

the 3m T bills rate if in discount, u need to convert to the bond equivalent yield

7. ### dmo

Yes I think you're right on that. Thanks for catching it.

I see that the current price for the 13-week T-bill contract is 99.86. By your calculations that would imply an annual risk-free rate of .56%, which I think is about right.

8. ### sync

Thanks for the explanation DMO.

9. ### dmo

No problem. Please believe me when I say that behind the scary-looking math, all this options stuff is just common sense. Honest.

10. ### Sniemiec

Haha ya. I was gonna say, where can I get 6.11% risk free??

#10     Feb 8, 2009
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