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# Cost of Carry Formulae

Discussion in 'Options' started by qazmax, Aug 2, 2002.

1. ### qazmax

In options K (carry) = i - dividend

or K = (i x day x strike) - div

Two questions for you option big brains...

1. what actual interest rate do you put into the formulae for "i"?
If I can collect 1% on cash and can borrow at 5% om margin
Then does K = 5% or fairvalue of the i rate say 3%

2. When calculating this for single stock futures...
which is stock + K

What will be the number that replaces the strike in the K formulae?

Thanks,

2. ### Maverick74

Most option traders use the 10 year govn't bond yield as the risk free interest rate for their option pricing models.

3. ### qazmax

But... if I want to make an interest rate play (Conv./Reversal/Jely Roll), don't I need to consider my actual charges for borrowing the stock?

Would the 10 year bond be what is plugged into the pricing model for the options trading floor?

4. ### Maverick74

Yes, the 10 year is plugged into the pricing model on the floor. When you trade on the floor you have your sheets which give you the printouts of all the conversions/reversals prices and what it cost to put them on. That way you can look to see if there is any edge or enough edge to do them. As far as what your actual costs are, if you are on the floor you have a clearing firm and the clearing firm will borrow you stock at the 10 year bond rate. If you are off the floor you can't do them anyway. You can't get the spreads off the floor.

5. ### metooxx

Are you trying that off the floor with typical retail commissions?

6. ### Trajan

It's not the ten year note which is used. They use short term rates. Here are the ones from today. The long BD rate hovers around 2.5%

Interest Rate Change

Old
New
Change
Broker Dealer Rate
2.5625
2.4375
-0.1250
Cross-Margin Broker Dealer
2.5625
2.4375
-0.1250
FOC Short Stock Rate
1.6625
1.5375
-0.1250
Equity Credit Rate (325 & 690)
1.3125
1.1875
-0.1250
Repo Rate
1.2125
1.0875
-0.1250
T-Bill Rate
1.0625
0.9375
-0.1250
Fed Rate Open
1.8125
1.6875
-0.1250
Targeted Fed Rate
1.75
1.75
0.00
Prime Rate
4.75
4.75
0.00
Index Box Rate
0.6250
0.6250
0.00

7. ### metooxx

There is no absolute answer; it all depends on whose model it is ...

8. ### dagve

Meteoxx and Trajan are correct. When pricing locks and synthetics, you should use two different rates, the long rate and the short rate. If you put on a conversion, you should price the position using the long rate because you are long stock, reversals should be priced using the short rate because you are short stock. The long and short rates vary among different trading firms. Large firms offer tight rate spreads(3% long rate 2.5% short rate), while other retail firms could pay you close to nothing for your short stock, and charge you an arm and a leg for your long stock. Make sure when you are pricing options that you use the rates that your clearing firm offers. Don't price a conversion using a 3% long rate when you will actually have to pay 5.5%. It is not uncommon for two different traders to price a lock or synthetic completely different from one another because their clearing firms offer different long and short rates.

Exactly.

10. ### Trajan

I was specifically refering to what Maverick said about clearing firms using the ten-year bond. I know some people advocate using this in models. Whatever number works for you is your business. There are a lot of ways a trader can manage their cash on their own. I don't know the inner workings of a cash trading desk, but, floor MMs interest rates aren't based on the ten-year bond. The numbers posted previously were taken from an email I received this and every morning from First Options. There is no number near where the 10-year is trading except the Prime Rate.

To go back and answer his question:

1. dagve covers it. I would adjust it to my net cash position. Typically, it was fairly average with a bias toward the long side. If my balances got extreme one way or another, I would adjust it so that my theos would have me make trades to widdle it down.

2. The number you should use is net credit or debit, or in futures case, the stock price.

k=s*(1+i)^n - d

where n is the number of periods.

#10     Aug 3, 2002
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