[R-SIG-Finance] option model for interest rate future

[James]

On Jun 16, 2007, at 1:44 AM, Robert Sams wrote:

> Hi James,
>
> Thanks for the reply. The Bloomberg valuation and greeks are  
> certainly correct. You seem to suggest that a price of 0.2215 for a  
> long-dated, near-the-money expiry is somehow low. But the  
> underlying is an interest rate future and the price here quoted is  
> 22.15 ticks, or $553.75 per option (25$ tick value) on 1 million  
> forward 3m libor deposit at 5.375 (100 - 94.625). Price vol (which  
> here is the same as basis point rate vol) is 12.35% and a bp change  
> in forward rate is worth 25$. Nothing unusual here.
>
> Robert


Robert,

After rethinking the issue, I'm wondering if the sigma you're using  
needs to be adapted to the Eurodollar contract pricing convention,  
since the contracts are priced at a discount (100-94.625).  So the  
volatility is really 12.35% on 5.375 not 12.35% on 94.625.  I looked  
around and found a spreedsheet from NYU that appears to make this  
adjustment.

http://www.stern.nyu.edu/~igiddy/edoptprice.xls

Plugging your numbers into the calculation (L6) from the spreadsheet  
yields

0.12382 (100 - 94.625) / 94.625  =  0.00703336856

If I use that for my sigma within R, I get

 > GBSOption("p",94.625, 94.50, 458/360, .05507, 0, .00703336856)

Title:
Black Scholes Option Valuation

Call:
GBSOption(TypeFlag = "p", S = 94.625, X = 94.5, Time = 458/360,
      r = 0.05507, b = 0, sigma = 0.00703336856)

Parameters:
           Value:
TypeFlag p
S        94.625
X        94.5
Time     1.27222222222222
r        0.05507
b        0
sigma    0.00703336856

Option Price:
0.2246195

Description:
Sat Jun 16 10:16:19 2007

Much closer to the price you got from Bloomberg.  Unfortunately, I  
don't have much experience with interest rate options to confirm this  
adjustment.

James