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

[Brian G. Peterson]

Top-quoting makes it quite confusing to read the message thread, and for 
future reference, is generally discouraged on this list.

S and X in GBSOption need to be in the same units as the price you want 
out on the other end.  I'm not at a computer with R on it, being the 
weekend, but I would suspect units confusion here.  If everything is in 
the same units, you should get a rational result.

Also without referring to the manual, isn't there a slightly different 
function for the Black Scholes calculation for an option on a futures 
contract, which is what your Eurodollar example is?

Regards,

    - Brian

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
> 
> 
> -----Original Message-----
> From: James [mailto:jctoll at gmail.com] 
> Sent: 16 June 2007 00:43
> To: Robert Sams
> Cc: r-sig-finance at stat.math.ethz.ch
> Subject: Re: [R-SIG-Finance] option model for interest rate future
> 
> Robert,
> 
> It seems unusual to me that a nearly at-the-money option with a year and a quarter left in it's life would only be worth $0.2215 according  
> to Bloomberg.  I would double-check the calculations from Bloomberg.   
> To me, they seem most suspect.  I'm wondering if you entered the time to expiration incorrectly on Bloomberg, because from the looks of the  
> Gamma and Vega, it looks like you might have entered a shorter time.   
> I hope this helps.  Let me know if you figure this out.
> 
> James
> 
> 
> On Jun 15, 2007, at 12:43 PM, Robert Sams wrote:
> 
>> Thanks for the reply Sylvain and Brian,
>>
>> I take it that GBSOption with b=0 is what I'm looking for. However, 
>> I'm confused by the results. As an example, let's take the 94.50 put 
>> on the Sep 2008 eurodollar contract, expiry 9/15/08. The price is 
>> 94.625 and (price) vol is 12.35%. So,
>>
>>> GBSOption("p",94.625, 94.50, 458/365, .05507, 0, .12382)
>> Title:
>>  Black Scholes Option Valuation
>>
>> Call:
>>  GBSOption(TypeFlag = "p", S = 94.625, X = 94.5, Time = 458/365,
>>      r = 0.05507, b = 0, sigma = 0.12382)
>>
>> Parameters:
>>           Value:
>>  TypeFlag p
>>  S        94.625
>>  X        94.5
>>  Time     1.25479452054795
>>  r        0.05507
>>  b        0
>>  sigma    0.12382
>>
>> Option Price:
>>  4.821096
>>
>> Description:
>>  Fri Jun 15 18:58:02 2007
>>
>>> GBSGreeks("delta","p",94.625, 94.50, 458/365, .05507, 0, .12382)
>> [1] -0.4372786
>>> GBSGreeks("gamma","p",94.625, 94.50, 458/365, .05507, 0, .12382)
>> [1] 0.02827910
>>> GBSGreeks("vega","p",94.625, 94.50, 458/365, .05507, 0, .12382)
>> [1] 39.34058
>>> GBSGreeks("theta","p",94.625, 94.50, 458/365, .05507, 0, .12382)
>> [1] -1.675517
>>> GBSGreeks("rho","p",94.625, 94.50, 458/365, .05507, 0, .12382)
>> [1] -6.049485
>>
>> But the correct values (using Bloomberg) are:
>> Price: 0.2215
>> Delta: -0.426371
>> Gamma: 0.499401
>> Vega: 0.022302
>> Theta: -0.000268
>> Rho: -0.277807
>>
>> What am I doing wrong?
>>
>> Thank you,
>> Robert
>>
>> -----Original Message-----
>> From: Sylvain BARTHELEMY [mailto:barth at tac-financial.com]
>> Sent: 14 June 2007 18:01
>> To: Robert Sams; r-sig-finance at stat.math.ethz.ch
>> Subject: RE: [R-SIG-Finance] option model for interest rate future
>>
>> Hi Robert,
>>
>> I think that the fOptions pack does that: GBSGreeks & GBSVolatility
>>
>>
>> ---
>> Sylvain Barthélémy
>> Research Director, TAC
>> www.tac-financial.com | www.sylbarth.com
>>
>> -----Message d'origine-----
>> De : r-sig-finance-bounces at stat.math.ethz.ch
>> [mailto:r-sig-finance-bounces at stat.math.ethz.ch] De la part de Robert 
>> Sams Envoyé : jeudi 14 juin 2007 17:54 À : r-sig- 
>> finance at stat.math.ethz.ch Objet : [R-SIG-Finance] option model for 
>> interest rate future
>>
>> Hi,
>>
>> Does anyone have R code to calculate implied vol and greeks of an 
>> option on an interest rate future (e.g., CME's eurodollar contract)?
>>
>> Thanks,
>> Robert