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

[Robert Sams]

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
>
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