Options on interest rates futures

[alafm]

Hello,

I have a question regarding the pricing and the hedging of options on Interest rates futures in Bloomberg. I don't really understand how the values are obtained by using the Normal model and the convention ( call on futures <=> put on the underlying).

Let's say I have an option on ERU3 Comdty:

Futures price = 99.583
strike = 100;
Time to expiry = 221 days
Implied volatility = 37.487 %;
risk Free rate = 0.398%

From bloomberg I have the following results (see the attached file):

price = 0.01
delta = 7.72%
gamma = 0.2054%
Vega = 2.62
Theta = - 0.22
Rho = -1.75

I am trying to get the same results from Matlab using the Black Model but it does not fit:

call = 0.4071;
put = 0;
delta = 0.97

And I could not find the right implied volatily by reversing the Black Model
Could someone explain carefully the formulae to use to obtain the right values?
I spent a lot of days on this issue..

Many thanks,

 

[Keith Tan]

by the no-arbitrage pricing, the cash you paid for the call and futures should be the same value as you sold the put and current stock.

i see you are trying to price an american call. by the black model why you want to find the implied volatility?
it's a little bit tricky for american calls, you would need to find the current prices of the underlying stock first for each binomial step. then get the intrinsic value of the call.

http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/tutorials/xlghtmlnode62.html

 

[alafm]

Thank you for your answer Keith Tan.
I want to express the implied volatility in my example just for training, it is like a second exercise.
I had a look at your link. You are right about the relationship between the put on current stock and the call on futures, this is what I have tried to use in my first message. Do you have any idea of why the values dont match?

Thank you

 

[Keith Tan]

can't really translate much from the pic. i suppose the prices on bloomberg are live trading prices?

hint: press F1 2 times

 

[alafm]

Just to give you a feedback. The model used in the screenshot is the Black Normal Model... That is why I could not find the right values by using the Black Scholes model...

Thank you