Option Pricer input parameters

[a_gnome]

I've knocked up a little Black-Scholes option pricer in a spreadsheet in order to look at trading some long-dated (e.g. June '10) DAX index options. I just want to check a few things regarding the input parameters to ensure that I am using the correct figures:

1. The interest rate: I was going to use the value implied by the Euribor future but should I use the nearest future (e.g. Dec '09) or the one that most closely corresponds to the expiry date of my option (June '10)?

2. What should I use for the dividend yield figure for the DAX? I know that for the most accurate model one should use the individual dividend payments of the underlying stocks but I am hoping that for a long-dated option an equivalent continuous yield figure should be a reasonable approximation.

3. The volatility: can anyone give me current ATM implied vols for June '10 DAX options for example?

As an example of where I've got to, I can match the ATM Eurex web-site prices most closely with: r = 1.07% (Euribor June '10) , Vol = 25% Div Yield = 0.7% but I'd like to know whether these figures are correct.

TIA
Gnome

 

[Martinghoul]

1. The Euribor future is a fwd rate. What you need is a spot rate. For Jun 10, use 0.84%.

2. I would use 0 as div yield.

3. I see 26.4% vol, as implied by the live mid px of the 5800 straddles.

 

[a_gnome]

Hi Martin (or should that be Mr. Ghoul?)

Thanks for the reply. You are of course correct wrt the euribor future. As the Euribor is I believe a 3 month forward, I should be using the Mar '10 euribor in order to get a handle on the Jun '10 price. This ties in pretty closely with the figure that you gave me yesterday

I've been fiddling around some more with it all. Firstly it's interesting to realise that the affect of the Div. yield is to change the balance between the put and the call prices whilst the ATM straddle price hardly changes with this parameter. However I've been trying to match the (delayed) prices on the Eurex web-site and I'm still getting a lower implied vol that you seem to be quoting:

Underlying: 5800
Strike: 5800
Interest: 0.82% (from March '10 euribor future)
Time to Exp: 213 days = 0.5836 years (expires 18th June '10)
Div Yield: 0.0%
Vol: 24.85%
Straddle Price: 875

c.f. Eurex Straddle Price: 875

I don't suppose it would be possible for you just to take a quick look at the parameters that I'm using and check that they're ok and perhaps run the same parameters through a calculator at your end. I'm using the Black-Scholes equation but am wondering whether I'm doing something stupid. Or maybe using a more sophisticated model requires a higher IV?

TIA
Gnome

 

[Martinghoul]

Nah, the vol looks fine, actually, using your inputs... I was using a different underlying (looking at the live prices for the underlying and the option both).

 

[a_gnome]

Nah, the vol looks fine, actually, using your inputs... I was using a different underlying (looking at the live prices for the underlying and the option both).

Thanks, that's good to know.

 

[Martinghoul]

Thanks, that's good to know.

Notice that, assuming the 437.5 price for both the call and the put, the vols on the put and the call will be different. I am sure you knew that already, though...

 

[jaspertrademaster]

Sounds like good advice.

 

[a_gnome]

Notice that, assuming the 437.5 price for both the call and the put, the vols on the put and the call will be different. I am sure you knew that already, though...

This is what I was talking about in my earlier posts: the Div Yield parameter affects the relative sizes of the Puts and Calls without affecting the overall straddle price. Using the same inputs as above:

Div Yield = 0.0%: Straddle Price = 875 Call = 451 Put = 424
Div Yield = 0.5%: Straddle Price = 874 Call = 442 Put = 432

Actual market prices Call = 443 Put = 432

If you set the Div Yield equal to the interest rate (as you do for an option on a future for example) then the Put and Call price come out equal.