XJO Help with creating a fair value options calculator

Re: XJO - Does anyone trade it?

Hi Everyone,

I am wondering what methods you are using to generate theoretical fair prices for XJO index options? I realise it's easy enough to go to the ASX web-site or my broker to get current quotes, but I'm interested in writing some software which needs to be able to calculate likely values at future points in time prior to the expiry date.

As the XJO options are all European-style exercise, at first I thought it would be a simple matter of using a typical Black-Scholes pricing model. But my early attempts with this always showed the Call Prices as overvalued and the Put Prices as undervalued. Then I concluded that perhaps I needed to take into account some form of dividend amount into the calculation, because although the XJO doesn't pay dividends, its value is affected as each of the 200 shares it's comprised of go ex-dividend. I've had limited success by incorporatating this, but not enough to make me happy.

Does anyone currently have a Pricing Model or some other method of calculating fair prices of XJO options? I'd very much appreciate any information you can provide. Thanks in advance for your help...


Kind Regards,

Jason.

Hi Synapse ... goes something like this ... others may be more definitive.

... my early attempts with this always showed the Call Prices as overvalued and the Put Prices as undervalued.

Click to expand...

You can calculate FAIR VALUE with the usual BSOPM Inputs of Type/Underlying/Strike/Time/Imp.Vol and add an extra one called RATIO (as for Warrants).

Index Options are $10.00 per point/Contract. Today XJOH6 Contract sold for $820/1000 = $0.82.

I simply add an extra Input for Ratio into my spreadsheet thus: (divide by 10/1000=100)

With Ratio in BOLD my tweaked BSOPM looks like: =IF($C$1="PUT",+Put_Eur((AE$2-$C$7),$C$4,($C$5+0.001-AE$1)/365,$C$6,AE$4)/$C$8,IF($C$1="CALL",+call_Eur((AE$2-$C$7),$C$4,($C$5+0.001-AE$1)/365,$C$6,AE$4)/$C$8,0))

On 18/05/05 a LONG entry was signalled for XJO (See other XJO thread) and the OTM Option XJOH6 sold at $0.24 at Imp/Vol of 11.0%. Today XJOH6 sold for $0.82 at 12.0% or a profit of 232.00%

Cheers ...

Hi Rembrandt,

Thanks for taking the time to reply.

I understand exactly what you're saying, but I'm still having the same problem. I require quotes on XJO Options which are at least 3 months away from expiry. The normal Black Scholes model doesn't generate anywhere near accurate figures, especially as the time frame increases.

For example, XJO closed yesterday at 4147.8. Going by the ASX web-site, here are a some "fair value" at-the-money quotes based on this (I've also included the IV that I needed to use in the Black Scholes model to generate these figures):

XJOI4 Sep05 4150 Call = 93.3 (IV = 6.6%)
XJOI5 Sep05 4150 Put = 91.5 (IV = 13.5%)
XJOJ3 Dec05 4150 Call = 136.5 (IV = 5.4%)
XJOJ4 Dec05 4150 Put = 123.0 (IV = 14.5%)
XJOKQ Mar06 4150 Call = 166.2 (IV = 1.2%) <-- Impossible!
XJOKP Mar06 4150 Put = 152.5 (IV = 15.7%)

As you can see, the IV's can't be accurate. There is no way a March 2006 Call Option should be priced with an IV of just 1.2%. Furthermore, you can see that the disparity between the IV of the Calls vs Puts increases as the time to expiry increases.

This is why I am assuming that the ex-dividend dates and dividend amounts of the underlying 200 shares making up the XJO are taken into account. This means that Put Options are naturally more expensive than the Call Options, just like when an individual stock has an ex-dividend date occuring within the life of its options.

Are you able to generate the correct prices for longer dated XJO Options, based on your spreadsheet version of the B-S pricing model?

Any further help on this topic would be greatly appreciated...


Jason.

I can see what you mean. I sold deep in the money 4900 Puts in XJO and want to roll it out to July for the same strike 4900 but the July 4900 were quoted at about 16 pts less than Intrinsic. I was doing a search on the divi of the components but most of the major components of the 200 index had dividends after July and I dont know why it was quoted 16 pts less.