# XJO Long Strangle - basic study



## RichKid (29 June 2005)

Hi folks,
Been following some of WayneL's posts and been doing some basic reading on options. I'm currently new to options so I'm looking at a simple strategy to get started while reducing risk. I've found the strangle to be attractive at this stage of the market as I expect some further movement in either direction of at least 100 points in the next 3 months or so and I can only allocate a small amount of my capital (ie strangle is cheaper than a straddle but riskier).

So here is a screen shot of some option prices I've been looking at (the XJOFF is just for comparison purposes) from the ASX site as of about 10 minutes ago. The top and bottom options are the ones that I am looking at for the strangle. My basic question to anyone who'd like to help is why is there such a difference between the theoretical and market (mm) price and is it too expensive in that sense? Unlike shares I know that I'm buying from other investors directly but here I'm not sure if it's just a numbers conjuring trick. How do you pros decide what to pay for an option? 

As for my strategy does anyone recommend another combination, this is a learning exercise so don't think it's a trade recommendation as I won't buy on your advice. You can suggest your own strangle combination if you like and we can debate it to draw out the theoretical & pricing issues. With strangles do you buy any combination of otm puts and calls eitherside of the current price or do you buy them at equal strike distances away from the current price (eg put strike approx 100 ticks away from current price and call approx 100 ticks away from current price??). I've also posted some info  from the ASX site about strangles (next post).

Real times prices for the options at the time were (average of spread): 

XJOI5 39c
XJOFF (no spread)
XJOJP 33c


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## RichKid (29 June 2005)

*Re: XJO Long Strangle- basic study*

From http://www.asx.com.au/investor/options/how/library/StrategyofWeek170103_AM4.htm


> *The Bought Strangle*
> The long strangle consists of buying a call option with a higher strike price and a put option with a lower strike price. The strategy is usually entered with the share price between the strike price of the call and the strike price of the put.
> 
> The success of the long strangle depends on an increase in the volatility of the underlying shares or a sharp movement in the share price. The direction of the movement is unimportant. For the investor to make a profit at expiry of the options, the share price must be above the strike price of the call option plus the cost of the strategy, or below the strike price of the put option less the cost of the strategy.
> ...


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## wayneL (30 June 2005)

*Re: XJO Long Strangle- basic study*

Hey Rk

*Straddles:* (and strangles)

There are two ways of trading these and to a large extent will determine option selection.

1/ All or nothing. That is to buy the straddle and leave on till expiry...collect a profit or accept the loss. In this case the risk is easily definable; the risk is what you paid for the spread.

2/ Sell the straddle before exiry at some optimum point. This will enable us to have a larger position size, but we will have to put a lot more effort into defining the risk. It's a bit of a balancing act and for this we will use the Greeks.

*Delta:*

If one buys an ATM straddle, the delta will be zero or close to it. I strongly reccommend that the delta *IS zero* when you buy the straddle, otherwise you will have a slightly directional strategy. In practice, this means buying straddle when the price of the underlying is right bang on top of the strike price....or slightly below the strike in some circumstances. This is often refered to *"delta neutral"*

Initially that means that no profit occurs when the price moves either way.

*Gamma:*

Gamma is the rate of change of Delta, and is the function whereby the bought straddle becomes profitable. The winning legs delta will *increase* the furher it goes into the money, as the losing legs delta is *decreasing* as the forther it goes out of the money.

Obviously we want HIGH Gamma for this strategy to become quickly profitable. In practice, this means that we want low extrinsic value options...i.e low Implied Volatility and not too long till expiry (however this must be balanced by low theta as we will see in a minute)

The more extrinsic value the options have, the lower gamma will be and *we want high gamma*.

*Theta:*

One of the disadvantages of this strategy is that you have double Theta, because you have two bought legs. The rate of theta *increases* the higher the implied volatility. The rate of theta *decreases* the further away from expiry.

Once again, this is a case for only buying a straddle when *IV is LOW*. 

It is also a case for long dated options to *minimise theta*. Notice how this flies in the face of our high gamma requirements? This is where we need make a decision. Do we want *more time* to allow a big move to develop, or do we want the *higher gamma*, so that we will be into profit sooner into any move, but paying for that luxury with higher theta.

*Implied Volatilty & Vega:*

What we definately do *NOT* want with the bought straddle is declining IV (negative vega). For this reason it is worth aquiring the IV history of the options we are trading.

*We only want to buy a straddle when IVs are in the lower quartile of the IV range.* (Unless you are expecting a HUGE MOVE one way or the other, then it won't matter too much) This way we may profit from increasing volatilty (positive vega).

Vega is highest ATM so any moves in IV will tell in the bought straddle.

*Risk:*

If the straddle is bought when IV is near its historical lows we need only be concerned with measuring risk with theta. Easily done in the hoadley strategy modeller. You will know that if this sucker doesn't move, it will cost you $x per day. If however, IV's are off the lows, we must consider vega risk if IV's decline. This is a little harder to quantify but you must be aware of it. 

Having an idea of risk, and how long we want the strategy to run, we can set position size according to money management rules.

*Conclusion:*

Even though this is a non-directional strategy, we need to have a view of how fast and how far the underlying might go.

This will determine your expiry month...or if the startegy is worth putting on with current conditions.

As an example, I have a straddle on SYMC that I bought early this month, with an October expiry. This is *further dated*, and hence *lower gamma than I would normally like*, but I expected some sideways movement before a decisive move one way or the other. I also anticipated this may need some time to play out.

So far it is going sideways as expected and theta is whittling away at the position. But vega risk was minimal and risk is inside expected parameters.

Now all it has to do is *GO SOMEWHERE* LOL.

Thats a lot to absorb but with experience it will all make sense....and there is only one way to get experience.....

It is truley not as complicated as it first seems.

Cheers


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## RichKid (4 July 2005)

*Re: XJO Long Strangle- basic study*



			
				wayneL said:
			
		

> Hey Rk
> 
> *Straddles:* (and strangles)
> 
> ...




Hi Wayne,
Apologies for not thanking you sooner but that's a great post and very very helpful to me!

My problem now is trying to figure out whether the market maker's price must be taken- for example in the options I mentioned in the first post one option in the strategy is way below fair value (compared to the mm price) and the other one is way above fair value- what's going on?? So even if I find an option with perfect greeks if the mm decided to ask for more than the calculators says is a fair price to pay does that mean we just have to consider the mm price to be the market price (ie pay them extra)? 
*Or is there some pricing element which I have missed out on that is not considered by the greeks?? *Just plug in the put and the call I mention and then compare the spread or just compare the 'theoretical value' in the table in my first post. Very confusing for us beginners! What gives??!!

It just means I'm outlaying more at the start since the options should move the same and I'd profit form the difference- assuming the mm don't get me again when it's time to close my position.


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## Synapse (4 July 2005)

*Re: XJO Long Strangle- basic study*

Hi RichKid,

You are quite right when you said:



			
				RichKid said:
			
		

> *Or is there some pricing element which I have missed out on that is not considered by the greeks??*



You will always find that the XJO Put Options _seem_ overpriced in real-life, whereas the Call Options _seem_ underpriced.  The longer the time remaining until the Expiry Date, the more significant the apparent difference.

The missing ingredient is this:

The XJO's value is derived from 200 x underlying share prices.  As you already know, when an individual share has an upcoming Ex-dividend date, this tends to cause an increase in its Put Option values and decreases the values of the Calls.  This is because the anticipated drop in share price (i.e., the "Ex-dividend effect") is taken into account by the Market Makers when pricing the Options.

Now, as you may already be guessing, when you've got 200 x shares making up an Index, this means that the actual Index itself is obviously going to be affected as these shares each reach their Ex-dividend dates!  Therefore, this means that there is definitely an additional factor that needs to be taken into account - the ex-dividend dates (and dividend amounts payable) of all 200 x shares comprising the Index!  

This can be really complicated to work out, however rest assured that the Market Maker's option quotes are definitely taking this into account.  This is why you'll see what appears to be XJO Put Options having *higher* _Implied Volatility_ than the Call Options.

Through some persistance, trial and error, and brainstorming (I don't usually give myself a wrap, but I figure it can't hurt once in a while!), I recently came up with a rather simple and elegant solution to this problem (you may remember I posted here 4 or 5 weeks ago looking for help with exactly this topic - my post was called "XJO Help with creating a fair value options calculator").  Here's what I personally came up with and now use as a method of generating "fair-value" XJO Option Quotes:

I use the Black-Scholes Option Pricing Model as usual, HOWEVER, I adjust the "Risk-free" interest rate amount *down* from 5.5% (our current true rate) to around 1% - 1.5% (roughly - there is a small degree of trial and error to this) until I find that the Pricing Model is giving reasonably accurate prices with a SINGLE Implied Volatility amount for both the Puts & Calls, based on the currently available live option quotes.  I have found that the "ex-dividend effect" on the XJO presently equates to roughly a 4% to 4.5% "continuous dividend yield effect", which is why changing the Risk-free rate in this manner actually ends up giving a reasonable result. 

Please bear in mind that whilst this greatly improves your accuracy in calculating theoretical prices, it's still not perfect.  One of the reasons is that different times of the year there are proportionately more (or less) of the underlying 200 x Shares reaching their ex-dividend date than at other times.  But, despite this, I have found that my pricing calculations are now sufficiently accurate for my purposes.

In case I haven't explained this too well, feel free to ask me more questions and perhaps I can give you an example to show you exactly what I mean.

I hope that helps answer your question... 


Kind Regards,

Jason.


P.S.  To wayneL:  Well done on a great post discussing the key points one needs to keep in mind when trading Straddles (or Strangles for that matter)!


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## wayneL (5 July 2005)

*Re: XJO Long Strangle- basic study*

Good work Jason!

I can't help thinking there are some risk free profits there though...if your brokerage is cheap enough 

RK,

One note on "fair value". I think this term is a bit of a misnomer.

"Fair value" is calculated using the statistical volatility. Of course statistical volatility is what *HAS happened*, and may not accurately reflect the markets view of *what is about to happen*.

Statistical volatility can, however, be used in a straight out statistical probabilty style of trading. This would entail buying or selling premium by finding skewed relationships between statistical and implied volatilty....a bookies style approach.

I rarely give fair value a second glance in my trading (but not implying that one won't find it useful; many obviously do)

Just one opinion.

Cheers


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## Synapse (5 July 2005)

*Re: XJO Long Strangle- basic study*



			
				wayneL said:
			
		

> Good work Jason!
> 
> I can't help thinking there are some risk free profits there though...if your brokerage is cheap enough



Hi Wayne,

I must admit that I intuitively feel the same way, and have been spending extra time lately keeping an eye on XJO Option quotes and playing around with multi-legged trades to see if there might be some hidden opportunities just waiting for me to find them.  The fact that XJO Options are all European-style exercise (and they are simply cash-settled upon the Expiry Date) is especially enticing.  Actually, using some sample quotes back on 24 June (a mix of real+theoretical prices), I fiddled around in Hoadley's Spreadsheet with this possible trade (XJO closed on this day at 4245.6):

24 June 2005 - Buy XJO 4250 Dec05 Call @ ~134c
24 June 2005 - Sell XJO 4250 Sep05 Call @ ~85c
24 June 2005 - Sell XJO 4250 Dec05 Put @ ~112c
24 June 2005 - Buy XJO 4250 Sep05 Put @ ~79c

You'll note this basically consists of two Calendar Spreads, i.e. a Sep/Dec 4250 Long Calendar using Calls and a Sep/Dec 4250 Short Calendar using Puts.  The initial debit when placing the trade would be 16c.

At first glance, using Hoadley's software with a standard Black-Scholes pricing model, it looked as though there may have been a risk-free profit of around 40c premium at virtually any subsequent value of the XJO as at the September Expiry Date (assuming the Implied Volatilities of the December Call & Put were to end up fairly equal at this point in time)!  

Of course, this was a trap, as when I took into account the ex-dividend effect as described in my previous post, I ended up realising that I would have locked in roughly a 3c loss (this was based on using 1.25% as the "Risk-free" rate instead of 5.5%, thus allowing for an effective continuous dividend yield of 4.25%).

So then I thought, what about if I flip it all around, i.e., swap all the buys & sells to end up with this trade instead:

24 June 2005 - Sell XJO 4250 Dec05 Call @ ~134c
24 June 2005 - Buy XJO 4250 Sep05 Call @ ~85c
24 June 2005 - Buy XJO 4250 Dec05 Put @ ~112c
24 June 2005 - Sell XJO 4250 Sep05 Put @ ~79c

This now means I'm starting with a 16c *credit*, and as at the September Expiry could close all legs at a net cost of 13c (if my projected prices are correct), thus leaving me with 3c credit for my troubles.   (I know, I know... slippage due to bid/ask spreads, not to mention brokerage fees, will undoubtably wipe out any chance of making a profit).  

I did, however, decide to "Paper Trade" this one - as I want to wait until the September Expiry Date to see how close my calculated values of the December 4250 Calls & Puts would have been, compared to the actual prices that will be available at this point in time.

In conclusion, I can't help but have this nagging feeling that there are definitely some risk-free trades out there.  My quest to find them shall quietly continue... 


Kind Regards,

Jason.


P.S.  This all becomes increasingly interesting when you consider that setting up a trade for an initial credit gives you the opportunity to earn interest on this credit.  This is still applicable even if the funds have been withheld from you to be used as security towards covering your Margin requirement.  My Stockbroker has confirmed that the interest rate payable is presently 5.15% p.a. on any cash amount required for margin cover.  _(Note to everyone:  This rate is only applicable to the Australian Market and most stockbrokers WON'T pay it - they keep it for themselves!)_


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## RichKid (5 July 2005)

*Re: XJO Long Strangle- basic study*



			
				Synapse said:
			
		

> I use the Black-Scholes Option Pricing Model as usual, HOWEVER, I adjust the "Risk-free" interest rate amount *down* from 5.5% (our current true rate) to around 1% - 1.5% (roughly - there is a small degree of trial and error to this) until I find that the Pricing Model is giving reasonably accurate prices with a SINGLE Implied Volatility amount for both the Puts & Calls, based on the currently available live option quotes.  I have found that the "ex-dividend effect" on the XJO presently equates to roughly a 4% to 4.5% "continuous dividend yield effect", which is why changing the Risk-free rate in this manner actually ends up giving a reasonable result.




Hi Synapse,
Thank you very much for a quick reply and a great explanation! It is so refreshing to have people here who know about this stuff. I did notice in the Commsec Protrader2 options calculator that there was a dividend amount included in the calculation (screenshot attached as of about 10min ago- all fields are default per Commsec) they must have been trying to do the same as you in a rougher way. 

My concern is that if you are changing the interest rate to match the market maker's price then the mm (rather than underlying market statistics and interests rates etc) is dictating the price since the mm's spread is the main yardstick- having said that some people may argue that the 'market maker' is the market- in which case they could change things at will. However, it's been suggested that mm's don't get too greedy or tricky in case people stop trading with them. So I assume that as long as the mm's price their options consistently (and provided we can mirror that pricing method) we can create some predictability into our options trading- is that what you have achieved to a certain degree by varying the interest rate- or have I misunderstood it? I guess backtesting is the only way to do it but I'm not sure if you have access to all the mm spread data- might leave this for your other thread on the options calculator.

I also do take your point about things not being perfect- good luck with your 'mission (im?)possible'. I'm just glad there is a logical explanation to this pricing issue. I do remember you mentioning it before, it didn't really sink in until I had to do the math in my option selections.

Wayne, thanks again for the explanation, so many variables that it's like a moving target- just when I think I've got something down then another issue pops up, eventually I guess it'll get simpler. I probably didn't help by going for index options either! I'll have to do some paper trading to see how it works out or maybe bet in very small amounts just to see how things work in real trading. I may also look at alternative instruments like warrants at this early stage for strangles, not much choice.

(If anything I said above sounds like nonsense it probably is as I'm still grappling with it all, so please excuse me). Thanks again folks!!

Also will have a look at those spreads Synapse mentions but I think they are too complex for me at the moment.


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## ice (5 July 2005)

*Re: XJO Long Strangle- basic study*

Terrific informative thread.

I know you're all aware of this but for newbies to XJO trading, a reminder:

"* A common misconception investors often have is believing that XJO options are priced against the ASX 200 index during their lifetime. Although at expiry the index is referenced to calculate the closing value of the XJO options it is in fact the * current futures price * that determines the value of an XJO contract during its trading life."   

http://www.asx.com.au/investor/options/how/library/StrategyofMonth20041103.htm

Emphasis is mine. Not normally a big issue but occasionally the SPI deviates substantially from the XJO. 
Whether that can offer an arbitrage opportunity is up to the judgment of the individual trader.

ice


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## RichKid (5 July 2005)

*Re: XJO Long Strangle- basic study*



			
				ice said:
			
		

> Terrific informative thread.
> 
> I know you're all aware of this but for newbies to XJO trading, a reminder:
> 
> ...




Thanks ice, I think I'll leave a technical reply to your post to the experts as I'm already confused but I do remember seeing something to that effect somewhere, thanks for the reminder!

(PS. The tags for BB code use square brackets [] rather than thos pointy arrow like thingies<>)


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## ice (5 July 2005)

*Re: XJO Long Strangle- basic study*



> (PS. The tags for BB code use square brackets [] rather than thos pointy arrow like thingies<>)




Thanks RichKid.  I was somewhat perplexed......


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