# Option Synthetics



## wayneL (30 May 2008)

I get a few PMs wanting to discuss various option strategies and I find myself quite often explaining exactly the same concept to help the person understand the strategy they are proposing. That is the concept of "synthetics".

What is a synthetic? In the real world, a synthetic is somthing artificial that mimics something natural. So vinyl is synthetic leather and so on. In the options world, a synthetic strategy is one that mimics a natural strategy.

So if we are looking at a straight out bought call option, we can consider that the "natural" strategy. A synthetic call is any strategy that duplicates the risks and rewards of the natural.

A strategy modeler is an indispensable tool for looking at naturals and their synthetics. You can download one free from: http://hoadley.net/options/strategymodel.htm

Why is this useful? To fully understand the strategy proposed, to simplify strategies, extra flexibilty, minimize margin.


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## wayneL (30 May 2008)

The first synthetic strategy I want to show I won't give the name of till afterwards (for reasons that will become obvious).

With XYZ trading at $80 it is constructed thus:

Long 1 x 80 call (expiry not important)
Short 1 x 80 put (same expiry as the call)

This will give a payoff diagram like this:







Recognise it? Yep, it is the same payoff as straight out long stock, hence the strategy's name, the "synthetic long stock".

The synthetic short stock is simply the reverse:

Long 1 x put
short 1 x call of same strike and expiry.

Why use a synthetic stock?

Less margin than stock
Stock may not be available to short
As an adjustmnet to neutralize greeks


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## wayneL (30 May 2008)

The next one is often quite contentious, the natural short put and it's synthetic.

So if the natural is: 

short 1 x $50 July put

The synthetic is:

Long 100 x stock (or 1000 if using Oz options)
short 1 x $50 July call

AKA *The Covered Call*

Yet I seen it argued that CCs (synthetic short put) are a very safe low risk strategy, and by the very same person that a natural short put as a very high risk strategy with unlimited risk!

WTF?

The risks and rewards are the same, the payoff diagram is the same.

Understand synthetics, it will help you heaps. You'll be able to see straight through any "options education" bozo.


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## wayneL (30 May 2008)

Lets suppose you just bought 100 XYZ shares at 51.75 and you think, hmm the overall market is a bit dodgy, I think I'll buy some puts to protect this position. You select the October 50 put.

So the position becomes:

100 x xyz shares
long 1 x $50 october put

This gives us a payoff diagram like this:






Which, is in fact a synthetic isn't it.

the natural being:

long 1 x $50 october call.

Armed with this knowledge, the question becomes: Why buy stock and a put? Why not just buy the call?

Remember that one, because it is handy when covered call spuikers start BSing.


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## sails (30 May 2008)

Ahha Wayne - one of my favourite subjects - understanding options synthetics. Very valuable and turned on quite a few light bulbs for me...  In fact, to re-inforce the understanding of synthetic equivalents, I would often look at my positions or a new strategy idea and then substitute puts for calls -  or calls for long stock + put - puts for short stock + call, etc, etc.  It really helped put things in perspective.



wayneL said:


> ...Armed with this knowledge, the question becomes: Why buy stock and a put? Why not just buy the call?...





My understanding so far is that it depends on the cost of carry on the stock vs. the interest component in the long call which is usually charged close to the risk free rate. 

I see cost of carry as either interest charged to own the shares (eg margin lending) or the interest one would have received if the funds were still in the bank.  So if one is receiving low or no interest in bank funds, it favours using the funds to purchase the stock + put.  Conversely, if costing high margin lending interest, then  favours purchasing the long call - but see the note below on bid/ask spreads.

The other thing to weigh up is the bid/ask spread.  OTM puts may have a narrower spread compared to the same strike/month ITM call.  On liquid stocks, the bid/ask spread is usually negligible.

Spruikers rarely mention the cost of carry for stock - and yet they so conveniently omit the significant, ongoing cost of interest when recommending highly leveraged positions using margin lending.

A spreadsheet is probably the simplest way to do all these calculations.  For example using an OTM put + stock vs. an ITM call (same strike/month):

LONG STOCK + LONG PUT:
1.  Establish a realistic purchase price for the put (perhaps half way between the mid point and the ask depending on how tough the MMs are!).   
2.  Calculate the total cost of interest (or loss of bank interest) for the full amount of time to the put expiry.
3.  Add these two together

LONG CALL:
1.  Establish a realistic purchase price for the long call.
2.  Subtract intrinsic value (eg. if the stock is at $10 and a $9 call is being considered, subtract $1 from the price of the call).  
3.  No need to calculate interest as it is already priced into the long call.

Now compare the two prices and this will give an estimate.  All things being equal (interest rates unchanhged, no dividends, etc, etc).  Dividends complicate the comparison even further so will leave that alone.

LOL this was supposed to be a quick reply - they're not called "options" for nothing, hey!

So my answer to your question above is - it depends... 

Cheers

PS I'm sure you will let me know if I've left anything out of the calculations!


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## Mofra (31 May 2008)

sails said:


> PS I'm sure you will let me know if I've left anything out of the calculations!



Excellent reply sails, however as someone who only trades Aussie ETOs I'd have to factor in slippage & brokerage into the equation which in turn scews strategy to favour positions with a lower number of legs; our MMs tend to be a reasonably efficient bunch.


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## sails (31 May 2008)

Mofra said:


> Excellent reply sails, however as someone who only trades Aussie ETOs I'd have to factor in slippage & brokerage into the equation which in turn scews strategy to favour positions with a lower number of legs; our MMs tend to be a reasonably efficient bunch.




Yes, I agree Mofra.  It was what I was trying to get at when suggesting finding a "realistic" price for the option legs.  I traded Aussie ETOs exclusively until early this year, so I know exactly what you mean.


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## wayneL (1 June 2008)

sails said:


> So my answer to your question above is - it depends...




Here's another "it depends" situation:

I remember discussing the use of DITM XJO options as a proxy for protected mutual fund purchase.

Using SP 500 instead:

If using SPX options, the DITM call options will do the job nicely.

But if using SP futures options (or ES) You can buy the future + the WOTM put (synthetic long call), and it becomes a SPAN margined position and subject to much less capital use (but subject to margin call).


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## sails (1 June 2008)

sails said:


> LONG CALL:
> 1.  Establish a realistic purchase price for the long call.
> 2.  Subtract intrinsic value (eg. if the stock is at $10 and a $9 call is being considered, subtract $1 from the price of the call).
> 3.  No need to calculate interest as it is already priced into the long call.




LOL I did leave something out of this one - your last post triggered the memory, Wayne. Anyway, due to reduced capital requirements of the long call, the balance of funds not required to purchase "long stock + put" would remain in the bank and earn interest.  That's if comparing same quantities.

Actually, interest (cost of carry) is a fascinating subject especially when looking at calendar type spreads with both puts and calls.  It not only affects option pricing with time but also with strong price moves.  Food for thought...


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## sails (1 June 2008)

wayneL said:


> Here's another "it depends" situation:
> 
> I remember discussing the use of DITM XJO options as a proxy for protected mutual fund purchase.
> 
> ...




On the subject of buying DITM calls - when I first considered that idea, I thought the put/call skew simply meant the puts had a higher IV level vs. the calls regardless of strike price.

I later discovered that it's the strikes below the stock price that have the increased IV and affects both puts and calls.  Didn't pick it up at the time as WebIress didn't have the option IVs available in spreadsheet view.

Have posted a spreadsheet from the TOS platform with NDX June08 options as it clearly shows the strikes below-the-money are definately higher in IV than the strikes above-the-money.  The horizontal red line is at-the-money and have outlined the IV columns.

Thought I would point this out should anyone else have the same misconception as I did.  While the strategy itself is OK as a proxy for index related managed funds, care would need to be taken during times of high IV where the below-the-money skew could be quite significant.

BTW - I took this snapshot today, so the option pricing is based on after-hours.  This probably explains some of the other noticable differences between the puts and calls of same strikes.


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## Vondelpark (1 July 2008)

Hi Sails,

Just joined up to the forum and have a taste for Options again (after 4 years complete detachement from them).  I notice you folks have an extensive knowledge of options and associated stuff and I just want to plead my ignorance of the Australian market so please do excuse me for it.

Sails -  from the chart above I was having a little looksy and found this thread very interesting.  I have a good story about Option Synthetics and how you can blow up your company being too long synthetic short puts (no I didn't do it but I saw some people who did and went close to doing) but will save it for later.  

Looking at the IV's from the stock you highlighted sails (I am anticipating it is an Australian stock???) I noticed that it seems to run skews that I was familiar with in europe = meaning +ve put skew, -ve call skew.  Is this the common theme in Australia?  Do most / all options markets here generally run option IV's this way on equities?  If you are or have traded, if this kind of skew consistency does happen here in Oz, do traders run fixed crux pricing models or do they operate floating skews???

Sorry about the bombarding of questions, but very interested to see how the domestic market works.

Synthetics are such a great tool for traders and when I learnt about them, it was drilled into me constantly. 

Looking forward to babbling about options again.  The only greeks I have been involved with in the last 4 years have been fetta, homous and spiro the local corner store owner.

VP


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## sails (4 July 2008)

Hi Vondelpark - glad you have found some interesting info here at ASF!



Vondelpark said:


> ... Sails -  from the chart above I was having a little looksy and found this thread very interesting.  I have a good story about Option Synthetics and how you can blow up your company being too long synthetic short puts (no I didn't do it but I saw some people who did and went close to doing) but will save it for later.




Sounds interesting.  Usually the synthetic counterpart to a short put is a covered call provided the short put strike/month is the same as the short call strike.  Quite mystified how one can be "long synthetic short puts"...  Perhaps you could elaborate?



> Looking at the IV's from the stock you highlighted sails (I am anticipating it is an Australian stock???) I noticed that it seems to run skews that I was familiar with in europe = meaning +ve put skew, -ve call skew.  Is this the common theme in Australia?  Do most / all options markets here generally run option IV's this way on equities?




No, it is a US index called NDX (NASDAQ-100).  Can't get nice tables like that for Oz options.  IB may have them by now, but my experience with IB and Oz options wasn't pretty so not with them anymore.

In my experience, these skews are common in index products to varying degrees including the Oz XJO options



> If you are or have traded, if this kind of skew consistency does happen here in Oz, do traders run fixed crux pricing models or do they operate floating skews???




I haven't traded the XJO much at all except for using it as a proxy for managed funds some time ago.  That's when I realised that the skews were actually more to do with being above or below the market (as explained in a previous post).  As index products may have dividends factored into their option pricing, the skew can appear to be a put/call skew due to the dividend increasing the price of puts and decreasing the price of calls.

Sorry, no idea with the pricing model question.



> Synthetics are such a great tool for traders and when I learnt about them, it was drilled into me constantly.




Yes, totally agree.  IMHO, understanding synthetics goes a long way to putting the jigsaw pieces of option pricing in place.

Cheers


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