Strike Adjusted Spread

asd · Post by **asd** » Sat Dec 11, 2004 1:54 am

Could someone please tell if SAS (Strike Adjusted Spread) is used to derive trading strategies in practice, or how commonly if it is used ?

( It appears that choosing an option based on the principle of Risk neutralizing the historical distribution would be profitable if a stock movement was trending in one direction, and would lose more money if there was a reversal after the option was chosen. I don't know if this interpretation is correct! Will the SAS work even if there was a reversal in stock movement?? )

Many thanks in advance!

FDAXHunter · Post by **FDAXHunter** » Sun Dec 12, 2004 4:33 pm

I'm not quite sure I know what you are talking about, but I think I've got the basic idea that you have.

You're thinking about that if you choose an inadequate window of historical returns, you will see a skewed distribution due to a trend in the dataset, correct?

SAS is about deriving the relative value of an with regard to it's historical value, which is derived by simulating the instantaneous hedging results of a multitude of theoretical options on the underlying, then deriving the RND that replicates these prices (or you can use another method, like entropy minimization between the current implied RND and the historical distribution, which is what GS do in their paper on SAS).

If you are sample is (for whatever reason, there are many) not reflective of the future path, then you always run the danger of overestimating/underestimating volatility/skewness/kurtosis.

If there is a trend reversal, you will see a skewness reversal... and you be phucked.

apine · Post by **apine** » Sun Dec 12, 2004 4:41 pm

do people use this type of method in practice (asd first question)? how would this compare to say, calculating ranges for realized skewness & kurtosis. then use that to come up with a few vol curves based on a gram-charlier expansion.

also, is there a reference on how to perform the entropy minimization for the mathematically challenged? if i recall correctly, the gs paper discusses the method but does not go into detail on how to actually work through it.

FDAXHunter · Post by **FDAXHunter** » Sun Dec 12, 2004 5:02 pm

There are even some specialized funds who try to trade skewness/vol (not many people try trading kurtosis... for obvious reasons) on the historical distribution.

Not many do that well with it, AFAIK.

The results should be similar to that of something obtained by Gram-Charlier? Rubinstein provides a better method however.

Didn't find much for a tutorial on cross distribution entropy minimzation, but this totorial deals with entropy and option pricing in general, so that's a good starting point, I think.

http://finance.wiwi.uni-karlsruhe.de/Lehre/SemOpt/Entropie/Content.html

TonyC · Post by **TonyC** » Sun Dec 12, 2004 5:06 pm

refresh my memory, ''entropy minimization'' amounts to minimizing the absolute values of the diffrence twixt the model's values and the observed values . . . similar to how regression is minimizing the square of the diffrences twixt the model and the observed values

have i got this right?

apine · Post by **apine** » Sun Dec 12, 2004 5:13 pm

thanks for the link.

i have thought about how to effect a trade trying to realize skew differences, but have not yet researched it. i think it would be very path dependent. have you looked into this? is this something that you make money using the portfolio effect or try to?

in other words, presume one knew what the three month realized skew and kurtosis were going to be. could one then construct a position that "arbitraged" that? would one need to know what vol would be realized? is there any existing work on this? i have to think that it would be constructed as some sort of wing spread to avoid holes and to make things fairly neutral. i am thinking of vanillas, but there may be exotics that cover this.

i realize my questions may not be fully formed, but this has not been on my front burner. it is one of my "to-do" projects.

Martingale · Post by **Martingale** » Sun Dec 12, 2004 6:55 pm

I think the way people doing entropy in pricing is like this, you got some sort of probability distribution P (either from historical or some sort of prior distribution you have in mind), But from market price you see a different distribution Q, what's the relationship? Well, in some sense, Q in cases can be think of the minimal entropy measure(out of the risk neutral measures) relative to P (this is usually in academics done when there is incomplete market, you have infinitely many martingale measures, the minimal entropy measure is one way to pick), this actually is equivalent to maximize some exponential utility function as shown by some dudes ( Fritelli(spelling?) and Avellenda etal)

asd · Post by **asd** » Sat Dec 18, 2004 8:10 am

FDAXHunter,Apine,TonyC,Martingale, Thanks a lot for your valuable comments! Smiley

I tried to start an implementation of the model as mentioned in http://finance.wiwi.uni-karlsruhe.de/Lehre/SemOpt/Entropie/2321.html

However, it looks like the equation 2.37 does not even converge, and is monotonicaly decreasing with decreasing gamma.

[img]/beta/User%20Files/33/MathML-Equation-1534.gif[/img]

eg. I used the returns for Freddie Mac and assumed r=1.01 (a dummy approx.)

I am getting the following results:

gamma = 0.50000

tmpsum = 55.848

>> entropy_test

gamma = 0.40000

tmpsum = 50.300

>> entropy_test

gamma = -0.40000

tmpsum = 21.804

>> entropy_test

gamma = -5.4000

tmpsum = 0.12232

gamma = -55.400

tmpsum = 2.0329e-23

The sum is thus decreasing as gamma is being decreased.

Could someone please point my mistake?

Many thanks in advance.

asd · Post by **asd** » Sat Dec 18, 2004 9:57 pm

It seems that "1" should be within the parantesis in eq. 2.37, and then it is able to get a minimum.

Regards

granchio · Post by **granchio** » Sun Dec 19, 2004 9:24 pm

[i]in other words, presume one knew what the three month realized skew and kurtosis were going to be. could one then construct a position that "arbitraged" that? would one need to know what vol would be realized? is there any existing work on this?[/i]

A v. bright guy I knew did some work and came with a "skew swap" a bit along the lines of the varswap. This was sometime ago, and I cannot release it. Just to say it is doable. Oh I also think it is not very useful.