- Your history
Monday's Sideshow Bob
Over the weekend, I had an interesting conversation with a friend of mine on today's surrealism reigning on financial markets. Referring to a previous posting - "Dude, where is my yield" - we quickly altered to another issue with the 64,000$ question at the end : If interbank market rates are manipulated (rigged libor) and if government bond rates are in 0%/negative territory, we have a problem with option & derivative pricing as well. And mind you, options and all kind of derivatives (interest rate swaps etc) are being traded in mass volumes and in many cases OTC (over the counter), meaning in a non-standardized or "à la carte" fashion :
Now let us turn to the basic Black & Scholes Formula, being awarded a nobel in 1997 and showing its explosive merits in 1998 (LTCM debacle) :
The most fundamental criticism up until today comes from Nassim Taleb (or more precisely from his tutor Benoit Mandelbrot) pointing out that the normal distribution does not apply in financial markets. The tail risk of the probability distribution - or things which are not supposed to happen in a zillion years - do happen and happen more often than one imagines : the so called black swan (>3 or 5 sigma events) of the normal distribution is in fact an ordinary grey pigeon. This induced Taleb to play the markets by buying far-out-of-the-money options because they are cheap, meaning mispriced. Next to this, we also have an additional set of problems when using these kind of models
1) the fact that we assume that volatility is constant over time : a very questionable assumption
2) the measurement of r or the risk free rate : currently a tricky calculation
Now let's take a look at the second issue here brought up by my good friend sideshow Bob. If r = 0% or negative, it has an impact on the option price. For example, suppose r = zero (slightly negative), it is 1 element towards the future which might give me the idea of having a free ride when buying long term options (rates can only go up and hence can only push the option price up). Now 0% or negative interest rates might be the ultimate proof of risk-free, it can hide more than we wish to discover, and worth a debate I believe. And these interest rates are important because they have an impact as well on implied volatility, another factor determining the model : when r changes frequently over time, so does implied volatility on different asset classes.
Are Sideshow Bob and me making too much of a fuzz about this. May be. Should we just accept the theory and models running day-in day-out ? Or as Humphrey Neil (contrary opinion) once stated : The crowd is actually correct for a substantial amount of time. It is at turning points in history that the majority get things wrong. I on the other hand take the more cautious approach advocated by Sideshow Bob. Or as he once warned Bart Simpson : Watch out Bart, no children have ever meddled with the Republican party and lived to tell about it !
http://www.oocities.org/televisioncity/set/2800/bob/quotes.html
13 Comments
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Kris Van der Plas
On 23 Jul, 2012
Hi Christof,
Been a fan of Taleb ever since he wrote his book 'Fooled by randomness' (preceeding 'the Black Swan'). Mandelbrot is (just like Turing in a previous blog) a mathematician who altered the world through his work. His fractal "discovery" set off others to work on chaos. For the life of me I can't imagine why students don't like mathematics. Maybe because the teachers don't explain how it affects our daily lives?
As for your above skepticism, I don't trust the normal distribution either. As Taleb so profoundly argues: it is actually only one specific case that has a limited field of application. To stay with Taleb, we've entered extremistan long time ago...
So,the formula above to me is a too narrow view of reality. And by the way, didn't one of those Nobel price winners (Scholes?) set up a hedge fund using his own formula as basis just to go belly up a couple of years later?
See ya!-
christof Govaerts
On 23 Jul, 2012
@Kris
Always put your trust in some one with a heathy interest in aviation (and certainly flight attendants)
See you Kris
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Theo
On 23 Jul, 2012
So what happens to the Greek on both call and put options if r = 0?
And how r = 0 is the "risk free rate" if you are loosing money?-
christof Govaerts
On 23 Jul, 2012
The way I see it, the lower r, the lower the option price becomes ; my colleague Nikolaas did a check this morning and apparently in the case of Cox/Ross/Rubinstein and Black/Scholes models, negative spot interest rates can be put into the equation.
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Nacht Und Nebel
On 23 Jul, 2012
Black and scholes was perfect for a spreadsheet :)They never toke the VIX into the equation.Neither the debt ratio nor the free cash flow or the pay out ratio of the company .Strange.Spain is in bigger trouble now then when interest were 15 percent over there
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Nacht Und Nebel
On 23 Jul, 2012
Another problem with black is 'gravity'.The Black-Scholes model also assumes stocks move in a manner referred to as a random walk; at any given moment, they are as likely to move up as they are to move down.That isn't so ..How big is the change that tomorrow spanish stocks go from a bear market into a bull market?Also stock prices fall about 3 times faster then they climb...
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christof Govaerts
On 23 Jul, 2012
@All
Not entirely and that was also Mandelbrot's merit to put Edwin Hurst into the picture with his exponent showing random walks (0,5), persistent (0,5-1) and anti persistent (0-0,5) time series
http://en.wikipedia.org/wiki/Hurst_exponent
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christof Govaerts
On 23 Jul, 2012
Sorry NuN, you are right on the random walk hypothesis not being applicable 100% (far from it by the way)
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Nacht Und Nebel
On 24 Jul, 2012
No need to say sorry.:)
As far as I am concerned the reason why you have become so good is that you have developed an instinct(by hard work) for this and not by some crappy formula that doesn't work but most traders believe in.
so r is current risk free interest rate and t time remaining so the interest rate is a constant even for a LEAP ?My God.No wonder they went broke:)
What happens if you excercise the options before expiration date.Lately IBM and Google became " volatile by machines" how does Black Scholes deals with this?
How does Black Scholes deals with the prices differences in call and put options
How does Black Scholes deal with 2 the same intrinsic companies.One has a share price of 500 S and they other trade at 5S.Why is there a difference in the option pricing yet the dividend is the same,the debt ratio and the free cash flow.
Why is there a difference in option pricing between 2 countries even if these 2 countries have the same interest rates and all the rest of the variables are the same?Why doesn't include black scholes open interest?
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christof Govaerts
On 23 Jul, 2012
@All
And because I love this man's quotes so much
http://www.imdb.com/title/tt0701045/quotes -
Theo
On 23 Jul, 2012
@ All
The most "accurate" measure of the economy is the 2-year sovereign bond. >1 year and < 5 years... (there is a reason there are such things as 5 year plans - they are in fact 1 + 2 + 2 = 5 years)
This is exactly the issue at the moment with the variable r in the calculation (from which the variable v is then derived)
The hypothesis says that you cannot predict future prices from studying past prices. Therefor in theory you cannot outperform the market without assuming additional risk.
In practice, in times of higher volatility (which happens first without adjusting the r ) and lower rate of return, you can actually outperform the market by not assuming the risk at all during that period in between or by moving during the time of the option (before it expires). So yes, the option price drops simply because the demand for options goes down and vice versa.... Well that's what I think. But I might be wrong.
There is no price for something nobody wants because there is no market for it at any price when volatility goes up without change in r. You need a real speculator (or CB) to come in and clear it off the table and sit on it. When r later goes to 0 it is clearly because the market has been manipulated by the actions taken by the Central Bank and not because that is the actual risk free interest rate.
I always remember my Corporate Finance professor (PhD in CAPM) telling us that r in CAPM is not the same concept as in options. -
Christof
On 24 Jul, 2012
@theo
About 1 2 and 5 : my colleague and I had a similar discussion this morning from another point of view but it comes down to the same. When you look at how curves react these days when the crisis intensifies, you see quite some volatility on the short end (2 and 3). And when the curve inverts, it's usually bad news and an omen, it was the case with Ireland, Greece, portugal and Spain is also heading towars this territory.-
Theo
On 24 Jul, 2012
@ christof
I don't know if the thing above makes much sense as I had to modify it a few times... it was too long ;-)
I know the (financial) options calculation formulas are binomial... so that's that. And they assume normal distribution. And we all know what we know about that.
I work mostly with real options and use fuzzy logic and fuzzy numbers. It's like constantly simulating a stall. (you graph above looks like the lift curve http://en.wikipedia.org/wiki/File:Lift_curve.svg )
It was while doing Advanced Finance during my MBA and learning how to calculate OTC options that I noticed the 1+2+2... and lost interest in financial options all together
I think your 2+3 is the same but you take the stable 2 first and then 2+1... which indeed would make the 3 year more uncertain (unpredictable outcome) than the 2 year
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