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 !