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Guest Post: How Options Should Be Valued
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options have gone far away from their original purpose...
despite the emasculated, effeminate, politically correct selection of pronouns in the article, it is thoughtful and worthwhile. it also fortifies my less mathematical aversion to black-scholes - something incubated in a university " so your graduate students can get jobs… " which doesn't need to track reality - at least not at the margins....but it is at the margins where money and history are made.
questioning sacred cows is a sign of a healthy society.
The formula is just a necessary part of the trading environment. It has no basis in scientific reality. So when realty bites, it bites harder.
HAVE A FRACTAL TRADING DAY
http://williambanzai7.blogspot.com/2010/09/have-fractal-trading-day-redu...
Great article. Thanks for an interesting read.
Superb post.
thanks much! perhaps you could lend a bit of your method to the HFT bashing brigade.
The guest post was in general very well-written, and for that reason a real pleasure to read. I must admit I am having trouble understanding why it was written.
Selling uncovered call options gives one greater economic downside than buying call options does. This is not new news. That said, selling call options does not have fatter tails than buying call options. It is exactly the same 'risk', just with a different sign.
The poster's rejoinder appears to apply to any aspect of selling naked optionality. This would, of course, include selling stock short, purchasing a house in a recourse state, and double so if you are using an adjustable rate mortgage (the "option" you are buying is not an option you are buying on your house but the fact that you sold a put on your house financed by your other assets; and you also sold a call on interest rates). In addition, you should never buy bank debt, because banks effectively sell puts on assets as their main business model in return for interest payments (so you buying bank debt is selling puts on the assets/business underlying the bank's loans). In addition, you should never buy a bond period, because you are shorting the value of money (vs what money can buy (effectively selling OTM calls on inflation)). That would probably mean one should not put money in a deposit account, or otherwise lend it. The logical conclusion is that one should always have all one's assets tied up in equity or call options, because that is the best way to avoid the downside to outlier risk.
The idea that options should be carried at different values on the balance sheet is cute but not very different from the concept that they should both be marked to the same price and should have different reserve methodologies. Which, in many cases on Wall Street, they do.
One assumes that the reason why it is important to address this issue is because of the "insanity" of the Wall Street mafia. One forgets that it was not selling puts or calls which got Wall Street in trouble. It was owning assets, being very highly levered, and being somewhat unaware of what markets can do to existing market mechanisms (i.e. the repo market). It was bad risk management.
All told, I half wonder whether the poster wrote this with tongue firmly planted in cheek. If not, I encourage more of this mindset because it is the inflexibility and fear of risk management boundary conditions that leads to this kind of thinking. That leads to all kinds of opportunities for more flexibly-minded people.
wow. you present some great alternative ways of looking at everyday transactions in the framework of options/call/puts, etc.
i'd never really thought of those interactions in those terms.
great stuff. tnx
The problem with Mr. Cloud's dogma is that it is dogmatic. People are short optionality in all kinds of ways - all you have to do is denominate the asset in terms of what might happen. Hell, getting married is for many people the equivalent of selling calls on their sex life.
classic... :^), so what's the black-sholes hedge on that?
like i said, i never really looked at these things through that lens before. i like the different perspective.
cheers.
Selling *any* option naked is such a complete stupid fucking thing to do, I can't even begin. I have personally seen the fruits of such a 'low hanging fruit' strategy, and let me tell you - there are plenty of broker groups and individuals that have had to eat "Black Swan" pie in a big way.
Say hello to your new blowup!
Honestly, the mind boggles that the unlimited risk is even comparable to the crappy limited profit you gain on the premium.
Agree with the 1st part of the post. However, in times of mean reversion (have we moved at all since Dec '09?) the almost limitless premium you can earn on vol spikes is attractive, especially for the big money who can go in and sell premium to the big boys.
Let's say I want to buy MSFT at $22 a share in order to own the stock over the next 5 years. I don't want to buy it at $24 or $23. Selling a put is like putting in a leave order to buy. If I am willing to buy at $22, why would I not be willing to sell a Jan $22.50 put at 70cts?
Two letters. "BP".
In fact I generally agree and I'm working on a strategy to create "synthetic dividends" from dividend stocks I don't (yet) own (and may never).
And then I will probably turn around and sell covered calls if the put gets exercised.
But - I'm still working on making the strategy "BP proof" (or at least BP resiliant).
This will probably involve spreads...
An amusing article. The mathematical analysis is wrong. Call options do have a finite value, but it is larger than the Back-Scholes value. I have found making money trading options to be difficult, not for any any esoteric reason, but because when I buy an option at $1 and it triples, the bid-ask is often $3.00-$3.40, rather than $3.18-$3.22, where I could make money.
In a former occupation, I was a pricing actuary. There was a product called group stop-loss, in which I had to predict the possibility that insurance claims for a group of people would exceed the predicted amount by 10-25%, and how fat the tail was. Since medical inflation is very volatile, plugged that volatility into the formula. As a result, we never sold any, as someone else always charged a naive (Black-Scholes) price. But there was always a price at which I was comfortable selling, as no sales, no business. Of course, that means I was acting as an owner.
There are no easy mathematical ways to figure the appropriate options values. However, given enough data and a creative mind, it is possible to hang the number into a range. In some cases, the actual bid-ask gaps do leave arbitrage possibilities. For the options buyer and seller, it means having lots of capital, so that if you have $1,000,000, options trading might net an extra $80,000-$200,000 beyond just buying and selling the individual stocks and commodities. Because of the wide bid-ask, it does mean patience and discipline.
Hey bIlluminati, I was wondering if you could explain why the mathematical analysis is wrong?
see my post at the bottom of the page
Great stuff.
Not sure there was any need for the 'if' clause.
niederhoffer, bitches
Confused junk. Amusing, historically informed, but junk. I'm sad Dr Cloud isnt in the market for options, I'd love to trade with him and his 'naive, simple minded' questions. Let me put his mind at ease, and then maybe sell him a bridge.
Not true. Some models that contain fat tails can show infinite moments for some parameter values, but not all parameters in all models, and almost never the second moment ie variance. If Dr Cloud reads this please provide references (Mandelbrot?) that he explicitly avoided doing in the article, and I'll provide mine. Not sure what "effectively infinite" means too, though maybe a smart philosopher like Dr Cloud can explain that one to a dumb mathematician like me.
Now, say I am worth $1M USD. I sell a call option on 1 MSFT share. Yes I can go bankrupt, but its highly unlikely MSFT goes to +1,000,100. If I sell a put option on 1 MSFT share I can not go bankrupt even at MSFT = 0. Of course I can sell that uncovered put.Saying I cant sensibly sell the put is like saying I cant sensibly buy the stock. Its just wrong.
Now do you see why large brokerage houses can make tight prices on options? What does Dr Cloud think senior equity derivative traders, desk heads and equity risk managers at IBs do all day? They make sure no hot-headed trader puts the firm at risk. Thats why Kerviel at SocGen was such a shock and why his bosses got fired as well as him. They didnt do their job.
One point follows from this, which is how to account for tail risk on large (eg corporate derivative) positions when the market is only available for small size. Usually the senior traders and risk managers will agree to value each large position at a level where it can be sold. In listed markets this is pretty easy. In structured OTC markets it is not, and traders always hate it, but it's very much necessary. However there isnt much theory involved here and buffers vary between firms and with the business cycle.
So you end up with a a world showing tight markets made by large firms who cannot go bust on each individual trade. And you need a framework to understand, regulate and protect for fat tails. We have the first, I dont think we dont have the second. Banks use conservative buffers to make up for the lack of theory.
In terms of pricing including fat tails, for a smarter and more useful approach than the philosophical nonsense above, anyone interested can google option pricing with Levy distributions or Student distributions, or search on the leverage effect.
NB I am discussing equity derivatives, not credit derivatives. Equity derivatives is a much more mature market, it had its crisis way back in 1987, survived and learned from it. Credit derivatives markets may or may not evolve similarly, but either way they are currently still naive, as we all learned. Maybe Dr Cloud could be a credit derivatives trader, he might fit in better in that world than in equities where people know what they are doing.
+lots.
The issue for large (corp deriv) positions shouldn't be the difference between whether the option is listed or it is not. If market conditions are such, and the position is large enough so that it becomes "an issue", "listed vs OTC marking policy" is no longer the problem because the listed market becomes irrelevant (which I think leads to your point about leverage effect). If you REALLY need to get rid of it, the price is substantially lower than if you didn't NEED to.
As to 'pricing' using a leptokurtic distribution... nothing you do there will mean that the reserve+pricing methodology will be conservative enough when really fat tails show up.
In the end we will not be able to regulate or protect against failure due to fat tails. That's what fat tails are for. Outlawing inefficient human behavior is unlikely to fly...
I'm starting to think that if one has any experience whatsoever in the field of what some blowhard amateur poster writes, and one points out where the poster doesn't measure up, it is a badge of honor to get junked.
Thank you for posting this interesting paper.
I enjoyed learning about Knight and how you connected his theories to the extraordinary stability (and sustainability!) of ancient Egypt.
Let me suggest to you that brokers, traders and marketmakers do not rely on Black-Scholes valuations to any material degree. Yes they are helpful approximations, both absolute and relative, but actual decisionmaking is based on experience.
A short call is essentially identical to a short stock position. If a theory holds that you should never short calls because of inability to calculate fatness of tails, then you can never short stock. Then you can't have marketmakers who cannot make markets without being short when their customers require it.
Thank u, i found this for a long time.
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The maths is wrong - in likely a lot of ways; but lets start with the obvious:
"As for d2, it’s just d1, or in other words infinity, minus
infinity times some insignificant number, or in other words infinity minus infinity, which is
zero. So we can pretty much ignore it. The main equation is just then:
C(S, t) = SN(d1)
As I just established that d1 is infinite, this means it’s actually:
C(S,t) = infinity
That is, unsurprisingly, with an infinite variance, the Black-Scholes value of a call option is also infinite. "
Obvious errors in the maths are: 1. If d2 were 0 as stated above the N(0) = 0.5 not 0 as the paper says. 2. If d1 is infinite then N(infinity) = 1 not infinity as the paper says Less obvious errors: 3. d2 is not 0 as sigma tends to infinity, it is also tends to infinity 4. If sigma is infinite or undefined then the process does not follow a brownian motion so the underlying assumptions of the model would not apply - the black scholes formula is not relevant in this case. There are probably more; but is it worth taking an order of magnitude check? the paper is basically saying time value in options has infinite value. If i am a cleaner with my own company earning $10 an hour with a list of clients; is a call option with one day to expiry on my company really worth more than all the rest of global wealth put together?