Hidden Assumptions in Option Pricing
Here was my response yesterday to Landsburg’s discussion of option pricing. From the conclusion:
Landsburg’s discussion of option pricing is fine, interpreted correctly. But whether he realizes it or not, his “lesson” is very misleading. All he has done is show that certain prices must bear a particular relationship to each other, lest arbitrageurs exploit a pure-profit opportunity.
The problem arises when people read too deeply into the significance of these results. For example, one could use an analogous argument to show that “all we need” to price stocks is to look up the interest rate and the price of a call option. We might erroneously conclude that no investor ever needs to worry about what the stock will actually do in the future.
Yet that is absurd; of course investors and speculators in the real world need to form expectations about the future levels of stock prices. It is the seductive elegance of the entire “Efficient Markets” approach that led Landsburg to suggest otherwise.
The nicest compliment I got was this:
This is of course exactly right, and (as I’d expect from you) exceptionally well put….Thanks for posting this. Your penultimate paragraph is perfect.
And the author of that comment was…Steve Landsburg. Which made it all the more ironic, when others in the discussion thread told me I had misunderstood Landsburg’s argument.
(Something similar happened at EconLog when David R. Henderson agreed that my criticism of one of his posts had been right, and so he retracted his claim. I really am nonplussed when this type of thing happens. I didn’t realize it was possible to resolve an internet argument. Most of the people I debate with are like soldiers on Bataan.)
“Most of the people I debate with are like soldiers on Bataan.”
Insofar as we are the victims of or the purveyors of relentless abuse and inhumanity?
The fact that I sincerely ask this is a hint at why resolution is so rare 🙂
I don’t know – there are instances where this would happen, but anyone that would change their mind over the course of a comment thread probably hadn’t really thought things through sufficiently in the first place. Which is good – those are precisely the minds that should be open to change. So long as stubbornness is a function of thoughtfulness and not a substitute for it, it’s probably not the worst thing in the world.
Which is not to say that other minds shouldn’t be open to change.
Perhaps I should have said “those are precisely the minds that should change with higher frequency”.
In case you hadn’t seen this:
http://xkcd.com/386/
“I didn’t realize it was possible to resolve an internet argument.”
Ha! Classic quote
“The problem arises when people read too deeply into the significance of these results.”
Yes, that is in fact the problem. His example was a simple binary outcome with all known variables. I n that case there is a correct option price. In the real world there isn’t.
You agree with that, right?
I’m not sure what you mean Jon. Landsburg assumed we knew what the two possible outcomes would be (which is unrealistic), but he thought we didn’t have to know the actual probabilities (which is realistic). But the point of my article was that even on his own terms, it’s not right. And Landsburg agreed with me, so take it up with him. 🙂
You just take on the pussies.
“I didn’t realize it was possible to resolve an internet argument. Most of the people I debate with are like soldiers on Bataan.)”
Joke.
Bob,
Bataan line. LOL.
Daniel Kuehn,
Great cartoon in your third post.