My friend Yi-wei and I were discussing today how useful it is to determine the "correct" price of financial securities using theoretical models. The conversation was sparked off when he commented:
It's quite fantastic when the same underlying model can be used to price so many different instruments.
To which I responded:
But I still keep hearing in my head one of the questions you once asked in class about whether market participants price a security according to a certain model because the model is correct, or because they believe the model to be correct. I remember the question was never really answered satisfactorily. You had referred to how options markets existed long before the Black Scholes model (for pricing options) was devised. So how were options priced before the model was developed?
Yi-wei:
I think people priced securities according to arbitrage... B-S is also based on arbitrage... after understanding B-S, it's not too bad a model... but it's a model after all.
Me:
Hmm.. but then how did participants know at what point to say, "I won't pay more than $x"
Yi-wei:
Because if you did, there would be arbitrage opportunities. If you pay less, there would be arb too.
Me:
No I think there is circular logic there.
Let's say the market consists of three participants. Or even just two. A certain security (does not have to be an option) is trading in the market.
I decide it is worth $5.
You agree.
Therefore the market price is $5.
But according to a theoretical model, it is worth $50.
I want to know how the individual participants arrive at $5 or 50 or whatever. Not how they take their cue from the market.
Yi-wei:
Any theoretical framework makes a lot of assumptions. The results (prices) differ to the extent that individuals' assumptions differ. We are all speculators, we speculate on the expectations we have of the future.
Me:
Exactly.. so then it means that the value one arrives at depends on the factors we use in our own mental models.. which may not agree with others' mental models or theoretical models.
So is there a "correct" model?
Or is it simply, "The market says so, so that's what the price is."
I tend to think it's the latter.
After all, take for example, HP's recent stock price movement. Before carly resigned, the price was X. After she resigned, the price was Y. Theoretically, i don't see why there should have been a large change. But the market disagreed.
So I conclude that there is no "correct" price.. only the price the market is willing to bear.
Yi-wei:
Haha.. I have some thoughts on that, but got to go now. Let's chat again after class.
So let's see where this discussion goes. I invite comments from readers and, since I'm sure this topic has already been debated by academics and practitioners, references to any resources on this topic are also welcomed.
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