Twofish's Blog

November 16, 2006

An Austrian theory of Shanghai warrant pricing

Filed under: china, finance, quantitative finance — twofish @ 7:31 am

I’m spending my time right now coming up with a theory of Shanghai warrant pricing and I’m finding that a lot of Austrian concepts are coming into play.

The question is this.  The price of an warrant should be determined by the price of the underlying asset, so in principle the number of warrants available to be sold shouldn’t affect the price of the warrant.  But it does.

The way that I’m resolving the problem uses the Austrian concepts of praxeology and economic subjectivism.  The key idea is that there is no rational disagreement over the probability of the underlying moving in a certain direction, the essential disagreement that causes markets to exist is disagreement over the subjective value of the option payoff.

So you assume a market in which each invididual has a different subjective payoff function.  This can be represented by a family of curves

U(c,x)  = where U is the utility, x is the payoff from the warrant, and c is a parameter expressing risk tolerance.

U has the following characteristics

U is monotonic – more money is better

U(c,0) = 0 – if you don’t lose or gain money, you are exactly in the same position as before

U(0,x) = x  if you have neutral risk preference U is the identty function.

Now we introduce a second function

P(c) is the probability distribution of people with risk preference c

What we know about P is that

area(P(c<0)) = area(P(c>0)) (why do we know this????)

Now what happens in a standard option market?

In a standard option market the number of buyers = number of sellers, and so the equlibrium price ends up where c=0.  This causes the utility function to be set to the identity function which causes the price to end up where standard option theory says it should be.

Where this ends up with a different results is when the market doesn’t clear and there is a overabundance of buyers and sellers.

Question: what implications does this have for market making?  Suppose everything is in balance and then the underlying shifts.  At this point things go out of balance and what has to be done to move things back into balance.

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