Twofish's Blog

July 15, 2006

Finally some time to think…

Filed under: china, quantitative finance — twofish @ 3:16 pm

I’ve been quiet the last two weeks because I’ve been totally snowed under getting something to work in my job that pays the mortgage.

But I finally have some time to think….

OK, what am I thinking about you might ask….

The standard option pricing models assume that the stock price goes up and down with a process called Brownian motion.  Basically a lot of little steps.  The trouble is that when you put the standard option pricing models with Chinese options, they don’t work very well (for that matter if you put them into any options they don’t work very well).  The reason that they don’t work very well is that there is a change that the price of the stock will “jump” suddenly, and the basic vanilla option pricing model doesn’t take that into account.

Now this is where the unique China stuff comes in.

In most markets, you can figure out the effects of a “jump” because you have a lot of different options valued at different strike prices.  When you graph those prices in a certain way, you get what is called a “volatility smile” (because the graph looks like a smile).  This smile tells you the effects of jumps.  The trouble with the Chinese market is that you only have at must two options per company.  So I’m trying to draw a curve with two points.  Ughhh….

(The mathematical language for this is that the basic option model assumes that the stock price follows a “Wiener process”.  What I’m trying to do is to use a more sophisticated model that takes into account “jumps.”  This is called a “Levy process.”  The key features of a Levy process is that they are “time homogenous” (the odds of a rise and fall in the market don’t change over time) and that it is “Markovian” (the odds of what happens today depends *only* on the price of the stock today, not what it did yesterday).)
The trick that I’m trying to do is that you actually have more than two points to draw the curve.  You have the prices today, you have the prices tomorrow, you have the prices the next day.  Assuming that the probability of a sudden move in the market stays the same, you should have a lot of points to figure out what the effects of “jumps” on the market are.

Now here is what I’ve figured out so far:

1) warrants in Shanghai are used to make bets on the stock market.  The idea is that if the stock price changes, the warrant price will change even more.  In a Western stock market, people would do this via margining, but that isn’t allowed in Shanghai.  The trouble with this is that the pricing models people are using for warrants in Shanghai I think are totally wrong, and the price of the warrant could act in pretty unexpected ways

2) the Chinese securities regulators are very, very strict about the rules for issuing warrants.  Basically to issue a warrant you have to have the stock in hand.  The technical term for this is called “superhedging.”  It is really expensive, and ties up huge amounts of money, but it is a good idea since the price of the warrants can act in weird ways, and you have to make sure that if anything happens, that the warrant issuer can cover the warrant.

3) the one suggestion I have for Chinese securities regulators is to allow the issuance of warrants with different option prices.  If they do that, you have more data to trace out the “volatility smile.”

4) this comes back to a nasty argument I had on Wilmott a few months back, but I don’t see any evidence that the “no short” rule influences the warrant price, and from a theoretical view, I have a few good arguments to assert that it doesn’t

Some bits of information that people might be able to help me with

1) what do people in Shanghai use warrants for other than gambling?

2) Suppose a graph a “volatility smile” at a certain time and the stock process is “Markovian” and “time homogenous”?  Does this give me the “volatility smile” for all times?

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