Wednesday, March 22, 2006

A look at derivative trading before Black and Scholes.

In a forthcoming Journal of Finance piece, Moore and Juh examine how options were priced 60 years BEFORE the Black-Scholes formula. They find that when markets were competitive, the pricing errors were about the same that we find today!

Summary: Previous research on the efficiency of option pricing is mixed. This may be because of poor data (example monthly data) or actual mispricing.

In this paper, Moore and Juh use option data from South African markets (the article contains an interesting history of these gold-dominated markets as well!), and find that while investors sort of "got it" they did misprice some and that this mispricing seems tied to the degree of competition in the market.

Specifically it appears that investors overestimated volatilty somewhat. For instance from the section on option pricing:
"Of the 112 stocks in our data set, 84 had more than half of the options quoted on them overpriced relative to Black-Scholes model prices (including 18 stocks forwhich all options written were overpriced)...."
As a percentage, this mispricing seems to be tied to market competitivenes:
"Our results suggest that findings of option mispricing that rely on a broker’s quotes are quite sensitive to the competitiveness of the market in which the broker operated. It is possible that differing levels of competition in the option writing market can explain the divergent findings of Boness (1964), Kruizenga (1964), Black and Scholes (1972), and Kairys and Valerio (1997)."
Of course in today's market we do not always get things correctly either and the authors compare the pricing errors of today with those of the earlier period. The finding? The errors are quite comparable. In the words of Moore and Juh:
"Comparing these warrants to derivatives trading between 2001 and 2003 on the same exchange and using the same methods to compute volatility, we find that early twentieth century investors mispriced in a comparable way using a historical measure of volatility and outperformed modern JSE investors using a perfect-foresight measure of volatility. Development of the modern theory does not appear to have improved the performance of South African investors."
and equally important (maybe more so) after showing that the mispricing was a function of the degree of competitiveness in the market:
"...these results suggest that a competitive market, whether through trading of derivatives on an exchange or competition among rival brokers, has been more important in driving derivativeprices to fair values than the development of a formal derivative pricing model...."
Cool paper!


Derivative Pricing 60 Years before Black-Scholes: Evidence
from the Johannesburg Stock Exchange by LYNDON MOORE and STEVE JUH. This review was based on a Northwestern University working paper. The version that is forthcoming in the JF is temporarily available here.


whiteline said...

BS-formula is a powerfull thing, but usualy i used linear aproximate from yesterday prace with impied volatility.

trading guy said...

It's funny how simple the Black Scholes model is. Considering it just uses basic stats to predict a future value. The paper definatly shows that the Black Scholes model and options trading don't always agree. Good old human error will always make sure the markets can never be efficient

Swogger said...

Can anyone help me in arbitration, or sensible hedging using Stock options. (The last time I had read about arbitration was in a pdf article known as Stocks Made Simple does anyone know where to find this article). If so please let me know regards