FINANCIAL OPTIONS CRITIQUE

Financial Options Critique

Financial Options Critique

Introduction

The article "Derivative Pricing 60 Years before Black-Scholes: Evidence from the Johannesburg Stock Exchange" by Lyndon Moore and Steve Juh is a very interesting work. Moore and Juh examine how options were priced 60 years before the Black-Scholes formula. Moore and Juh find that when markets were competitive, the pricing errors were about the same that Moore and Juh find today! Previous research on the efficiency of option pricing is mixed. This may be because of poor data (example monthly data) or actual mispricing.

Discussion of Assumptions

Moore and Juh (2000) obtain daily prices for market-traded warrants on the Johannesburg Stock Exchange (JSE) from 1909 to 1922 and utilizing the Black-Scholes (1973) model assess whether the market prices of these warrants were “fairly” priced. Moore and Juh compile daily prices of 15 warrant price series from 1909 to 1922 and a broker's daily call option quotes written on 112 companies' stocks between January 1908 and May 1911.

In this article, Moore and Juh use option data from South African markets (their research 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. (Moore and Juh, 2000)

In this article Moore and Juh describes that few decades back, Black and Scholes (1972) and Merton (1973) showed that one could exploit an arbitrage argument to obtain a relatively simple formula for a call stock option. This result led to the rapid development of a whole range of variations on this model. Finance traders and bankers were interested in the models for providing pricing formulae for an ever-increasing array of derivative financial assets being traded in financial markets. Because these models exploited techniques used in physics (i.e. stock returns follow a diffusion process, In addition they showed that by taking appropriate limits, one could obtain the Black-Scholes formula. Although not stressed in the article, the underlying model used arbitrage arguments to derive new prices, so that the pricing formula was a discounted martingale with old prices acting as probabilities.

Another interesting development was the derivation of the Black-Scholes formula from a discrete-time incomplete markets equilibrium model. (Moore and Juh, 2000) By assuming consumer aggregation, the economy achieved a trivial Pareto optimal allocation and the Arrow-Debreu prices supported the consumer optimum. This was the first representative consumer model where the martingale pricing result was obtained, albeit in a restricted form. In the next decade this general insight was exploited in finance and particularly in macroeconomic representative.

This article is compact. Both authors spend no time on unnecessary derivations. Moore and Juh (2000) analyzed stock markets where agents had asymmetric information, and explored the idea that stock prices could completely or partially reveal private information. These ideas were explored in detail by a number of writers.

Theoretical Framework

This article adds to the existing literature by comparing the mispricing of early twentieth century exchange-traded warrants with the mispricing ...