11
Mar 18

## Option chain and efficient market hypothesis

Figure 1. Option chain for AAPL with 26 days to expiration

In charting software, option prices for a given stock and expiration date are given in a table called an option chain.

## Option chain description

1. The light colored column in the center contains strike prices. They take discrete values. The tick (the step between two nearest strike prices) depends on the stock price. It is large for expensive stocks and small for inexpensive ones.
2. As one can see in the upper right corner, the current price of Apple stock is \$176.94. This would be the theoretical at the money strike. However, since strikes can take only discrete values, the one closest to the current stock price is said to be at the money. It is \$177.5. At this value the option chain is divided by color in two parts: with in the money calls (the upper part of the chain) and out of the money calls (the lower part).
3. The leftmost column shows the open interest, which is the number of options currently in circulation. You can see that for the 155 strike the open interest is zero.
4. In column 2 you can see the trade volume for the day.
5. In the next column you can see the bid size (total number of buy orders).
6. Next is the pair (bid price, ask price). The bid price is the highest of all bids across all buy orders. The ask price is the lowest of all ask prices across all sell orders. For example at the 175 strike the bid is 6.80 and the ask is 7.00. If you want to buy a call, you can submit a buy order at the midprice (the average of the ask and bid), which is 6.90, and most likely, your order will be filled. If you think the stock will quickly grow, you can be more aggressive and buy at the ask.
7. The fifth column contains ask sizes.
8. The sixth column shows the implied volatility, the king among option price determinants.
9. The next three columns contain option greeks, which are derivatives of the option price with respect to various variables. We'll talk about them separately. The look of the option table depends on the software and user's choices. I am using the Trader WorkStation from Interactive Brokers, and my option chain doesn't contain one more greek - Gamma.
10. I chose to see strikes within two standard deviations from the current price (see the upper right corner). The option "SMART" means that my broker will automatically choose the best price from several exchanges. The "100" is the multiplier, which shows that one option commands 100 shares of stock, and it implies that the option price listed as, say, 6.90 means that in fact the option costs \$690.

## Efficient market hypothesis

This hypothesis is a standard assumption in Economics. It states that market prices reflect "all relevant" information. The exact definition of the "relevant" information depends on how strong economists want the hypothesis to be. The main practical implication is that it's impossible to make profits in financial markets. I fail to logically connect the statement "market prices reflect all information" with the statement that "it's impossible to make profits". But my main point is not this.

The main point is that economists themselves indicate reasons why the efficient market hypothesis may not hold. One is the cost of obtaining information. The option chain for Apple for each expiration date contains dozens of strikes, and each strike means a separate market, although there is a high correlation between these markets. Multiply that number of markets by the number of expiration dates (weekly options give about 50 expiration dates and monthly options give another 12, that's for one year), and you will see that Apple alone generates hundreds, if not thousands, of markets.

Another reason why the hypothesis may not hold is transaction costs. The bid-ask spread (which is the difference ask-bid)  in the lower part of the above option chain is \$7 and in the upper part is \$50. In the options markets, the transaction costs and the cost of obtaining information will prevent any big player from attempting to capture all profits.

Dare, and you will be rewarded!