Mar 18

Intro to option greeks: delta and its determinants

Intro to option greeks: delta and its determinants

I started trading stocks in 2010. I didn't expect to make big profits and wasn't actively trading. That's until 2015, when I met a guy who turned $10,000 into $140,000 in four years. And then I thought: why am I fooling around when it's possible to make good money? Experienced traders say: trading is a journey. That's how my journey started. Stocks move too slowly, to my taste, so I had to look for other avenues.

Two things were clear to me. I didn't want to be glued to the monitor the whole day and didn't want to study a lot of theory. Therefore I decided to concentrate on the futures market. To trade futures, you don't even need to know the definition of a futures contract. The price moves very quickly, and if you know what you are doing, you can make a couple of hundreds in a matter of minutes. It turned out that the futures markets are the best approximation to the efficient market hypothesis. Trend is your friend (until the end), as they say. In the futures markets, trends are rare and short-lived. Trading futures is like driving a race car. The psychological stress is enormous and it may excite your worst instincts. After trying for almost two years and losing $8,000 I gave up. Don't trade futures unless you can predict a big move.

Many people start their trading careers in the forex market because the volumes there are large and transaction fees are low. I never traded forex and think that it is as risky as the futures market. If you want to try it, I would suggest to trade not the exchange rates themselves but indexes or ETF's (exchange traded funds) that trace them. Again, look for large movements.

One more market I don't want to trade is bonds. Actions of central banks and macroeconomic events are among strong movers of this market. Otherwise, it's the same as futures. Futures, forex and bonds have one feature in common. In all of them institutional (large) traders dominate. My impression is that in absence of market-moving events they select a range within which to trade. Having deep pockets, they can buy at the top of the range and sell at the bottom without worrying about the associated loss. Trading in a range like that will kill a retail (small) investor. Changes in fundamentals force the big guys to shift the range, and that's when small investors have a chance to profit.

I tried to avoid options because they require learning some theory. After a prolonged resistance, I started trading options and immediately fell in love with them. I think that anybody with $25,000 in savings can and should be trading options.

Definition. In Math, the Greek letter \Delta (delta) is usually used to denote change or rate of change. In case of options, it's the rate of change of the option price when the stock price changes. Mathematically, it's a derivative \Delta=\frac{\partial c}{\partial S} where c is the call price and S is the stock price. In layman's terms, when the stock price changes by $1, the call price changes (moves in the same direction) by \Delta dollars. The basic features of delta can be understood by looking at how it depends on the strike price, when time is fixed, and how it changes with time, when the strike price is fixed. As before, we concentrate on probabilistic intuition.

How delta depends on strike price

Intro to option greeks: delta and its determinants

Figure 1. AAPL option chain with 26 days to expiration

Look at the option chain in Figure 1. For the strikes that are deep in the money, delta is close to one. This is because if a call option is deep in the money, the probability that it will end up in the money by expiration is high (see how the call price depends on the strike price). Hence, stock price changes are followed by call price changes almost one to one. On the other hand, if a strike is far out of the money, it is likely to remain out of the money by expiration. The stock price changes have little effect on the call price. That's why delta is close to zero.

How delta depends on time to expiration

Intro to option greeks: delta and its determinants

Figure 2. AAPL option chain with 5 days to expiration

Now let us compare that option chain to the one with a shorter time to expiration (see Figure 2). If an option is to expire soon, the probability of a drastic stock movement before expiration is low, see the comparison of areas of influence with different times to expiration. Only a few options with strikes lower than at the money strike have deltas different from one. The deeper in the money calls have deltas equal to one: their prices exactly repeat the stock price. Similarly, only a few out of the money options have deltas different from zero. If the strike is very far out of the money, the call delta is 0 because the call is very likely to expire worthless and its dependence on the stock price is negligible.

Mar 18

Option chain and efficient market hypothesis

Option chain and efficient market hypothesis

Option chain for AAPL with 26 days to expiration

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!