Marketside chats #2: Options for non-dummies

This article will explain some common misconceptions about options, using some simplifications. (1) It is not applicable to typical startup call options. (2)

A call option allows you to buy a stock at a specified strike price by a specified expiration date. For a put option, replace ‘buy’ with ‘sell’. An option can be thought of as insurance; e.g. if I buy a put option, I am protected against downward moves in a stock. Options are tradable; you can sell your option before it reaches its expiration.Pricing options at exercise

Options are odd. Computing the payout of an option is easy: e.g. if I own a call option to buy at $100, my profit per share is $14 if the stock is at $114 at the time of exercise. One can enter into a collection of related options trades. That is, you can buy N and sell M options (N+M>=2) on the same stock with same/different expiration dates & strike prices. These are called strategies; they have odd names: straddle, strangle, condor, iron butterfly, christmas tree, etc. However, in the end it is only slightly harder to compute the payout of these N+M options once you know what the stock price will be at exercise time. A linear combination of simple things is usually simple.

Pricing options before expiration

You obviously never know that final stock price ahead of time. You can only make assumptions about the future statistical distribution of the stock price. Therefore, computing the price of an option is fiendishly difficult. This is mostly because the outcomes are asymmetric: I only make money on a call if the price rises above the strike price, while lose nothing if it’s below. (3)

Example: I have an option to buy a stock at $100 by next month, and the stock is currently at $99. The intrinsic value is $0, because I would never exercise my right to buy at $100 for a stock that I can buy for less ($99) at the open market. However, I’d be willing to pay some money for the time value, as the stock can end up above $100 by expiration date. That is, there is a possibility for a profit, while there’s no possibility for a loss (other than the cost of the option).

Let’s think about this qualitatively. At the limit, if this is a stock that barely moves, the chance it ends up above $100 in a month is nil => profit potential is nil => the option is worth nothing. On the other hand, if this is a very volatile stock, it barely matters if it’s at $98 or $102 right now, as it will not affect the final price much. In practice, and all else being equal (stock price, strike price, time to expiration, etc.) an option on an average utilities company will be cheaper than that of a biotech company awaiting FDA approval for that one blockbuster drug it’s been building.

One can therefore think of a call option as a bet that, before the expiration date,

a) the stock will go up
b) the stock will become more volatile early enough before expiration that the option can increase in value (i.e. if it becomes more volatile 1 day before expiration, it won’t matter much).

Options trading firms want to trade volatility. They neutralize (hedge) any implicit bets on stock prices, because they typically don’t have an opinion on stock prices – only their volatilities. For example, if they own put options, they will buy stock (by an appropriate ratio) so that e.g. a small stock drop will cause a gain in the put option and an offsetting loss from the stock.

A (poor) analogy is placing bets on the (untradeable) cost of building a house (volatility) by trading land (stock) and single-family homes on existing land (options). You can buy land, and you can buy homes and land, but not homes without land (ignoring mobile homes); likewise, you can trade stocks and options, but you cannot trade volatility.

However, for an individual option buyer/seller, it is complicated to do all this in a concerted fashion. This means that an option gives you a second way to lose money.

Call option dropping in value after stock goes up

This happens all the time.

Take, for example, a drug company with ticker XYZ – currently trading at $10 – which is awaiting FDA approval in September for a drug. Sales projections for that drug imply that it would add $4 to the price of the stock if it gets approved, and there’s a 25% chance it gets approved. This implies that the stock will go to $9 if the drug is rejected (with 75% chance), and to $13 if it gets approved (with 25% chance). Why $9 and $13?

a) stock price of good scenario (Pg) – stock price at bad scenario (Pb) = $4 (our assumption)
b) 0.75 * Pb + 0.25 * Pg = $10 (i.e. the current market price discounts the expected benefit)

For simplicity, assume that the FDA decision is non-reversible. Also, assume for simplicity that the only price movement on XYZ is due to this decision – i.e. the stock will not move after that. If I have an call option to buy XYZ at $10.20, there’s a 25% chance that the stock will end up at $13, giving me $2.80 if I were to exercise it, and a 75% chance it will end up at $9, giving me nothing. So call price = 25%*$2.80 = $0.70.

Now, for the first time in history, and without anyone expecting it, FDA decides to delay this decision to a date after my option’s expiration date (4). However, it also issues a statement that implies they are more than 25% likely to approve the drug. This causes the stock price to go up to (say) $10.30. The intrinsic value is now $0.10 ($10.30 – $10.20), but the time value has been completely destroyed. In other words, the stock went up, but my call option is worth less because the volatility component dropped in value by an even bigger amount.

Conclusion

When you are buying/selling an option, you may gain or lose money if volatility changes, even if the stock moves in your favor. Even if you intend to keep the option until expiration, you could have over/underpaid for that option, based on the “cost of volatility” at the time of your trade.

(1) Ignoring (for those who know): 100 shares per contract; interest rates; lognormality of stock prices (i.e. a stock price halving and doubling is just as likely); etc.

(2) This is because they almost always are ‘deep in the money‘ (for calls: stock price >> strike price), i.e. they behave essentially like stock. For example, if I own a call option to buy a $200 stock at $3, it’s kind of like owning the $200 stock and and owing $3. That is, every time the stock goes up (or down) by $1, my options go up (or down) in value by $1.

(3) Moreover, options traded in US exchanges are American options, meaning they can be exercised earlier than their expiration date (unlike European options, which can only be exercised at expiration time but not before). This means that in most cases one cannot even use well-known closed-form formulas (such as Black-Scholes).

(4) W.l.o.g, they could announce a delay that was highly unexpected by the market.