Option Price Behavior

Options typically do not move as much as their underlying stock unless they are deep-in-the-money and/or very close to expiration. There are valid mathematical reasons for this.

Delta is the amount you can expect an option premium to change given a one-point move in the underlying stock (all other conditions being equal). We derive Delta from the Black-Scholes formula for pricing options. It represents roughly how much the option behaves like the underlying stock. A Delta of .50, for example, means that an option can be expected (all other things being equal) to move about $0.50 for every one-point move in the underlying product. Delta changes with time to expiration as the option moves more in- or out-of-the-money. Volatility of the underlying stock also affects Delta.

The six inputs that determine an option's value are stock price, strike price, time to expiration, interest rate, dividend yield and volatility (over the life of the option). Normally, if the stock price goes up and the other factors remain the same, then a call option goes higher. Therefore, if the call option has gone down, then one of the other factors must have changed.

The passage of time can certainly push an option's value lower. A dividend payment may also have an impact. The real wild card is implied volatility. Sometimes, the market bids up the implied volatility in anticipation of a market-moving event such as earnings release or a major speech by an important person. After the event, the implied volatility often drops sharply, especially if the event failed to have the expected impact. Visiti our learning center to learn more about Volatility. 

Use our website’s calculator to see how volatility changes can affect option premiums. Visit our learning center for more information on Options Pricing. 

Why do option prices rise when interest rates rise? This seems odd since stock prices drop in this situation.

In general, call option premiums rise when interest rates rise. That is because options are priced on a risk-neutral basis (i.e., on a Delta-neutral or fully-hedged basis). Therefore, a long call is hedged with short stock, and a short stock position generates interest revenue. That makes the call option worth more. If interest rates go up, the interest revenue from the short stock position increases, which makes the call worth still more. Note that for put options, it works the opposite way. Dividends also work in the opposite direction.

A stock's value is equal (theoretically) to the present value of all its future dividends, so an increase in the interest rate used to discount the future dividends reduces the value of the stock. When someone says higher interest rates make call options worth more, there is an implicit assumption all other things are equal. However, in reality, all other things are rarely equal, and the decline in a stock's price due to an interest rate increase often overwhelms the effect of the higher interest rate on the option itself.

Recently it seems that option prices have been out of line (with intrinsic value, underling security, etc.). Why?

The price of an option is a function of the market: buyers and sellers. In other words, when more people want to own an option, there may be a rise in the price, as the forces of supply and demand become more pronounced. In times of large market movement, the secondary markets may experience some increased volatility. For further information on the various components of an options theoretical price, please visit our Options Pricing learning center. 

If you are interested in additional information,visit our Options Pricing page. 

When someone refers to a deep-in-the-money option, they are referring to a call or a put with a Delta close to 1.00 (or -1.00 for puts). This option moves very close to a 1:1 ratio with stock movement up and down, often viewed as the equivalent of long or short stock. We also consider an option to be in-the-money with a Delta closer to say 0.75, (or -0.75 for a put). The difference is that although these options move with the stock, they do not move at the same 1:1 ratio. Instead, if the stock went up $1, we could expect the 0.75 Delta calls to gain $0.75.

Any option with at least $0.01 of intrinsic value is technically in-the-money.

If you are interested in additional information, visit our Options Pricing page.