While stock option pricing models can become extremely complex, the underlying factors they are taking into account to put a fair value estimate on the option contracts remain the same.
Stock options are generally priced based on 6 factors.
- The current share price of the stock.
- The strike price of the options contract.
- The amount of time remaining until the option contract expires.
- Any dividends that the stock may accrue during the option time frame.
- The expected volatility of the underlying stock.
- Current interest rates.
While this may seem complicated, it is all fairly intuitive when you think about it a little more closely. The position of the current stock price relative to the strike price of the option is likely the most influential factor in the price of every option contract. If you own a call option with a strike price of $20, and the underlying stock is currently trading at $10, there is no inherent value because the strike price is higher than the current price. A logical person would just purchase shares on the open market rather than exercise the option contract. If the reverse were true and a $10 strike price existed with the underlying stock trading at $20, there is $10 of inherent value to each share.
The expected volatility of the option and time remaining until the contract expires also play important roles in the pricing. If an underlying security has higher volatility, there is a greater chance for the value of the option to be higher at expiration. Similarly, the more time that remains until the option contract expires, the more opportunity there is for the option contract to be worth more at expiration. This is a risk for the seller of the option contract, and they expect to be compensated for this risk. Generally speaking the higher the volatility and the more time remaining until the contract expires, the more the option contract will be worth (all else being equal).
Dividends have a very obvious effect on options pricing. When a stock pays a dividend, it can be expected that the price of the stock will fall on the ex dividend date proportionately to value of the dividend paid per share. Since a dividend is expected to lower a stock’s price, this has a negative effect on call options price and a positive effect on put options price (positive meaning higher contract value). Because sellers of option contracts understand this effect and are aware of ex-dividend dates, the market will price this into the option contract value if the underlying stock is affected by dividend payments during the option contract’s life.
Perhaps the most difficult concept to understand is the effect of interest rates on option prices. American stock options are unlike their European counterparts in that the owner can choose to exercise the contract at any point before the expiration date, whereas in Europe the contract can only be exercised upon expiration. This means that each trader hypothetically has an opportunity cost of not being invested elsewhere, the opportunity cost generally given to be the current risk free rate of return.
This means that if a trader purchases the underlying security rather than the options, he will have greater capital tied up in the position, and therefore a greater opportunity cost than if he purchased the less expensive options contracts. If interest rates rise, this means that call options become more expensive to account for this increased opportunity cost in owning the position. Put another way, a buyer is willing to pay more for option contracts because of the higher opportunity cost of actually owning the position. The opposite is true for put options. Since a short seller takes possession of the capital from the sale of securities, if interest rates rise the trader can now expect a higher rate of return on the short proceeds. This makes buying put options comparatively less attractive as it ties up capital that would elsewhere be earning interest.
These are the general factors that go into creating pricing models, but the actual pricing models can become extremely complex. It is important to first have a solid grasp intuitively on how different factors affect pricing before one gets caught up in the quantitative application.