Options course · Lesson 3 of 10
An option price is intrinsic value plus time value.
Part of an option price is what you get if you exercise now. The rest pays for time. Five inputs set the total, and one of them you cannot see.
Two parts of every price
Intrinsic value is what the option is worth if you exercise it now. Time value is the rest of the price. It is what buyers pay for the chance that the option gains more value before expiration.
| Call strike | Price | Intrinsic value | Time value |
|---|---|---|---|
| $90 | $12.00 | $10.00 | $2.00 |
| $95 | $8.34 | $5.00 | $3.34 |
| $100 | $5.43 | $0.00 | $5.43 |
| $105 | $3.31 | $0.00 | $3.31 |
| $110 | $1.89 | $0.00 | $1.89 |
The 90 call costs $12.00. Exercise now gives $10.00, so the time value is $2.00. The 100 call has no intrinsic value, so all of its $5.43 is time value.
Time value is largest at the money. Deep in the money, the option acts almost like the stock. Far out of the money, a gain is unlikely, so the price is small.
Five inputs set the price
The Black-Scholes model calculates an option price from five inputs. They are the stock price, the strike, the time to expiration, the volatility and the interest rate. A dividend is a sixth input, and our example stock pays none.
| One change from the base case | 100 call price | Change |
|---|---|---|
| Base case: stock $100, 25% volatility, 90 days, 4% rate | $5.43 | |
| Stock price rises to $105 | $8.59 | +$3.16 |
| Volatility rises to 35% | $7.39 | +$1.96 |
| Time falls to 30 days | $3.02 | -$2.41 |
| Rate rises to 5% | $5.56 | +$0.13 |
In this example, the stock price and the volatility have the largest effect. The rate has a small effect on a 90-day option. You can see four of the five inputs on a screen. Volatility is the one that you cannot see.
Implied volatility
The future volatility of a stock is not known. So the market works backward. It takes the option price that buyers and sellers agree on, and it finds the volatility that gives that price in the model.
That number is the implied volatility. For the same strike and expiration, a higher implied volatility means a more expensive option. To compare two options, look at their implied volatility, not only their price.
Calls and puts are linked
Take a call and a put with the same strike and expiration. The call price minus the put price equals the stock price minus the present value of the strike. This is put-call parity. It holds exactly for European-style options on a stock with no dividends.
In our example, the 100 call costs $5.43 and the 100 put costs $4.45. The difference is $0.98. The stock price minus the present value of $100 is $100 minus $99.02, which is also $0.98.
If the two sides were not equal, a trader could buy the cheap side and sell the expensive side for a profit with no risk. Trades like that keep the two sides equal.
Key points
- An option price is intrinsic value plus time value.
- Time value is largest at the money.
- Volatility is the only input that you cannot see. The market quotes it as implied volatility.
- Put-call parity links each call to the put at the same strike.
Sources
- Fischer Black and Myron Scholes, The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 1973, for the model that gives every price in this course.