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CFA® Level I · Derivatives · free lesson
Pricing and Valuation of Options
An option's price combines what it would be worth if exercised now with the value of the right to wait. This module splits option value into exercise value and time value, sets the no-arbitrage boundaries every European option price must respect, and explains how the underlying price, exercise price, time to expiration, interest rates, volatility and carry affect calls and puts.
What you will learn
1. Explain the exercise value, time value and moneyness of an option and calculate each from market prices.
- Exercise value: max(0, S - X) for calls, max(0, X - S) for puts.
- Time value = option price - exercise value; it is zero at expiration.
- In the money: S > X for calls, S < X for puts; out of the money is the reverse.
- Out-of-the-money and at-the-money options consist entirely of time value.
- Time value is generally largest at the money and decays as expiration nears.
2. Identify the no-arbitrage lower and upper bounds of European option prices and explain how a price outside the bounds creates an arbitrage.
- European call: max[0, S_0 - X(1 + r)^-T] <= c_0 <= S_0.
- European put: max[0, X(1 + r)^-T - S_0] <= p_0 <= X(1 + r)^-T.
- Lower bounds use the present value of X, not X itself.
- A price outside the bounds allows a riskless, self-financing profit.
- American call on a no-income asset = European call; American put can be worth more than a European put.
3. Explain how the underlying price, exercise price, time to expiration, risk-free rate, volatility, and carry benefits and costs affect the values of calls and puts.
- Calls rise with S, T, r, volatility and carry costs; fall with X and income.
- Puts rise with X, volatility and income; fall with S, r and carry costs; usually rise with T.
- Volatility increases both call and put values.
- Deep in-the-money European puts can lose value with longer time to expiration.
- Implied volatility is the volatility input that matches an option's market price.
Module at a glance
- Option price = exercise value + time value; time value is zero at expiration.
- Calls are in the money when S > X; puts when S < X.
- European call: max[0, S_0 - X(1 + r)^-T] <= c_0 <= S_0.
- European put: max[0, X(1 + r)^-T - S_0] <= p_0 <= X(1 + r)^-T.
- Prices outside the bounds create riskless, self-financing arbitrage.
- Volatility raises both calls and puts; rates and dividends move them in opposite directions.
- American calls on no-income assets equal European calls; American puts can be worth more.
This free module has 3 lessons, 14 practice questions with full explanations.