Title LM08 Pricing and Valuation of Options IFT Notes.pdf ✅

LM08 Pricing and Valuation of Options 2025 Level I Notes © IFT. All rights reserved 1 LM08 Pricing and Valuation of Options 1. Introduction ........................................................................................................................................................ 2 2. Option Value relative to the Underlying Spot Price ............................................................................ 2 3. Option Exercise Value ..................................................................................................................................... 2 4. Option Moneyness ............................................................................................................................................ 3 5. Option Time Value ............................................................................................................................................ 4 6. Arbitrage .............................................................................................................................................................. 4 7. Replication .......................................................................................................................................................... 5 8. Factors Affecting Option Value .................................................................................................................... 6 Summary ................................................................................................................................................................... 9 Required disclaimer: IFT is a CFA Institute Prep Provider. Only CFA Institute Prep Providers are permitted to make use of CFA Institute copyrighted materials which are the building blocks of the exam. We are also required to create / use updated materials every year and this is validated by CFA Institute. Our products and services substantially cover the relevant curriculum and exam and this is validated by CFA Institute. In our advertising, any statement about the numbers of questions in our products and services relates to unique, original, proprietary questions. CFA Institute Prep Providers are forbidden from including CFA Institute official mock exam questions or any questions other than the end of reading questions within their products and services. CFA Institute does not endorse, promote, review or warrant the accuracy or quality of the product and services offered by IFT. CFA Institute®, CFA® and “Chartered Financial Analyst®” are trademarks owned by CFA Institute. © Copyright CFA Institute Version 1.0
LM08 Pricing and Valuation of Options 2025 Level I Notes © IFT. All rights reserved 2 1. Introduction This learning module covers:  The exercise value, moneyness, and time value of an option  How arbitrage and replication concepts can be applied to options  Factors affecting the value of an option 2. Option Value relative to the Underlying Spot Price Options have a non-linear or asymmetric payoff. Their value depends on whether the spot price crosses an exercise threshold at maturity. To gauge an option’s value before maturity, investors frequently rely on three measures – exercise value, moneyness, and time value. Recall from an earlier reading that American options can be exercised at any time, while European options can be exercised only at maturity. This reading will only focus on European options. 3. Option Exercise Value At expiration, the value of a call and put option can be calculated as: CT = max (0, ST – X ) PT = max (0, X − ST) At any time before expiration (t < T), an option’s value is made up of its exercise value and its time value. The exercise value is the option's value if it could be exercised immediately, whereas the time value captures the possibility that the passage of time and the volatility of the underlying price will increase the profitability of exercise at maturity. Calculating an Option’s Exercise Value: At any time before expiration (t < T), we can calculate an option’s exercise value by comparing the underlying spot price (St) with the present value of the exercise price (X). Call Option Exercise Value = max (0, St – X (1 + r)(T−t)) Put Option Exercise Value = max (0, X (1 + r)(T−t) − St) Example: Put Option Exercise Value (This is based on Example 1 from the curriculum.) Consider a 1-year put option with an exercise price of EUR 1,000, an initial price of EUR 990, and a risk-free rate of 1%. What is the exercise value of the option in six months if the spot price equals EUR 950? Solution:
LM08 Pricing and Valuation of Options 2025 Level I Notes © IFT. All rights reserved 3 Put Option Exercise Value = max (0, X (1 + r)(T−t) − St) Put Option Exercise Value = max (0, 1,000 (1 + 0.01) (0.5) − 950) = max(0, 45.04) = 45.04 Similarity with Forwards: If we assume an exercise price X, equal to the forward price F0(T), the exercise value of a call option is the same as the value of a long forward commitment: St – PV(F0(T)), provided that the spot price is greater than the present value of X. Note that this comparison ignores the upfront call premium paid by the option buyer. 4. Option Moneyness An option’s moneyness expresses the relationship between the underlying price and the exercise price. It refers to whether an option would result in a profit or loss if exercised immediately.  If immediate exercise of the option would result in a positive payoff, then the option is in the money.  If immediate exercise would result in loss, then the option is out of the money.  If immediate exercise would result in neither a gain nor a loss, then the option is at the money. The table below shows the moneyness of an option for various relative values of S and X. Call Option Put Option In the money S > X S < X At the money S = X S = X Out of the money S < X S > X Moneyness is used to compare options on the same underlying but with different exercise prices and/or times to maturity. Also, the degree to which an option is in or out of the money affects the sensitivity of its price to changes in the price of the underlying.  Deep-in-the-money options, are highly likely to be exercised, and are therefore highly sensitive to changes in the price of the underlying.  Whereas, deep-out-of-the money options, are very unlikely to be exercised, and are therefore far less sensitive to changes in the price of the underlying. Example: Put Option Moneyness (This is Example 2 from the curriculum.) Recall in Example 1 that at time t, a put option with six months remaining to maturity had an exercise price (X) of EUR 1,000 and an underlying spot price (St) of EUR 950. Describe the
LM08 Pricing and Valuation of Options 2025 Level I Notes © IFT. All rights reserved 4 moneyness of the put option at time t. Solution: Given that the underlying spot price is below the exercise price, the put option is in the money by EUR 50. 5. Option Time Value Prior to expiration an option also has time value in addition to exercise value. The time value of an option is the amount by which the option premium exceeds the exercise value. The longer the time to expiration the higher the time value. The time value of an option is always positive but it declines to zero at maturity. This process is referred to as time value decay. Example: Put Option Time Value (This is based on Example 3 from the curriculum.) Example 1 showed that a one-year put option with an exercise price (X) of EUR 1,000 had an exercise value of EUR 45.04 with six months remaining to maturity when the spot price (St) was EUR 950. If we observe a current put option price (pt) of EUR 50, what is the time value of the put option? Solution: Put option price = Exercise value + Time value 50 = 45.04 + Time value Time value = 4.96 6. Arbitrage A key distinction between forwards and options is that a forward buyer enters into a contract with no cash paid upfront and has an unlimited gain or loss; in contrast, an option buyer pays an upfront premium and will exercise an option at maturity only if it is in the money. This conditional nature of payoff establishes an upper and lower no-arbitrage price bounds for an option at any time t. Upper and Lower Bounds for Call Options The lower bound of a call option is its exercise value. An option which trades below its exercise value violates the no-arbitrage condition. Similarly, the upper bound of a call option is the price of the underlying. A call buyer will not pay more for the right to purchase an underlying than the price of the underlying. Therefore,