Pricing and Valuation of Options | CFA Level I Derivatives

In this lesson, we’ll explore the pricing and valuation of options. We’ll start with a review of basic option concepts, discuss the concept of moneyness, and learn about intrinsic and time values. Finally, we’ll go through the six factors that affect option values.

Basics of Options and the Concept of Moneyness

First, let’s recall that a call option gives the holder the right, but not the obligation, to buy an underlying asset at a given price, while a put option gives the right to sell. Options can be either American-style (exercisable any time up to and including expiration) or European-style (exercisable only on the expiration date).

For the Level 1 curriculum, we’ll focus on European options. To summarize, we can say that a European option has value before its expiration, even if it’s not yet exercisable. This introduces the concept of moneyness:

• In-the-money: Immediate exercise would generate a positive payoff.
• Out-of-the-money: Immediate exercise would result in a negative payoff.
• At-the-money: The spot price equals the exercise price, and there’s no payoff.

Intrinsic Value and Time Value of Options

An option’s value consists of its intrinsic value and its time value. The intrinsic value of a call option is the maximum of 0 and the spot price at time t minus the exercise price. For a put option, the intrinsic value is the maximum of 0 and the exercise price minus the spot price at time t.

Before 2023, the CFA curriculum defined intrinsic value or exercise value before expiration without considering the time value of money aspect. The current definition includes the present value of the exercise price discounted by the risk-free rate (denoted as PV of X).

Intrinsic value (call option) = max(0,S_t-PV(X))
Intrinsic value (put option) = max(0, PV(X)-S_t)

Time value, or speculative value, is the other component of an option’s value. The sum of an option’s intrinsic value and time value equals its option premium. Unlike forwards and futures contracts, which have 0 value at initiation, options have value at initiation, which is the time value. As the contract progresses, the time value decreases, and at expiration, the entire price of the option is its intrinsic value.

Theoretical Bounds for Option Values

At any time T, the theoretical lower and upper bounds for option values can be calculated:

• Call option lower bound: Intrinsic value
• Call option upper bound: Spot price
• Put option lower bound: Intrinsic value
• Put option upper bound: Strike price

6 Key Factors Affecting European Options

Now that you understand the mechanism of option valuation, let’s dive deeper into the factors affecting the intrinsic value and time value of European options. The CFA curriculum lists 6 factors. Let’s explore them in detail with some humor sprinkled in!

1. Spot Price

The spot price has a significant impact on the intrinsic value of options:

• Call options: Higher spot price → greater intrinsic value → higher option value
• Put options: Higher spot price → lower option value

2. Strike Price

The strike price, or exercise price, influences the intrinsic values of options:

• Call options: Higher strike price → lower intrinsic value
• Put options: Higher strike price → higher intrinsic value

The first two factors, spot price and strike price, affect the intrinsic value of options. The remaining factors affect the time value.

3. Time to Expiration

Time to expiration generally affects the time value of options:

• Longer time to expiration → higher time value for both call and put options
• Shorter time to expiration → lower time value for both call and put options

Note: This relationship holds true for call options but may not always hold for European put options due to exceptional cases.

4. Risk-free Rate

The risk-free rate impacts the time value of options:

• Higher risk-free rate → higher value for European call options, lower value for European put options
• Lower risk-free rate → lower value for European call options, higher value for European put options

5. Volatility of the Underlying

Volatility of the underlying asset affects the time value of both call and put options:

• Higher volatility → higher time value
• Lower volatility → lower time value

6. Costs and Benefits of Holding the Underlying Asset

Costs and benefits of holding the underlying asset can influence the value of options:

• Call options: Expected costs increase the option value, while expected benefits decrease it.
• Put options: Expected costs decrease the option value, while expected benefits increase it.

In summary, these 6 factors affect the value of European call and put options. Remember, the option value, or option premium, is the sum of its intrinsic value and time value. Understanding the reasoning behind each factor is crucial for mastering options valuation. We’ll continue with options valuation in the next lesson, where we’ll explore the put-call parity for European options.