# Pricing and Valuation of Options | CFA Level I Derivatives

Glad you’re back! 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. Let’s dive in!

## 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:

## 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,St-PV(X))
Intrinsic value (put option) = max(0, PV(X)-St)

EXAMPLE

A one-year European put option on ABC stock was initiated with a strike price of \$80. Three months later, ABC’s stock price is \$78, and the risk-free rate is 5%. What is the intrinsic value of the option at this point?

PV(X)-St = X/(1 +Rt)T-t-St
= \$80/(1.05)0.75-78
= -\$0.87

Since the value to the long cannot be negative, the intrinsic value of the put option is 0.

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:

EXAMPLE

## 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:

### 2. Strike Price

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

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:

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:

### 5. Volatility of the Underlying

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

### 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. See you again!

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