Options Pricing & Valuation Explained | CFA Level 1 Derivatives

Options pricing and valuation involve determining the fair market value of an option contract based on the probability of future price movements of the underlying asset. The value of an option is influenced by several factors, including the current price of the underlying asset, the strike price, time remaining until expiration, volatility, interest rates, and expected dividends. The two most commonly used models for valuation are the Black–Scholes model and the Binomial model. 

The Black–Scholes model provides a closed-form formula for pricing European options, while the Binomial model evaluates possible price paths over time and is useful for valuing American options. An option’s price consists of intrinsic value (the immediate exercise value) and time value (the additional value from the possibility of favorable future price movements). Accurate valuation helps investors assess risk, develop trading strategies, and make informed decisions in derivatives markets.

Understanding Call and Put Options

Options are contracts that give the holder the right, but not the obligation, to buy or sell an underlying asset at a predetermined price before or on a specified date.

Call Option

A Call Option gives the buyer the right to purchase an underlying asset at a predetermined strike price.

Investors buy Call Options when they expect the market price of the asset to rise.

Example

• Current Share Price: ₹1400

• Strike Price: ₹1400

• Option Premium: ₹50

If the share price rises above ₹1400, the option holder can buy at the lower strike price and benefit from the increase.

Put Option

A Put Option gives the buyer the right to sell an underlying asset at a predetermined strike price.

Investors buy Put Options when they expect the market price of the asset to fall.

Example

• Current Share Price: ₹1400

• Strike Price: ₹1400

• Option Premium: ₹20

If the share price falls below ₹1400, the holder can sell at the higher strike price and earn a profit.

Core Mechanics of an Option: Right vs. Obligation

Every option contract involves two parties:

Option Buyer

• Has the right to exercise the contract.

• Pays the option premium.

• Faces limited risk.

Option Seller (Writer)

• Has an obligation to fulfill the contract if exercised.

• Receives the option premium.

• Faces potentially unlimited risk.

Key Point

The maximum loss for an option buyer is limited to the premium paid, whereas the seller may face substantial losses depending on market movements.

Applications of Options

Options serve various purposes in financial markets:

1. Hedging Risk: To reduce risk associated with existing asset holdings, acting as insurance (e.g., buying Put Options to protect shares).

2. Speculation: To profit from anticipated price movements of an underlying asset without owning it (e.g., buying a Call Option if expecting a price rise).

3. Portfolio Protection: To prevent an entire portfolio's value from falling excessively during market downturns.

4. Income Generation: Shorting options to collect option premiums, especially in stable markets, profiting from time decay.

Important Option Terminology

Before understanding valuation, it is important to know the key terms used in options trading.

Underlying Asset: The asset on which the option contract is based.

Strike Price: The predetermined price at which the underlying asset can be bought or sold.

Option Premium: The amount paid by the option buyer to acquire the option.

Expiration Date: The date on which the option contract expires.

Moneyness of Options

Moneyness indicates whether an option would be profitable if exercised immediately.

Option Premium Components

An option's premium consists of two major components:

Option Premium = Intrinsic Value + Time Value

Intrinsic Value

Intrinsic value represents the immediate benefit obtained by exercising the option today.

Call Option Formula

Intrinsic Value = Max(0, Stock Price − Strike Price)

Put Option Formula

Intrinsic Value = Max(0, Strike Price − Stock Price)

Example

For a Call Option:

• Stock Price = ₹1500

• Strike Price = ₹1400

Intrinsic Value = ₹100

Time Value

Time value reflects the possibility that the option may become more profitable before expiry.

Formula

Time Value = Option Premium − Intrinsic Value

Example

• Option Premium = ₹50

• Intrinsic Value = ₹10

Time Value = ₹40

The longer the time remaining until expiration, the greater the time value tends to be.

Factors Affecting Option Premiums

Several factors influence the price of an option.

1. Time to Expiry: Options with longer expiration periods generally command higher premiums because they offer more opportunities for favorable price movements.

2. Volatility: Higher volatility increases option premiums because large price movements increase the probability of profit.

3. Underlying Asset Price: Changes in the market price of the underlying asset directly affect option value.

4. Strike Price: The relationship between the strike price and market price determines an option's moneyness and value.

5. Interest Rates: Interest rate changes can influence option pricing, particularly for long-dated options.

6. Probability of Profitability: Options expected to become profitable due to market events or news often trade at higher premiums.

Option Expiry Frequencies: Monthly vs. Weekly

Options contracts are available with different expiration periods, allowing traders to choose strategies based on their investment horizon and risk appetite. The two most common expiry frequencies are monthly and weekly options.

Monthly Options

Monthly options are commonly available for individual stocks and typically expire once every month. They provide traders with a longer time frame, allowing more time for the anticipated price movement to occur.

Weekly Options

Weekly options are most commonly offered on stock indices and expire every week. Due to their shorter duration, they generally have lower premiums and are popular among short-term traders and speculators seeking quick trading opportunities.

Categories of Options: American vs. European

Options are categorized by their exercise rules: 

Users of Options

Different market participants use options for distinct purposes: 

• Investment Banks and Hedge Funds: Primarily for speculation.

• Mutual Funds and Pension Funds: Primarily for hedging and risk management.

• Individual Investors: Mostly for trading and speculation.

Limitations of Options Trading

Options trading comes with inherent limitations: 

1. Time Decay (Theta): The time value of an option decreases as it approaches expiry, potentially leading to losses for buyers.

2. Difficulty in Short-Term Estimation: Predicting short-term price movements is challenging due to high volatility and unpredictable events.

3. Risk of Worthlessness: Options can expire out of the money and become worthless if the underlying price doesn't move as anticipated.

4. High Volatility: While creating opportunities, extreme fluctuations can lead to significant, rapid losses.

5. Complex Valuation: Determining an option's fair value requires specialized models and expertise.

Option Valuation Models

Valuing options involves sophisticated mathematical models:

1. Black-Scholes-Merton (BSM) Model: A widely recognized model for pricing European-style options.

2. Binomial Model: A simpler, discrete-time model.

3. Monte Carlo Model: A simulation-based model for complex options.