Basics of Derivative Pricing and Valuation (2021 Level I CFA® Exam – Reading 46)

Introduction

This tutorial provides a comprehensive overview of the basics of derivative pricing and valuation, tailored for the Level I CFA® exam. Understanding derivatives, including forwards, futures, options, and swaps, is crucial for financial analysis and investment strategies. This guide will break down key concepts such as arbitrage, replication, risk neutrality, and the valuation of various derivative instruments.

Step 1: Understand Key Concepts in Derivative Pricing

• Arbitrage: The practice of taking advantage of a price difference between two or more markets. In derivatives, it ensures that prices reflect true value.
• Replication: Creating a portfolio of assets that mimics the cash flows of a derivative. This is fundamental in pricing derivatives accurately.
• Risk Neutrality: The assumption that investors are indifferent to risk, which simplifies the pricing model. Under this assumption, the expected returns of the derivative and the underlying asset are equal.

Step 2: Differentiate Between Value and Price

• Value refers to the intrinsic worth of a derivative based on its expected future cash flows.
• Price is the market price at which the derivative is traded.
• Understand that prices can fluctuate due to market conditions, while value is more stable and based on fundamental analysis.

Step 3: Value and Price of Forward Contracts

• At Initiation: The price of a forward contract is set based on the spot price of the underlying asset and the cost of carry (storage, financing).
• During the Life of the Contract: The value can change due to fluctuations in the underlying asset's price.
• At Expiration: The value equals the difference between the spot price and the forward price.

Step 4: Analyze Costs and Benefits of Holding Assets

• Monetary Benefits: Income generated from the underlying asset (dividends, interest).
• Non-Monetary Costs: Storage costs, insurance, and other holding costs.
• These factors influence the value and price of a forward contract, as they affect the net cash flows expected from the underlying asset.

Step 5: Understand Forward Rate Agreements

• A Forward Rate Agreement (FRA) is a contract that locks in an interest rate for a future period.
• Used to hedge against interest rate fluctuations and manage financial risk.

Step 6: Compare Forward and Futures Prices

• Recognize that futures prices may differ from forward prices due to:
  • Margin requirements
  • Daily settlement (marking to market)
  • Market liquidity

Step 7: Explore Swap Contracts

• Swaps are agreements to exchange cash flows, typically based on interest rates or currencies.
• Similarities to forwards but involve multiple cash flow exchanges over time.

Step 8: Determine the Value of Options at Expiration

• The value of a European option at expiration is determined by:
  • Exercise Value: The profit if exercised.
  • Time Value: The extra value due to the time remaining until expiration.

Step 9: Understand Option Valuation Factors

• Key factors influencing option value include:
  • Underlying Asset Price: Higher prices generally increase call option values.
  • Strike Price: Lower strike prices increase call option values and vice versa for puts.
  • Time to Expiration: More time typically increases option value due to uncertainty.
  • Volatility: Higher volatility leads to higher option values.
  • Interest Rates: Changes can affect the present value of future cash flows.

Step 10: Learn About Put-Call Parity

• Put-Call Parity states that the price of a call option and a put option with the same strike price and expiration date should relate to the underlying asset's price and the present value of the strike price.
• This relationship helps in identifying arbitrage opportunities.

Step 11: Apply the One-Period Binomial Model

• A simple method to determine the value of options:
  • Create a binomial tree with possible future prices.
  • Calculate the option payoff at expiration.
  • Discount back to present value using the risk-free rate.

Step 12: Differentiate Between European and American Options

• European options can only be exercised at expiration, while American options can be exercised at any time before expiration.
• This flexibility adds value to American options.

Conclusion

This tutorial has introduced you to the fundamentals of derivative pricing and valuation. Key concepts such as arbitrage, replication, and risk neutrality are essential for understanding how derivatives are valued in the market. Familiarize yourself with the distinctions between value and price, the dynamics of various contracts, and the factors influencing option valuation. As a next step, consider practicing with real-world examples or taking mock exams to solidify your understanding.