Module 9: Derivatives
Derivatives in CFA Level 2 focus on advanced pricing models and valuation techniques.
Unlike Level 1, which introduces basic derivative instruments, Level 2 requires candidates to:
- understand pricing models
- analyze derivative payoffs
- value contracts using financial theory
- apply derivatives in portfolio and risk management
This module is important for careers in trading, risk management, and quantitative finance.
Options are financial contracts that derive value from an underlying asset. In Level 2, the focus is on pricing models used to estimate the fair value of options.
Binomial Model
The binomial model values options by modeling possible future price movements of the underlying asset.
It assumes that the price can move in two directions over each period:
- upward movement
- downward movement
Key Features of Binomial Model
Step by Step Approach
The model divides time into multiple periods.
Price Tree
A tree is constructed showing possible price paths.
Risk Neutral Valuation
Probabilities are adjusted to reflect risk neutral expectations.
Basic Concept
Option Value Today = Discounted expected value of future payoffs
The model works backward from expiration to determine the current option value.
Advantages
- flexible and easy to understand
- can handle American options
- allows early exercise
Black Scholes Model
The Black Scholes model is a widely used formula for pricing European options.
It provides a closed form solution based on several inputs.
Key Inputs
- current stock price
- exercise price
- time to maturity
- risk free interest rate
- volatility of the underlying asset
Key Assumptions
- markets are efficient
- no transaction costs
- constant volatility and interest rates
- no arbitrage opportunities
Importance
The Black Scholes model is widely used in financial markets to estimate option prices and understand how different factors affect option value.
Futures contracts are priced based on the relationship between the spot price and the cost of holding the underlying asset.
Cost of Carry Model
The cost of carry model explains how futures prices are determined.
Futures Price Formula
Futures Price = Spot Price × (1 + Carry Cost)
Carry costs include:
- storage costs
- financing costs
- insurance costs
If the underlying asset provides income, such as dividends, this reduces the futures price.
Relationship Between Spot and Futures Prices
If futures prices deviate significantly from fair value, arbitrage opportunities may arise.
Traders exploit these differences to earn risk free profit, bringing prices back to equilibrium.
Swaps are agreements between two parties to exchange cash flows based on predefined terms.
In Level 2, candidates must understand how to value swaps over time.
Interest Rate Swaps
An interest rate swap involves exchanging fixed interest payments for floating interest payments.
Basic Structure
One party pays a fixed rate
The other party pays a floating rate
Valuation Concept
The value of a swap is the difference between:
- present value of fixed payments
- present value of floating payments
If interest rates change, the value of the swap changes accordingly.
Currency Swaps
Currency swaps involve exchanging cash flows in different currencies.
Key Features
- exchange of principal amounts in different currencies
- periodic interest payments in each currency
- re exchange of principal at maturity
Valuation
The value of a currency swap depends on:
- exchange rate movements
- interest rate differences between countries
Currency swaps are widely used by multinational companies to manage foreign exchange risk.
This module is important because it helps candidates:
- understand pricing models used in financial markets
- evaluate derivative contracts
- manage financial risk using derivatives
- analyze arbitrage opportunities
In CFA Level 2, questions often require candidates to apply pricing models and interpret results, making this a high scoring but concept intensive module.