1  Introduction to Financial Derivatives

References
  • HULL, John. Options, futures, and other derivatives. Ninth edition. Harlow: Pearson, 2018. ISBN 978-1-292-21289-0.
    • Chapter 1 - Introduction
    • Chapter 4 - Interest Rates
  • PIRIE, Wendy L. Derivatives. Hoboken: Wiley, 2017. CFA institute investment series. ISBN 978-1-119-38181-5.
    • Chapter 1 - Derivative Markets and Instruments

Learning Outcomes:

1.1 What Are Derivatives?

  • A derivative is a financial contract whose value is derived from the price of an underlying asset.
  • The underlying asset can be a stock, currency, interest rate, commodity, bond, index, or even non-financial elements like weather conditions or insurance claims.
  • The market price of the underlying is called the cash price or spot price.

The Significance of Derivatives

Derivatives play a critical role in modern financial markets by offering several key benefits:

  • Risk Management: Allow parties to hedge and transfer various types of financial risks.
  • Investment Strategies: Enable the construction of complex strategies and returns beyond simple stock or bond investments.
  • Market Expectations: Reflect future price expectations and offer valuable market information.
  • Cost Efficiency: Reduce transaction costs compared to trading the underlying asset.
  • Capital Efficiency: Require lower initial capital outlay due to leverage.
  • Short Selling: Simplify taking short positions compared to shorting the underlying directly.
  • Liquidity and Market Efficiency: Improve liquidity and enhance the functioning of the underlying asset markets.

1.2 Derivative Markets

The global derivatives market is one of the largest financial markets. Derivatives are traded in two main venues:

  • organized exchanges and
  • over-the-counter (OTC) markets.
Feature Exchange-Traded Derivatives OTC Derivatives
Contract Standardization Standardized terms (size, expiry, asset) Fully customizable
Clearing Mechanism Guaranteed by a clearing house No central clearing (except post-2008 for some)
Counterparty Risk Low (due to clearing house) Higher credit risk
Transparency High (regulated, prices public) Lower (private negotiations)
Flexibility Limited High
Capital and Margin Requirements Margin required Negotiated, often lower pre-2008

OTC Market Evolution

  • Prior to 2008: Largely unregulated, dominated by banks as market makers; transactions governed by master agreements, some cleared through central counterparties (CCPs).

  • Since 2008: Regulatory reforms introduced:

    • Standardized OTC transactions must be cleared through CCPs.
    • All trades must be reported to a central repository.
    • Aim: Reduce systemic risk and enhance transparency.
The Lehman Bankruptcy
  • Event: Lehman Brothers filed for bankruptcy on September 15, 2008—the largest in U.S. history.
  • Role in OTC Market: Heavily involved in high-risk derivatives.
  • Cause: Inability to refinance short-term debt.

At the time of its bankruptcy, Lehman Brothers had an extensive network of transactions, with hundreds of thousands outstanding across approximately 8,000 counterparties. The process of unwinding these transactions has posed significant challenges for both the Lehman liquidators and the involved counterparties, illustrating the complex and interconnected nature of modern financial markets.

1.3 Unconditional vs. Conditional Derivatives

Both unconditional (Forward Commitments) and conditional derivatives (Contingent Claims) are essential financial instruments that derive their value from the performance of an underlying asset, playing pivotal roles in global financial markets for hedging, speculation, and arbitrage.

Unconditional Derivatives (Forward Commitments)

Unconditional derivatives create a binding obligation to buy or sell an asset at a predetermined future date and price. They include:

  • Forwards
  • Futures
  • Swaps
Conditional Derivatives (Contingent Claims)

Conditional derivatives offer the holder the right, but not the obligation, to buy or sell an asset under specified conditions. The primary form is:

  • Options

1.4 Types of Derivatives

Forward Contract

Definition

A forward contract is a customized, over-the-counter derivative agreement between two parties, where the buyer agrees to purchase, and the seller agrees to sell, an underlying asset at a predetermined future date and price established at the contract’s inception (forward price).

  • Long Position: The party committing to purchase the asset.
  • Short Position: The party committing to sell the asset.

Key Points

  • Popularity in Foreign Exchange: Forward contracts are frequently used for hedging in the foreign exchange markets.
  • OTC Markets: Typically involves at least one financial institution, allowing for customization.
  • Market Dynamics and Pricing: Forward prices reflect the market’s consensus on future price movements, adjusted for the time value of money, influenced by factors such as the underlying asset’s current price, interest rates, and expected volatility.

Futures Contract

Definition

A futures contract is a standardized derivative, similar to a forward contract but traded on futures exchanges, like the CME Group or Intercontinental Exchange, facilitating the buying and selling of underlying assets at future dates.

Forwards Futures
Customized terms, traded over-the-counter. Standardized terms, traded on regulated exchanges.
Counterparty risk, with less regulatory oversight. Mitigated counterparty risk through clearinghouses.
Settlement occurs at contract maturity. Daily mark-to-market settlement.

Swap Contract

Definition

A swap is an OTC derivative where two parties exchange cash flow series over time. It can be viewed as a series of forward contracts. Swaps address multi-period risks and are commonly used to manage interest rate, currency, or commodity exposure.

  • Key Usage: Interest rate swaps exchange fixed for floating interest rate payments to manage interest rate risk, while currency swaps exchange cash flows in different currencies to hedge currency risk.

Options

Definition

Options are versatile financial derivatives allowing the holder to buy (call option) or sell (put option) an underlying asset at a predetermined price (strike price) within a specific timeframe. The buyer of the option pays a premium to the seller (writer) for this right, without the obligation to execute the transaction.

Types of Options

  • Call Options: Grant the holder the right to purchase the underlying asset at the strike price. Investors buy calls when they anticipate the underlying asset’s price will increase.
  • Put Options: Provide the holder the right to sell the underlying asset at the strike price. Puts are purchased when an investor expects the underlying asset’s price to decline.

Exercise Styles

  • American Options: Can be exercised at any point up to and including the expiration date, offering maximum flexibility to the holder.
  • European Options: Can only be exercised on the expiration date itself, limiting the timing of execution to this single moment.

1.5 Applications of Derivatives

Hedging

Hedging aims to reduce risk by protecting against adverse price movements. It is widely used by businesses, investors, and financial institutions to manage exposure.

  • Forward Contracts: Lock in a future price, eliminating uncertainty.
  • Options: Provide insurance-like protection while allowing upside potential; the cost is the premium paid.
Examples
  1. Currency Hedge: A U.S. company expects to pay GBP 10 million in 3 months. It uses a forward contract to secure a fixed exchange rate, avoiding currency risk.
  2. Stock Hedge: An investor holds 1,000 Microsoft shares at $28 each. To protect against price drops, they buy put options with a $27.50 strike price, limiting losses while keeping upside potential. A two-month put option costs $1 per share.

Arbitrage

Arbitrage exploits price differences across markets to earn risk-free profits. It relies on the Law of One Price: identical assets should have the same price.

  • Buy low in one market, sell high in another.
  • Arbitrage aligns prices and improves market efficiency.
Example

A stock trades at GBP 100 in London and USD 150 in New York, with the exchange rate at 1.5300 GBP/USD.

  • Buy in New York for USD 150.
  • Sell in London for GBP 100.
  • Convert GBP 100 to USD 153 for a risk-free profit of USD 3.

Speculation

Speculators seek profit from price movements, accepting higher risk for potential reward.

  • Futures: High risk and reward; obligates buying/selling at a future date.
  • Options: Lower risk; limited loss (premium), but potential for large gains.
Examples
  1. Buying Shares: An investor with $2,000 buys stock directly, gaining full exposure to price movements.
  2. Buying Call Options: The investor buys call options, controlling more stock with less money; loss is limited to the premium.
  3. Futures: The investor takes a futures position betting on a price increase; potential for large gains but also large losses.

1.6 Criticisms and Misuses of Derivatives

While derivatives are vital for risk management and price discovery, they have been criticized for their potential misuse and the risks they can pose to the financial system. Key concerns include:

  1. Excessive Speculation: Derivatives can encourage speculative trading akin to gambling, leading to large losses when markets move unexpectedly.
  2. Systemic Risk: Large-scale or complex derivative positions can amplify financial instability. Failures can spread through interconnected markets, as seen in the 2008 crisis.
  3. Complexity: Many derivatives are difficult to understand and value, even for experienced investors, increasing the risk of mispricing and misuse.
  4. Blurring of Roles: Market participants may shift between hedging, speculation, and arbitrage, leading to excessive risk-taking under the guise of risk management.
  5. Need for Regulation: Without adequate oversight, derivatives can be misused, increasing market instability. Strong controls ensure derivatives serve their intended purpose.

Risk Mitigation and Regulatory Measures

  • Central Clearing Counterparties (CCPs): Reduce counterparty risk and increase transparency by acting as intermediaries.
  • Margin Requirements: Ensure traders hold sufficient capital to cover potential losses.
  • Post-2008 Reforms: Regulations like the Dodd-Frank Act (U.S.) and EMIR (EU) enhance market transparency, reduce systemic risk, and promote responsible use of derivatives.

1.7 Practice Questions and Problems

Time Value of Money

  1. A bank quotes an interest rate of 7% per annum with quarterly compounding. How much you will earn from $100 investment after (a) 1 year and (b) 3 years? What is the equivalent rate with (a) continuous compounding and (b) annual compounding? Verify your results.

Theoretical Foundations of Derivatives

  1. Explain carefully the difference between hedging, speculation, and arbitrage.
  2. What is the difference between the over-the-counter market and the exchange-traded market?
  3. “Options and futures are zero-sum games.” What do you think is meant by this statement?
  4. What is the difference between a long forward position and a short forward position?
  5. What is the difference between entering into a long forward contract when the forward price is $50 and taking a long position in a call option with a strike price of $50?
  6. Explain carefully the difference between selling a call option and buying a put option.
  7. When first issued, a stock provides funds for a company. Is the same true of an exchange-traded stock option? Discuss.

Practical Applications of Forwards and Futures

  1. A trader enters into a short cotton futures contract when the futures price is 50 cents per pound. The contract is for the delivery of 50,000 pounds. How much does the trader gain or lose if the cotton price at the end of the contract is (a) 48.20 cents per pound; (b) 51.30 cents per pound?
  2. An investor enters into a short forward contract to sell 100,000 British pounds for US dollars at an exchange rate of 1.5000 US dollars per pound. How much does the investor gain or lose if the exchange rate at the end of the contract is (a) 1.4900 and (b) 1.5200?

Practical Applications of Options

  1. A trader buys a call option with a strike price of $30 for $3. Does the trader ever exercise the option and lose money on the trade. Explain.
  2. Suppose that you write a put contract with a strike price of $40 and an expiration date in three months. The current stock price is $41 and the contract is on 100 shares. What have you committed yourself to? How much could you gain or lose?
  3. Suppose you own 5,000 shares that are worth $25 each. How can put options be used to provide you with insurance against a decline in the value of your holding over the next four months?
  4. You would like to speculate on a rise in the price of a certain stock. The current stock price is $29, and a three-month call with a strike of $30 costs $2.90. You have $5,800 to invest. Identify two alternative strategies, one involving an investment in the stock and the other involving investment in the option. What are the potential gains and losses from each?

Hedging Strategies

  1. Explain why a futures contract can be used for either speculation or hedging.
  2. A US company expects to have to pay 1 million Canadian dollars in six months. Explain how the exchange rate risk can be hedged using (a) a forward contract and (b) an option.
  3. The CME Group offers a futures contract on long-term Treasury bonds. Characterize the investors likely to use this contract.