Financial Derivatives Mid-Term PDF

# Lecture (1) ## Financial Derivatives ### Introduction (Part 1) ## I. Introduction to Financial Derivatives ### Derivatives: Definition and using #### What are financial derivatives? Financial derivatives are financial contracts whose value is derived from an underlying asset. This underlying...

# Lecture (1) ## Financial Derivatives ### Introduction (Part 1) ## I. Introduction to Financial Derivatives ### Derivatives: Definition and using #### What are financial derivatives? Financial derivatives are financial contracts whose value is derived from an underlying asset. This underlying asset can be anything from a stock or commodity to an interest rate or currency. The value of the derivative fluctuates based on the performance of the underlying asset. #### Why use derivatives? - **Risk Management:** Derivatives can be used to hedge against potential losses in investments. For example, a farmer might use futures contracts to lock in a price for their crops, protecting them from price fluctuations. - **Speculation:** Derivatives can also be used to speculate on price movements. For instance, a trader might buy a call option on a stock if they believe the stock price will rise. - **Leverage:** Derivatives often involve a small initial investment compared to the potential payoff. This can amplify both gains and losses. ### Common types of derivatives: - **Futures:** Contracts that oblige the buyer to purchase a specific asset at a predetermined price on a future date. - **Options:** Contracts that give the buyer the right, but not the obligation, to buy or sell an underlying asset at a predetermined price on or before a certain date. - **Forwards:** Similar to futures but traded over the counter (OTC) markets "broker-dealer network" rather than on an exchange market. - **Swaps:** Agreements to exchange one asset for another, often involving interest rates or currencies. ### Future contracts: A Simplified Explanation Futures contracts are one of the most common types of derivatives. They're standardized agreements to buy or sell a specific asset at a predetermined price on a future date. #### Key features of futures contracts: - **Standardization:** Futures contracts have specific terms, such as the underlying asset, quantity, delivery date, and trading exchange. This makes them highly liquid. - **Leverage:** Futures contracts often require a small margin deposit, allowing investors to control a large amount of the underlying asset with a relatively small investment. - **Risk and Reward:** Leverage can amplify both gains and losses. A small price movement in the underlying asset can lead to significant profits or losses. ## Hedging: Futures contracts can be used to hedge against price fluctuations in the underlying asset. For example, a farmer might buy futures contracts on wheat to lock in a selling price for their crop. ## Speculation: Futures contracts can also be used to speculate on price movements. For instance, a trader might buy futures contracts on gold if they believe the gold price will rise. ## Example: Let's say a farmer is concerned about a potential drop in wheat prices. To protect themselves, they could buy a futures contract for wheat. This contract would obligate them to buy a certain amount of wheat at a predetermined price on a future date. If the market price falls below the contract price, the farmer can sell their physical wheat at a higher price than the market rate. ## Options Contracts: A Simplified Explanation Options contracts are another popular type of derivative that give the buyer the right, but not the obligation, to buy or sell an underlying asset at a predetermined price on or before a certain date. #### Key features of options contracts: - **Call Options:** Give the buyer the right to buy the underlying asset at a predetermined price (strike price). - **Put Options:** Give the buyer the right to sell the underlying asset at a predetermined price (strike price). - **Premium:** The buyer pays a premium to acquire the option. #### In-the-Money, Out-of-Money, at-the-Money: - **Time Value:** The option's premium is influenced by the time remaining until expiration and the volatility of the underlying asset. - **In-the-Money:** The option premium is influenced by the time remaining until expiration and the volatility of the underlying asset. An option is in-the-money if it would be profitable to exercise immediately. It's out-of-money if it would be a loss to exercise, and at-the-money if you believe that the price of a particular stock would be a loss to exercise. ## Example: Imagine the strike price is equal to the current market price, XYZ, will rise significantly in the next month. You could buy a call option on XYZ with a strike price of $50. If the stock price rises to $60, you can exercise the option and buy XYZ at $50, then sell it for $60, making a profit. However, if the stock price falls below $50, your option will expire worthless, and you'll only lose the premium you paid. ## Swaps: A Simplified Explanation Swaps are agreements between two parties to exchange one asset for another. They're often used to manage risk or to obtain specific financial benefits. #### Common types of swaps: - **Interest Rate Swaps:** Two parties agree to exchange interest payments for a notional principal amount. This can be used to hedge against interest rate risk or to obtain a more favorable interest rate. - **Currency Swaps:** Two parties agree to exchange principal amounts in different currencies. This can be used to hedge against foreign exchange risk or to obtain a more favorable exchange rate. - **Commodity Swaps:** Two parties agree to exchange the price of a commodity. This can be used to hedge against commodity price risk or to obtain a more favorable commodity price. ## Example: A company with a floating rate loan might want to lock in a fixed interest rate. They could enter an interest rate swap with another party, agreeing to pay a fixed interest rate in exchange for receiving a floating rate interest payment. This would effectively convert their floating rate loan into a fixed rate loan. ## Forwards: A Simplified Explanation Forwards are similar to futures contracts in that they involve an agreement to buy or sell an asset at a predetermined price on a future date. However, there are some key differences: #### Key Features of Forwards: - **Customization:** Forwards are typically customized contracts negotiated between two parties, while futures contracts are standardized and traded on exchanges. - **Settlement:** Forwards can be settled physically (by delivering the underlying assets) or cash. Futures contracts are typically settled in cash. - **Counterparty Risk:** Forwards involves counterparty risk, meaning that one party may default on the contract. Futures contracts are backed by a clearinghouse, which reduces counterparty risk. #### Key Uses of Forwards: - **Hedging:** Forwards can be used to hedge against price fluctuations in underlying assets, similar to futures contracts. - **Speculation:** Forwards can also be used for speculation on price movements. - **Financing:** Forwards can be used as a financing tool. For example, a company might enter into a forward contract to sell its products at a future date, which can provide them with cash flow up front. ## Example: A company that expects to need a large amount of copper in three months might enter into a forward contract to buy copper at a predetermined price. This would protect the company against potential price increases in copper. ## Derivatives and Risk Management Derivatives are powerful tools that can be used to manage a variety of risks. Here are some common ways derivatives are used in risk management: ## Hedging - **Protecting Against Price Fluctuations:** Derivatives can be used to hedge against price fluctuations in underlying assets, such as stocks, commodities, or currencies. For example, a company that produces oil can use futures contracts to lock in a price for their oil, protecting them against potential price declines. - **Interest Rate Risk:** Interest rate swaps can be used to manage interest rate risk, such as the risk of rising interest rates on a company's debt. ## Speculation - **Profiting from Price Movements:** Derivatives can also be used to speculate on price movements. For example, a trader might buy a call option on a stock if they believe the stock price will rise. ## Arbitrage - **Exploiting Price Differences:** Arbitrage involves buying and selling an asset at the same time in different markets to profit from price differences. Derivatives can be used to facilitate arbitrage. ## Example: Let's assume the following: - Spot exchange rate: 1 USD = 100 JPY - 1-year forward exchange rate: 1 USD = 98 JPY - This indicates that the market expects the Japanese yen to appreciate against the US dollar over the next year. - risk-free interest rate in Japanese banks is 2% ## Arbitrage Opportunity: 1. **Borrow USD:** A trader borrows $1 million. 2. **Convert to JPY:** The trader converts the $1 million to 100 million JPY. 3. **Enter into a forward contract:** The trader sells 100 million JPY forward for delivery in one year at the rate of 98 JPY/USD. 4. **Invest JPY:** The trader invests the 100 million JPY in a Japanese bank at a risk-free interest rate. ## Profit Calculation: - **After one year:** The trader receives the principal plus interest from the Japanese bank, this amounts to 102 million JPY. - **Deliver forward contract:** The trader delivers 100 million JPY as per the forward contract. - **Convert JPY to USD:** The trader receives 102 million JPY / 98 JPY/USD = $1,040,816. - **Repay loan:** The trader repays the $1 million loan. - **Profit:** The trader earns a risk-free profit of $40,816. ## Portfolio Optimization - **Improving Risk-Return Trade-offs:** Derivatives can be used to optimize investment portfolios by adjusting the risk-return profile. For example, a hedge fund might use options to create synthetic positions that have a desired risk-return characteristic. ## It's important to note that while derivatives can be effective risk management tools, they also involve significant risks. Misuse of derivatives can lead to substantial losses. Investors should have a thorough understanding of derivatives and their risks before using them. # Lecture (2) ## Financial Derivatives ### Introduction (Part 2) ## Underlying Assets and Their Role in Derivative Pricing Underlying assets are the fundamental assets upon which derivatives are based. These assets can be anything from stocks, bonds, commodities, currencies, to interest rates or even weather indices. The value of a derivative is directly linked to the performance of its underlying asset. ## How Underlying Assets Influence Derivative Pricing: - **Price Fluctuations:** The price movements of the underlying asset directly affect the value of the derivative. For example, if the price of a stock increases, a call option on that stock will also increase in value. - **Volatility:** The volatility, or the degree of price fluctuation, of the underlying asset is a key factor in derivative pricing. Higher volatility generally increases the value of options but can also increase the risk associated with holding them. - **Time to Expiration:** For derivatives with a finite lifespan, the time remaining until expiration affects the price. As time passes, the opportunity for the underlying asset's price to move significantly decreases, which can impact the derivative's value. - **Interest Rates:** Interest rates can influence the pricing of derivatives, especially those based on interest-bearing assets like bonds. Higher interest rates can reduce the present value of future cash flows, affecting the price of derivatives. - **Dividends:** For equity derivatives, dividends paid by the underlying stock can influence the price. Dividends reduce the value of the stock, which can affect the value of options and other equity-based derivatives. ## Examples of Underlying Assets: - **Stocks:** Derivatives based on stocks include options, futures, and swaps. - **Bonds:** Derivatives based on bonds include interest rate swaps and bond options. - **Commodities:** Derivatives based on commodities include futures contracts for oil, gold, wheat, and other commodities. - **Currencies:** Derivatives based on currencies include currency futures, options, and swaps. - **Indices:** Derivatives based on indices, such as the S&P 500 or the Nasdaq, include index futures and options. ## In essence, understanding the underlying asset is crucial for understanding the pricing and risk associated with derivatives. By analyzing the price movements, volatility, and other factors related to the underlying asset, investors can make informed decisions about trading derivatives. ## The Historical Development of Derivatives Markets Derivatives markets have evolved significantly over time, driven by various economic, financial, and technological factors. Here's a brief overview of their historical development: - **Early Origins** - **Ancient Babylon:** One of the earliest recorded derivatives contracts was a type of futures contract used to hedge agricultural risks. Farmers would agree to sell their crops at a predetermined price at a future date. - **Medieval Europe:** Derivatives were used to manage risks associated with maritime trade and currency exchange. - **Modern Era** - **18th Century:** The futures market for commodities, particularly grains, began to develop in the United States. - **19th Century:** Options markets emerged in the United States and Europe. - **20th Century:** - **1930s:** The Chicago Board of Trade (CBOT) became a major center for futures trading. - **1970s:** The introduction of financial derivatives, such as options on stocks and indexes, expanded the scope of derivatives markets. - **1980s:** The development of over-the-counter (OTC) derivatives markets, particularly for interest rate swaps, led to a significant increase in the size and complexity of the derivatives industry. - **1990s:** Technological advancements, such as electronic trading platforms, facilitated the growth of derivatives markets. - **21st Century** - **Financial Crisis of 2008:** The crisis exposed the risks associated with complex derivatives, leading to increased regulation and scrutiny of the derivatives industry. - **Continued Growth:** Despite the challenges, derivatives markets have continued to grow and evolve, driven by factors such as globalization, increased market volatility, and the need for risk management tools. ## Key Factors Driving the Development of Derivatives Markets: - **Risk Management:** Derivatives provide a way for businesses and individuals to manage risks associated with price fluctuations, interest rate changes, and other uncertainties. - **Speculation:** Derivatives can be used for speculative purposes, allowing investors to profit from price movements. - **Hedging:** Derivatives can be used to hedge existing positions, reducing the potential for losses. - **Technological Advancements:** Electronic trading platforms and other technological innovations have made it easier to trade derivatives. - **Regulatory Changes:** Regulatory frameworks have evolved to address the risks and benefits of derivatives markets. ## The historical development of derivatives markets has been marked by periods of growth, innovation, and challenges. As the global economy continues to evolve, derivatives markets are likely to play an increasingly important role in financial markets. # Lecture (3) ## Financial Derivatives ### Future Contracts (Part 1) ## II. Futures Markets - **Future contract:** Definition and Characteristics and common types - **Futures Contracts:** Trading mechanics and margin requirements - **Pricing of futures contracts** - **Hedging and speculation using futures** ## Future contract: Definition and Characteristics and Common Types ### Definition of Futures Contracts: Futures contracts are standardized agreements to buy or sell a specific asset at a predetermined price on a future date. They trade on organized exchanges, such as the Chicago Mercantile Exchange (CME) or the Intercontinental Exchange (ICE). ### Characteristics of Futures Contracts: - **Standardization:** Futures contracts have specific terms, such as the underlying asset, quantity, delivery date, and trading exchange. This standardization makes them highly liquid and easy to trade. - **Leverage:** Futures contracts often require a small margin deposit, allowing investors to control a large amount of the underlying asset with a relatively small investment. This can amplify both gains and losses. - **Liquidity:** Due to their standardization and trading on exchanges, futures contracts are highly liquid, meaning they can be bought or sold easily. - **Mark-to-Market:** Futures contracts are marked-to-market daily, meaning that any gains or losses are realized and reflected in the investor's account balance. This can lead to significant gains or losses even if the contract is not held until expiration. - **Settlement:** Most futures contracts are settled in cash, rather than by physical delivery of the underlying asset. The cash settlement is based on the difference between the contract price and the market price of the underlying asset on the delivery date. - **Counterparty Risk:** While futures contracts are backed by a clearinghouse, which reduces counterparty risk, there is still a risk that the clearinghouse may default. ### Common types of futures contracts: - **Interest Rate Futures:** Interest rate futures are contracts that allow investors to speculate on or hedge against changes in interest rates. The underlying asset for these contracts is typically a bond index, such as the Eurodollar futures contract or the 10-year Treasury note futures contract. #### Key Uses of Interest Rate Futures: - **Interest Rate Hedging:** Companies and individuals can use interest rate futures to hedge against the risk of rising interest rates on their debt or investments. - **Speculation:** Traders can use interest rate futures to speculate on the direction of interest rates. For example, if a trader believes that interest rates will rise, they can sell a futures contract on a bond index. - **Currency Futures:** Currency futures are contracts that allow investors to speculate on or hedge against changes in exchange rates. The underlying asset for these contracts is a specific currency pair. #### Key Uses of Interest Rate Futures: - **Currency Hedging:** Companies that do business in foreign markets can use currency futures to hedge against fluctuations in exchange rates. - **Speculation:** Traders can use currency futures to speculate on the direction of exchange rates. For example, if a trader believes that the euro will appreciate against the U.S. dollar, they can buy a euro futures contract. - **Commodity Futures:** Commodity futures are contracts that allow investors to speculate on or hedge against changes in commodity prices. The underlying asset for these contracts can be a variety of commodities, such as agricultural products, metals, and energy. #### Key Uses of Interest Rate Futures: - **Commodity Hedging:** Producers and consumers of commodities can use futures contracts to hedge against price fluctuations. For example, a wheat farmer can sell a futures contract for wheat to lock in a price for their crop. - **Speculation:** Traders can use commodity futures to speculate on the direction of commodity prices. For example, if a trader believes that oil prices will rise, they can buy an oil futures contract. ## Note: All three types of futures contracts can be used for both hedging and speculation, depending on the investor's objectives. ## Futures Contracts: Trading Mechanics and Margin Requirements: ### Trading Mechanics Futures contracts are traded on organized exchanges, such as the Chicago Mercantile Exchange (CME) or the Intercontinental Exchange (ICE). Traders can buy or sell futures contracts through a brokerage firm. The trading process for futures contracts typically involves the following steps: 1. **Opening a Futures Account:** To trade futures contracts, you need to open a futures account with a brokerage firm. 2. **Placing an Order:** Traders can place orders to buy or sell futures contracts at a specific price or at the best available price. 3. **Margin Requirements:** To open a futures position, you need to deposit a margin, which is a percentage of the contract's value. The margin serves as a guarantee that you will fulfill your obligations under the contract. 4. **Daily Mark-to-Market:** As mentioned earlier, futures contracts are marked-to-market daily. This means that any gains or losses are realized and reflected in your account balance. If your account balance falls below the maintenance margin level, you may be required to deposit additional margin. 5. **Closing the Position:** To close a futures position, you can simply sell a futures contract if you have bought one, or buy a futures contract if you have sold one. ### Margin Requirements Margin requirements for futures contracts vary depending on the underlying asset and the volatility of the market. However, they are typically a small percentage of the contract's value. #### Factors that affect margin requirements: - **Underlying Asset:** Futures contracts on more volatile assets generally have higher margin requirements. - **Market Conditions:** Margin requirements can change based on market conditions, such as increased volatility or market stress. - **Exchange Rules:** Each exchange has its own rules regarding margin requirements. #### Types of Margins: - **Initial Margin:** The amount of margin that must be deposited to open a new futures position. - **Maintenance Margin:** The minimum amount of equity that must be maintained in a futures account to avoid a margin call. If your account balance falls below the maintenance margin level, you will receive a margin call, requiring you to deposit additional margin to bring your account balance back up to the required level. Failure to meet a margin call can result in the liquidation of your position. ## It's important to note that leverage can amplify both gains and losses in futures trading. While margin requirements can provide some protection against losses, there is always the risk of losing more than your initial investment. ## A Numerical Example of Futures Trading Mechanics and Margin Requirements ### Scenario: Let's assume you want to trade a futures contract on the S&P 500 index. The contract size is $250 per point, and the initial margin requirement is 5%. ### Step 1: Open a Futures Account You open a futures account with a brokerage firm. ### Step 2: Place an Order The current price of the S&P 500 index is 4,500 points. You believe the index will rise, so you buy one S&P 500 futures contract. ### Step 3: Margin Requirements The initial margin requirement for the contract is 5% of the contract value, which is 5% * $250 * 4,500 = $5,625. You deposit this amount into your futures account. ### Step 4: Daily Mark-to-Market Suppose the S&P 500 index closes at 4,600 points at the end of the day. Your futures contract has gained 100 points. The daily profit is 100 points * $250 per point = $25,000. Your account balance will now be $5,625 (initial margin) + $25,000 (profit) = $30,625. ### Step 5: Closing the Position The next day, you believe the S&P 500 index has reached its peak, so you decide to close your position. You sell your futures contract at a price of 4,550 points. Your loss is 50 points * $250 per point = $12,500. Your account balance will now be $30,625 (previous balance) - $12,500 (loss) = $18,125. ### Margin Call: If the S&P 500 index had fallen significantly, your account balance could have fallen below the maintenance margin level. In that case, you would have received a margin call, requiring you to deposit additional margin to bring your account balance back up to the required level. Failure to meet a margin call could result in the liquidation of your position. # Lecture (4) ## Financial Derivatives ### Future Contracts (Part 2) ## Pricing of Futures Contracts The price of a futures contract is determined by the relationship between the spot price of the underlying asset and the interest rates prevailing in the market. This relationship is captured by the cost of carry model. ## Cost of Carry Model The cost of carry model states that the futures price (F) is equal to the spot price (S) plus the cost of carrying the asset until the delivery date, minus any income earned from holding the asset. Mathematically, it can be expressed as: $F = S * e^(r - q) * t$ Where: - F: Futures price - S: Spot price - e: Euler's number (approximately 2.71828) - r: Risk-free interest rate - q: Dividend yield (for stocks) or storage cost (for commodities) - t: Time to expiration ## Key Factors Affecting Futures Prices: - **Spot Price:** The current market price of the underlying asset. - **Interest Rates:** Higher interest rates generally lead to higher futures prices for assets that pay no dividends (e.g., commodities). - **Dividend Yield:** For stocks, a higher dividend yield can lead to lower futures prices. - **Storage Costs:** For commodities, higher storage costs can lead to higher futures prices. - **Contango and Backwardation:** - **Contango:** When the futures price is higher than the spot price, it's known as contango. This occurs when the cost of carry is positive. - **Backwardation:** When the futures price is lower than the spot price, it's known as backwardation. This occurs when the cost of carry is negative. ## Example: If the spot price of gold is $1,800 per ounce, the risk-free interest rate is 3%, and the time to expiration is 3 months, then the futures price can be calculated as: $F = 1800 * e^(0.03 - 0) * (3/12) ≈ 1813.50$ This indicates that the futures price for gold is slightly higher than the spot price due to the cost of carry. ## Note: This is a simplified explanation of futures pricing. In reality, other factors such as market sentiment, supply and demand, and geopolitical events can also influence futures prices. ## Hedging and Speculation Using Futures Futures contracts can be used for both hedging and speculation. ### Hedging with Futures Hedging involves using futures contracts to offset potential losses in another market. Here are some examples of hedging with futures: - **Commodity Price Hedging:** A farmer can use futures contracts to lock in a price for their crops, protecting them against potential price declines. For example, a wheat farmer can sell a futures contract for wheat, ensuring that they will receive a certain price for their wheat regardless of the market price at harvest time. - **Interest Rate Hedging:** A company that is concerned about rising interest rates on its debt can use interest rate futures to hedge against potential increases in interest expenses. - **Currency Hedging:** A company that does business in foreign markets can use currency futures to hedge against fluctuations in exchange rates. ### Speculation with Futures Speculation involves using futures contracts to profit from price movements in the underlying asset. Here are some examples of speculation with futures: - **Bullish Speculation:** If a trader believes that the price of an asset will rise, they can buy a futures contract. If the price does rise, they can sell the contract for a profit. - **Bearish Speculation:** If a trader believes that the price of an asset will fall, they can sell a futures contract. If the price does fall, they can buy the contract back for a profit. ### Key Differences Between Hedging and Speculation: - **Purpose:** Hedging is about reducing risk, while speculation is about making a profit. - **Strategy:** Hedgers typically use futures contracts to offset existing positions, while speculators use futures contracts to take positions based on their market outlook. - **Risk Tolerance:** Hedgers are generally more risk-averse than speculators. ## It's important to note that both hedging and speculation involve risk. Futures trading can be highly volatile, and it's possible to lose more than your initial investment.