Fiche de révision : Fundamentals of Futures, Options, and Arbitrage

📋 Course Outline

1. Futures and Derivatives
2. Equity and ETFs
3. Risk Management Strategies
4. Market Arbitrage Opportunities
5. Futures Pricing Components
6. Options Types and Strategies
7. Options Pricing and Greeks
8. Black-Scholes Model

📖 1. Futures and Derivatives

🔑 Key Concepts & Definitions

• Commodity trading is mostly in futures contracts: The primary method of trading commodities involves agreements to buy or sell a specific quantity at a predetermined price for future delivery, minimizing price uncertainty (source content).
• Derivatives facilitate risk management by providing certainty of future costs/revenues: Financial instruments like futures, options, and swaps allow market participants to lock in prices or revenues, reducing exposure to adverse price movements (source content).
• Speculative use of derivatives involves trading for profit: Traders engage in derivatives transactions aiming to profit from expected price changes, without necessarily intending to take physical delivery (source content).
• Hedging uses derivatives to offset adverse price movement risk: Market participants, such as farmers or producers, use derivatives to lock in prices and protect against potential losses from unfavorable market shifts (source content).
• Arbitrage exploits price discrepancies between markets: Traders capitalize on differences in asset prices across different markets or locations by simultaneously buying low and selling high, ensuring risk-free profit (source content).
• Futures maturity dates vary by commodity, e.g., oil monthly: The expiration or settlement dates for futures contracts depend on the commodity, with some like oil having monthly maturities, affecting trading and delivery schedules (source content).

📝 Essential Points

• Most commodity trading occurs through futures contracts, which are standardized agreements to buy or sell an asset at a future date (source content).
• Derivatives are crucial for risk management, as they provide certainty regarding future costs or revenues and help set maximum or minimum values for key variables such as prices (source content).
• The use of derivatives can be speculative, aiming for profit, or hedging, to mitigate risk, with arbitrage serving to exploit market inefficiencies (source content).
• Futures prices incorporate current spot prices, costs of carrying the asset (cost of carry), and benefits of holding the asset (convenience yield), reflecting forward expectations (source content).
• The majority of futures contracts settle in cash rather than physical delivery, with only about 2.00% resulting in actual transfer of commodities (source content).
• Futures maturity dates are specific to each commodity, influencing trading strategies and risk management practices (source content).

💡 Key Takeaway

Futures and derivatives are essential tools in commodity markets, enabling risk management, speculative profit, and arbitrage opportunities, with futures contracts primarily used for trading and hedging purposes, and their maturity dates varying by commodity.

📖 2. Equity and ETFs

🔑 Key Concepts & Definitions

• Purchasing equity (stocks): Buying shares of a company, which provides direct exposure to the company's performance and value. Examples include shares of Exxon and Shell.

• Equities: Financial instruments representing ownership in a company, such as shares of Exxon or Shell, giving investors a claim on the company's assets and earnings.

• ETFs (Exchange-Traded Funds): Investment funds traded on stock exchanges that hold a diversified portfolio of assets, often linked to specific indices or commodities, providing passive exposure. Examples include SPDR Gold Trust (GLD), SLV, and OLIK.

• Index funds: A type of mutual fund or ETF that aims to replicate the performance of a specific market index, offering broad market exposure with passive management.

• Equity options valuation: The process of determining the fair value of options on stocks, which considers factors such as dividends that can affect option prices.

📝 Essential Points

• Purchasing equities provides investors with direct exposure to companies, making their returns closely tied to company performance. Examples include shares of Exxon and Shell.

• ETFs and index funds offer passive investment strategies, often linked to commodity prices or market indices, enabling investors to diversify and reduce risk.

• ETFs like SPDR Gold Trust (GLD), SLV, and OLIK are designed to track commodity prices, providing exposure without directly owning the physical commodities.

• Equity options valuation incorporates dividends, which can influence the premium and fair value of options on stocks. Dividends reduce the stock price and thus impact the intrinsic value of options.

💡 Key Takeaway

Investing through equities provides direct company exposure, while ETFs and index funds offer passive, diversified exposure often linked to commodities or market indices; understanding how dividends influence equity options valuation is essential for accurate pricing.

📖 3. Risk Management Strategies

🔑 Key Concepts & Definitions

• Derivatives (source content): Financial instruments used strategically for hedging risk, allowing parties to set maximum or minimum values for key variables such as the price of the underlying asset, thereby managing potential adverse price movements.

• Hedging (source content): The practice of using derivatives to offset the risk of an adverse price movement in an asset. For example, a farmer can lock in a selling price for their crop by selling futures contracts, effectively securing a known profit margin.

• Arbitrage (source content): Exploiting price discrepancies between markets by simultaneously buying low in one market and selling high in another, thus locking in a risk-free profit. For example, buying gold in New York and selling it in London when prices differ.

• Maximum/Minimum Values (source content): Risk management involves setting boundaries for key variables, such as price limits, to prevent losses beyond acceptable levels. Derivatives facilitate this by providing contractual agreements that specify these limits.

• Price Uncertainty Management (source content): Derivatives help manage the unpredictability of underlying asset prices by providing certainty of future costs or revenues, thus enabling better planning and risk mitigation.

📝 Essential Points

• Derivatives are primarily used for hedging, which involves strategically offsetting potential losses from adverse price movements (source content). They help set maximum or minimum thresholds for key variables, reducing exposure to volatility.

• Hedging examples include locking in profits through futures contracts, such as a farmer securing a fixed selling price for their crop, thereby protecting against price drops.

• Arbitrage opportunities arise when market inefficiencies cause price discrepancies, allowing traders to buy low in one market and sell high in another simultaneously, resulting in risk-free profits (source content).

• Futures contracts typically have specific maturity dates (e.g., monthly for oil), but only about 2% result in physical delivery; most settle in cash based on the difference between the contract price and the spot price at expiration.

• Futures prices incorporate forward expectations, including interest rates and storage costs, reflecting the anticipated future value of the underlying asset (source content).

💡 Key Takeaway

Derivatives are essential tools in risk management, enabling market participants to hedge against adverse price movements, lock in profits, and exploit market inefficiencies through arbitrage, thereby reducing overall exposure to price uncertainty.

📖 4. Market Arbitrage Opportunities

🔑 Key Concepts & Definitions

Arbitrage (source content): The practice of taking advantage of a price discrepancy in a market to generate risk-free profit by simultaneously buying and selling in different markets.

Example of Arbitrage (source content): Gold priced at $4 in New York and$5 in London; a trader can buy gold in New York and sell it in London to lock in a risk-free profit.

Market Inefficiencies (source content): Situations where prices of assets do not align across different markets, creating opportunities for arbitrage.

Simultaneous Transactions (source content): The requirement in arbitrage to buy and sell assets at the same time to lock in risk-free profit, minimizing exposure to price changes.

Use of Derivatives in Arbitrage (source content): Arbitrage often involves derivatives to exploit price discrepancies, as derivatives can facilitate riskless profit strategies.

📝 Essential Points

• Arbitrage involves risk-free profit from price discrepancies, such as differing gold prices in New York and London markets, which allows traders to buy low in one market and sell high in another simultaneously.
• Arbitrage opportunities arise from market inefficiencies, where asset prices are not aligned across different markets or platforms.
• Most futures contracts do not result in physical delivery (only 2.00%), with the majority settling in cash based on the difference between the spot and futures prices at expiration.
• Arbitrage requires precise timing and execution of simultaneous buying and selling to avoid exposure to market risk.
• Derivatives are a key tool in arbitrage strategies, enabling traders to lock in riskless profits by exploiting price discrepancies.

💡 Key Takeaway

Arbitrage exploits market inefficiencies by executing simultaneous transactions across different markets to secure risk-free profits, often utilizing derivatives to enhance these strategies.

📖 5. Futures Pricing Components

🔑 Key Concepts & Definitions

• Futures Price Formula:
  The theoretical price of a futures contract is calculated as:
  Futures Price = Spot + Cost of Buying - Benefits of Buying
  This formula incorporates the current spot price, the costs involved in acquiring the asset, and the benefits gained from holding the asset until delivery or settlement.

• Cost of Carry:
  The Cost of Buying now, which includes expenses such as storage, insurance, financing, and other costs associated with holding the underlying asset until the futures contract's maturity (see "Cost of Buying" in the futures price formula).

• Convenience Yield:
  The Benefits of Buying now, representing the advantages of holding the physical commodity, such as ensuring supply, avoiding shortages, or gaining access to scarce resources (see "Benefits of Buying" in the futures price formula).

• Futures Prices Reflect Forward Expectations:
  Futures prices incorporate market expectations about future interest rates, storage costs, and other relevant factors, thus providing a forward-looking valuation that accounts for these variables (see "Futures prices reflect forward expectations including interest rates and storage costs").

• Physical Delivery vs. Cash Settlement:
  Only a small percentage (about 2.00%) of futures contracts result in physical delivery of the underlying asset. Most settle in cash, based on the difference between the futures price and the spot price at expiration, reducing the need for actual transfer of commodities.

📝 Essential Points

• The futures price is derived from the spot price adjusted for costs and benefits associated with holding the asset until delivery.
• The Cost of Carry encompasses all expenses incurred from holding the asset, such as storage and financing costs, which increase the futures price relative to the spot.
• The Convenience Yield offsets some of the costs by providing benefits like inventory availability, which can reduce the futures price below the cost of carry in certain cases.
• Futures prices are forward-looking, reflecting market consensus on future interest rates, storage costs, and other variables, making them more than just current spot prices (see "Futures prices reflect forward expectations including interest rates and storage costs").
• Most futures contracts are cash-settled, with only a small fraction leading to physical delivery, emphasizing their role in financial risk management rather than commodity transfer.

💡 Key Takeaway

Futures prices are determined by the current spot price adjusted for the costs of holding the asset and the benefits of holding it, reflecting market expectations of future interest rates, storage costs, and other relevant factors. Most futures settle in cash, serving primarily as financial instruments for hedging and speculation.

📖 6. Options Types and Strategies

🔑 Key Concepts & Definitions

• Calls (right to buy): Options that give the holder the right, but not the obligation, to purchase the underlying asset at a specified strike price before the option expires. (Source: Week 4)

• Puts (right to sell): Options that give the holder the right, but not the obligation, to sell the underlying asset at a specified strike price before expiration. (Source: Week 4)

• Buying and writing (selling) options:

  • Buying options: paying a premium to acquire the right (call or put).
  • Writing options: selling options to collect premiums, creating an obligation if the option is exercised. (Source: Week 4)

• Option cost calculation: The total cost of an option is determined by multiplying the premium per share by the contract size (usually 100 shares). For example, a premium of $0.50 per share for a contract covering 100 shares costs$50. (Source: Week 4)

• Breakeven price for a call option: The underlying asset's price at which the holder neither makes a profit nor incurs a loss, calculated as:

  $\text{Breakeven} = \text{Strike Price} + \text{Premium}$

  For example, if the strike price is $250 and the premium is$0.50, the breakeven is $250.50. (Source: Week 4)

• FX options: Financial derivatives that give the holder the right to buy or sell a currency at a specified exchange rate, providing flexibility in foreign currency transactions. (Source: Week 4)

📝 Essential Points

• Graphical representation: Calls and puts can be graphically illustrated to show payoff profiles:

  • Calls: profit increases as underlying price exceeds the strike price plus premium.
  • Puts: profit increases as underlying price falls below the strike price minus premium.

• Option strategies: Combining calls and puts allows for various strategies such as spreads, straddles, and protective options, which can be visualized through payoff diagrams.

• Premium and contract size: The premium is the price paid per share for the option, and the total cost depends on the contract size (usually 100 shares). This is crucial for calculating initial investment and breakeven points.

• FX options: They provide the right, not the obligation, to buy or sell foreign currency at a predetermined rate, useful for hedging currency risk or speculating on exchange rate movements.

💡 Key Takeaway

Options are versatile financial instruments that provide rights to buy or sell assets at predetermined prices, with their costs and payoff profiles easily represented graphically, enabling strategic risk management and speculative opportunities.

📖 7. Options Pricing and Greeks

🔑 Key Concepts & Definitions

• Options Price Components: The total value of an option is composed of Intrinsic Value, Cost of Money, Probability of a Profitable Move, and Share Price Adjustment. These factors collectively determine the premium an option commands in the market.

• Intrinsic Value of a Call: Defined as the difference between the Underlying Price and the Strike Price, i.e., Intrinsic value of a call = Underlying Price - Strike Price. It represents the immediate profit if the option is exercised.

• Intrinsic Value of a Put: Defined as the difference between the Strike Price and the Underlying Price, i.e., Intrinsic value of a put = Strike Price - Underlying Price. It indicates the immediate profit from exercising the put.

• Effect of Underlying Price Changes:

  • Increase: Call prices will increase, and put prices will decrease.
  • Decrease: Call prices will decrease, and put prices will increase.

• Effect of Interest Rate Changes:

  • Increase: Call prices increase, and put prices decrease.
  • Decrease: Call prices decrease, and put prices increase.

• Effect of Dividends (when underlying is equity):

  • Increase: Call prices decrease, and put prices increase.
  • Decrease: Call prices increase, and put prices decrease.

📝 Essential Points

• The Options Price formula incorporates four main components: Intrinsic Value, Cost of Money (reflecting interest rates and financing costs), Probability of a Profitable Move (the likelihood of favorable price movements), and Share Price Adjustment (effects due to dividends or other factors).

• The Black-Scholes Model aligns with these components, providing a theoretical framework for valuing options based on volatility, time, interest rates, and underlying asset price (see section 6).

• Changes in the underlying price directly impact call and put prices: rising underlying prices increase call values and decrease put values, and vice versa.

• Interest rate fluctuations influence option prices inversely: higher rates tend to favor call options and diminish put values, reflecting the cost of carrying the position.

• Dividends reduce call prices and increase put prices when the underlying is an equity, due to the expected cash flows affecting the underlying's value.

💡 Key Takeaway

Option prices are driven by intrinsic value, interest rates, the probability of favorable movements, and dividends; understanding how these factors interact helps in effective options valuation and strategic decision-making.

📖 8. Black-Scholes Model

🔑 Key Concepts & Definitions

• Black-Scholes model: A mathematical framework used for option valuation that provides theoretical prices based on underlying assumptions, incorporating factors such as volatility, time, and interest rates (see source content for application in options pricing).
• Options pricing components: The elements that determine an option's theoretical value, including intrinsic value, cost of money, probability of a profitable move, and share price adjustment (see options pricing considerations).
• Volatility: A measure of the price fluctuation of the underlying asset, which significantly influences the option's premium in the Black-Scholes model. Higher volatility increases the likelihood of profitable moves, thus raising option prices.
• Time: The remaining time until the option's expiration, impacting the value as longer durations provide more opportunity for favorable price movements. The Black-Scholes model explicitly incorporates this through the time to maturity.
• Interest rates: The risk-free rate used in the model to account for the cost of carrying an option position, affecting the theoretical valuation of calls and puts (see options pricing components).
• Theoretical option prices: The calculated values derived from the Black-Scholes model, assuming market efficiency and no arbitrage opportunities, serving as benchmarks for actual market prices.

📝 Essential Points

• The Black-Scholes model is fundamental for option valuation and assumes markets are efficient, with no arbitrage opportunities.
• It considers volatility, time to expiration, interest rates, and the current share price to compute a theoretical option price.
• The model is used to draw strategies like Bull Call Spread and Bear Put Spread, which involve combining options to manage risk and optimize payoffs.
• The intrinsic value of options (call = underlying price - strike, put = strike - underlying price) is a key component, but the Black-Scholes model extends beyond this by incorporating time value and volatility.
• Changes in underlying price, interest rates, and volatility directly influence the option's theoretical price as per the model's considerations.

💡 Key Takeaway

The Black-Scholes model provides a systematic way to estimate the fair value of options by integrating key factors like volatility, time, and interest rates, and it underpins many advanced options strategies such as spreads.

📊 Synthesis Tables

⚠️ Common Pitfalls & Confusions

1. Confusing derivatives used for speculation versus hedging; hedging aims to reduce risk, speculation aims for profit.
2. Assuming all futures contracts result in physical delivery; in reality, over 98% settle in cash.
3. Misunderstanding the role of convenience yield in futures pricing; it reflects benefits of holding the physical commodity.
4. Overlooking dividend effects when valuing equity options; dividends reduce stock prices, impacting option premiums.
5. Mistaking arbitrage for riskless profit; arbitrage requires execution risk management.
6. Confusing the Black-Scholes model's assumptions with real market conditions; it assumes constant volatility and interest rates.
7. Ignoring the impact of transaction costs and bid-ask spreads on arbitrage and trading strategies.

✅ Exam Checklist

• Know the primary use of futures contracts in commodity markets and their standardization (source content).
• Understand Smith's definition of the invisible hand and its relevance to market efficiency.
• Be able to explain how derivatives facilitate risk management and the difference between hedging and speculation (source content).
• Recognize the key components of futures pricing: spot price, cost of carry, and convenience yield (source content).
• Know that most futures contracts settle in cash, with only about 2% resulting in physical delivery (source content).
• Be familiar with the concept of arbitrage and how it exploits price discrepancies across markets (source content).
• Understand the role of equity and ETFs, including the difference between direct stock ownership and passive funds (source content).
• Know how dividends influence equity options valuation and the importance of incorporating dividends into pricing models (source content).
• Be able to describe risk management strategies using derivatives, including setting maximum and minimum values (source content).
• Master the Black-Scholes model, including its assumptions, inputs, and Greeks (delta, gamma, theta, vega, rho).
• Recognize the differences between options types: calls and puts, and their strategic uses.
• Understand the importance of futures maturity dates and their impact on trading strategies.
• Be aware of common pitfalls in derivatives trading and valuation, including assumptions and market realities.