💲Intro to Investments Unit 9 – Derivatives: Options and Futures

What Are Derivatives?

• Financial instruments that derive their value from an underlying asset (stocks, bonds, commodities, currencies, interest rates, market indexes)
• Enable investors to manage risk, speculate on price movements, and leverage their positions
• Value is determined by fluctuations in the underlying asset rather than the derivative itself
• Contracts between two parties that specify conditions under which payments are made
• Facilitate the transfer of risk from one party to another without exchanging the underlying asset
• Provide exposure to an asset without requiring full investment in the asset itself
• Offer flexibility in terms of customizing contract terms (expiration dates, strike prices, and settlement methods)

Types of Derivatives: Options and Futures

• Options grant the right, but not the obligation, to buy (call option) or sell (put option) an underlying asset at a predetermined price (strike price) within a specific timeframe (expiration date)
  • American options can be exercised any time before expiration
  • European options can only be exercised on the expiration date
• Futures are standardized contracts that obligate the buyer to purchase an asset (or the seller to sell an asset) at a predetermined future date and price
  • Futures contracts are traded on exchanges and have standardized terms (quantity, quality, delivery time and location)
• Swaps involve the exchange of cash flows between two parties based on a notional principal amount
  • Interest rate swaps exchange fixed-rate and floating-rate cash flows
  • Currency swaps exchange principal and interest payments in different currencies
• Forwards are customized contracts traded over-the-counter (OTC) that specify the sale of an asset at a future date and price
• Credit derivatives, such as credit default swaps (CDS), transfer credit risk from one party to another

How Options Work

• Call options give the buyer the right to purchase the underlying asset at the strike price, while put options give the right to sell
• Option buyers pay a premium to the option seller for this right, which represents the maximum potential loss for the buyer
• If the market price is favorable (above the strike for calls, below for puts), the option is exercised, and the buyer profits from the difference between the market and strike prices minus the premium
• If the market price is unfavorable, the option expires worthless, and the buyer loses only the premium paid
• Option sellers (writers) receive the premium and are obligated to fulfill the contract if the buyer exercises the option
  • Covered call writers own the underlying asset and face limited risk
  • Naked call writers do not own the underlying asset and face unlimited potential losses
• Options have time value (the portion of the premium attributable to the remaining time until expiration) and intrinsic value (the difference between the market price and strike price)

Understanding Futures Contracts

• Futures obligate both parties to transact at a future date, unlike options where the buyer has the choice
• Standardized contracts traded on exchanges with terms including the underlying asset, quantity, delivery date, and minimum price fluctuation (tick size)
• Buyers and sellers post margin (a percentage of the contract value) as collateral to ensure fulfillment of the contract
  • Initial margin is required to open a position
  • Maintenance margin is the minimum balance required to keep the position open
• Daily settlement process (marking to market) where gains and losses are credited or debited to each party's account based on the current market price
• Futures positions can be closed before expiration by entering an offsetting trade (selling a long position or buying back a short position)
• Futures prices converge with spot prices as the delivery date approaches, a process known as convergence

Pricing Models for Derivatives

• Black-Scholes-Merton (BSM) model is widely used for pricing European options on stocks and other securities
  • Inputs include the current stock price, strike price, time to expiration, risk-free interest rate, and implied volatility
• Binomial option pricing model uses a tree diagram to represent possible price paths of the underlying asset over time
  • Suitable for pricing American options and incorporating early exercise
• Monte Carlo simulation generates random price paths for the underlying asset to estimate the option's value
• Futures pricing considers the spot price, risk-free interest rate, time to expiration, storage costs, and convenience yield (for commodities)
  • Cost of carry model: Futures price = Spot price × (1 + Risk-free rate - Dividend yield)^Time to expiration
• Option Greeks measure the sensitivity of an option's price to various factors
  • Delta: change in option price per unit change in the underlying asset price
  • Gamma: change in delta per unit change in the underlying asset price
  • Theta: change in option price per unit of time decay
  • Vega: change in option price per unit change in implied volatility
  • Rho: change in option price per unit change in the risk-free interest rate

Trading Strategies with Options and Futures

• Hedging involves using derivatives to offset the risk of an existing position
  • Long put options can protect against price declines in a stock portfolio
  • Short futures can hedge against falling prices for commodity producers
• Speculation seeks to profit from anticipated price movements without owning the underlying asset
  • Buying call options or futures to benefit from expected price increases
  • Buying put options or selling futures to profit from expected price decreases
• Spread strategies combine multiple options or futures contracts to limit risk and/or reduce the cost of establishing a position
  • Bull call spread: long a lower-strike call and short a higher-strike call with the same expiration
  • Bear put spread: long a higher-strike put and short a lower-strike put with the same expiration
  • Calendar spread: long and short options with different expirations or futures with different delivery months
• Arbitrage exploits price discrepancies between related assets or markets to lock in a risk-free profit
  • Index arbitrage: simultaneously buying (selling) the undervalued (overvalued) asset and taking the opposite position in the fairly valued asset

Risk Management Using Derivatives

• Derivatives allow investors to transfer, mitigate, or assume various types of risk
• Market risk (price fluctuations) can be managed using futures, options, and swaps to lock in prices or limit potential losses
• Interest rate risk (changes in interest rates) can be hedged with interest rate swaps, futures, and options
  • Companies can swap floating-rate debt for fixed-rate payments to achieve predictable interest expenses
• Currency risk (exchange rate fluctuations) can be mitigated using currency futures, options, and swaps
  • Exporters can sell currency futures to lock in future exchange rates and protect against depreciation
• Credit risk (default by a counterparty) can be managed with credit derivatives like credit default swaps (CDS)
  • CDS buyers pay a premium to the seller and receive a payout if a specified credit event occurs (bankruptcy, failure to pay)
• Volatility risk (changes in implied volatility) can be managed using options strategies like straddles and strangles
  • Long straddles (buying both a call and put with the same strike and expiration) profit from increased volatility
  • Short strangles (selling an out-of-the-money call and put with the same expiration) profit from decreased volatility

Real-World Applications and Case Studies

• Airlines use fuel futures and options to hedge against rising jet fuel prices and protect profit margins
• Agricultural producers employ futures to lock in selling prices for their crops and mitigate the impact of price volatility
• Pension funds and insurers use interest rate swaps to match the duration of their assets and liabilities, reducing interest rate risk
• Multinational corporations manage currency risk by hedging foreign exchange exposures with currency forwards and options
• Speculators use futures to gain leveraged exposure to various markets (commodities, currencies, indexes) without owning the underlying assets
• In the 2008 financial crisis, credit default swaps (CDS) on mortgage-backed securities (MBS) played a significant role in spreading credit risk throughout the financial system
• The collapse of Long-Term Capital Management (LTCM) in 1998 highlighted the potential risks of leveraged derivatives trading and the importance of proper risk management
• In 2012, JPMorgan Chase suffered a $6.2 billion trading loss known as the "London Whale" incident, which involved complex credit derivatives and inadequate risk oversight