Notes on Derivatives and Options

Definition of Derivatives: Financial instruments whose value derives from the price of an underlying asset or index.
- Underlying assets can include stocks, bonds, commodities, currencies, etc.
- Ownership of a derivative does not imply ownership of the underlying asset; it is mainly a contract between two parties.
Uses of Derivatives:
- Hedging: To offset risk and stabilize cash flows.
- Speculation: To increase exposure to risk with the hope of earning a profit.
- Arbitrage: Taking advantage of price discrepancies in different markets.
Leverage: Derivatives require small initial investments relative to their potential exposures, leading to amplified gains and losses.

Definition of Options: A subtype of derivatives that grants the holder the right (but not the obligation) to buy or sell an underlying asset at a predetermined price on or before a specified date.
- Other types of derivatives (swaps, futures) involve mandatory cash flow obligations at set times.

Call Options: Grant the right to buy an asset at a specified price (exercise/strike price) at expiration.
Put Options: Grant the right to sell an asset at a specified price at expiration.

Expiration Date: The date on or before which the option can be exercised.
Intrinsic Value: The difference between current price and strike price, adjusted for in-the-money status.
American vs European Options:
- American can be exercised anytime before expiration.
- European can only be exercised at expiration.

Definition: A forward contract obligates the parties to buy/sell an asset at a specific future date for a price agreed upon today.
Example: Ordering a textbook that is out of stock enters into a forward contract.

Definition: Similar to forward contracts but are standardized and traded on exchanges; they settle daily (marked to market).
Standard Features Include:
- Contract Size: Specific amount of asset per contract.
- Delivery Dates: Pre-defined expiration dates.
- Initial Margin: Typically around 4% of the contract value, held by brokerage.

Definition: A strategy used by firms to reduce their risk exposure using derivatives.
Types of Hedges:
- Long Hedge: Taking a long position in a futures contract to lock in a purchase price.
- Short Hedge: Taking a short position in futures to lock in a selling price.

Copper Futures: If you purchase 10 copper contracts at $0.70/lb (totaling $17,500) and the price rises by 5 cents, you'd gain $12,500.

Interest Rate Futures: Used to manage exposure to fluctuations in interest rates.
- Pricing of these contracts can involve standard bonds.
Swaps: Involve exchanging cash flows between parties at periodic intervals. Key types include:
- Interest Rate Swaps: Fixed for floating.
- Currency Swaps: Involving exchange rates between currencies.

Valuation: Options in corporate finance allow for decision flexibility by investing in projects today with the option to delay, expand, or abandon them based on future information.

Executive Stock Options: Rewarding executives with the option to buy shares at a specific price.
Expansion Options: The ability to grow operations in future periods if initial tests perform well (e.g., a startup).
Shutdown and Restart Options: Allows firms to assess when to shut down and re-open projects based on market conditions.

The value of derivatives in managing risks and firm flexibility is crucial. Real options provide a valuable framework for making informed investment decisions and managing uncertainty in corporate finance.