Ch8. Derivatives Basics — Futures, Options, and Swaps

What Are Derivatives?

Derivatives: Financial instruments whose value is derived from an underlying asset.

Types of Derivatives:
Forward:  OTC, customized contract
Futures:  Exchange-traded, standardized, requires margin
Options:  Right but not obligation
Swap:     Exchange of cash flows between two parties

Uses:

Hedging: Eliminate price risk
Speculation: Profit from price movements
Arbitrage: Exploit price discrepancies

Futures

Futures Contract: An agreement to buy or sell an underlying asset at a specified price on a future date.

Futures Positions:
Long  Position: Obligation to buy  → Profits when price rises
Short Position: Obligation to sell → Profits when price falls

Profit/Loss:
Long:  P&L = Settlement Price − Futures Price
Short: P&L = Futures Price − Settlement Price

Hedging Example:

Scenario: You need to buy 100 barrels of crude oil in 3 months (worried about price increases)
Action:   Take a LONG position in crude oil futures
Result:   If oil prices rise, the futures gain offsets the higher purchase cost

Options

Call Option

The right to buy the underlying asset at the strike price.

Call Option:
Strike Price (K): Price at which you can buy
Spot Price (S):   Current price of the underlying

Payoff at Expiry:
Call Buyer:  max(S_T − K, 0) − Premium
Call Seller: Premium − max(S_T − K, 0)

S_T > K: In-the-money (ITM)  → Exercise
S_T < K: Out-of-the-money (OTM) → Let expire

Put Option

The right to sell the underlying asset at the strike price.

Payoff at Expiry:
Put Buyer:  max(K − S_T, 0) − Premium
Put Seller: Premium − max(K − S_T, 0)

S_T < K: In-the-money → Exercise (sell at the higher strike price)

Put-Call Parity

Call Price − Put Price = S_0 − K / (1 + r)^T

S_0: Current underlying price
K:   Strike price
r:   Risk-free rate
T:   Time to expiration

Option Pricing Factors

Factors that increase the CALL price:
- Underlying asset price rises
- Volatility increases (greater chance of large moves)
- Longer time to expiration
- Higher risk-free rate
- Lower strike price

Factors that increase the PUT price:
- Underlying asset price falls
- Volatility increases
- Longer time to expiration
- Lower risk-free rate
- Higher strike price

Swaps

Interest Rate Swap: Exchange of fixed-rate and floating-rate cash flows.

Interest Rate Swap:
Party A (wants to pay fixed) ←→ Party B (wants to pay floating)
A pays B the floating rate
B pays A the fixed rate
→ Each party exploits its comparative advantage

Currency Swap: Exchange of principal and interest payments in different currencies.

Key Concept Cards

Futures P&L ★★★★★ : Long = S_T − F (futures price); Short = F − S_T. Symmetric profit-and-loss structure. Memory tip: Long buyer profits from price rises; short seller profits from price falls

Call Option ITM Condition ★★★★★ : S_T > K → in-the-money → exercise. S_T < K → out-of-the-money → let expire. Maximum loss = premium paid. Memory tip: Call ITM = spot price > strike price

Volatility and Option Prices ★★★★☆ : Higher volatility → higher prices for both calls and puts. Greater chance of large moves increases option value. Memory tip: Volatility ↑ → both calls and puts rise

Practice Quiz

Q. You buy a call option with a $50 strike for a$ 2 premium. At expiration the stock trades at $55. What is your net profit?

Payoff = $55 −$ 50 = $5. Net profit =$ 5 − $2 (premium) = **$ 3**

Q. You hold a stock portfolio and want to hedge against a decline. Which options strategy should you use?

Protective Put — buy put options on the stock. If the stock falls, the put gains in value to offset the loss. If the stock rises, your only cost is the premium paid for the puts.

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