Options Strategies, Greek Logic, and Case Studies in Derivatives

Scenario: Expect Huge Move

Strategy: Long Straddle (Buy Call + Buy Put at same strike).

Scenario: Expect Huge Move (But want to pay less)

Strategy: Long Strangle (Buy OTM Call + Buy OTM Put).

Scenario: Own Stock + Want Income

Strategy: Covered Call (Short Call).

Scenario: Own Stock + Fear Crash

Strategy: Protective Put (Long Put).

Scenario: Bullish but want to reduce cost

Strategy: Bull Spread (Buy Low Strike Call, Sell High Strike Call).

Scenario: Bearish but want to reduce cost

Strategy: Bear Spread (Buy High Strike Put, Sell Low Strike Put).

Payoff Math: Straddle Break-Even

Upper BE = Strike + Total Premium. Lower BE = Strike - Total Premium.

Payoff Math: Max Loss for Long Option

Premium Paid.

Payoff Math: Max Gain for Short Option

Premium Received.

Greek Logic: Long Option & Time

Negative Theta (Time decay hurts you).

Greek Logic: Long Option & Volatility

Positive Vega (Rising volatility helps you).

Greek Logic: Short Option & Time

Positive Theta (Time decay helps you/Profit from time passing).

Greek Logic: Short Option & Volatility

Negative Vega (Rising volatility hurts you).

Greek Logic: Delta Hedging

If you are Short Call (Negative Delta), you must Buy Stock (Positive Delta) to be neutral.

Calculation: Beta Hedging Direction

If you want to REDUCE Beta, you SELL (Short) Futures.

Calculation: Beta Hedging Gap

Formula N uses (Target Beta - Current Beta). If Target < Current, N is negative (Sell).

Calculation: Effective Price Logic

Cash Price Paid minus Futures Profit (or plus Futures Loss).

Concept: Basis Risk

The risk that (Spot Price - Futures Price) changes unexpectedly.

Concept: Strengthening Basis

Spot Price rises relative to Futures. Good for Short Hedgers (Sellers).

Case Study: Barings Bank

Rogue Trading + No Separation of Duties (Nick Leeson).

Case Study: LTCM

Convergence Trades failed (Spreads widened/blew out) + Excessive Leverage.

Case Study: Orange County

Interest Rate Bet (Rates rose unexpectedly).

Case Study: Metallgesellschaft

Mismatched Maturity (Rolling short futures to hedge long contracts) -> Margin Call death.

Pricing: Put-Call Parity Formula

Stock + Put = Call + Bond (PV of Strike).

Pricing: Implied Volatility (IV)

The market's expectation of future volatility, derived from the option price.

Strategy: Butterfly Spread

Betting on LOW volatility (Price stays at the middle strike).

Formula: Beta Hedging (N)

N = (Target Beta - Current Beta) * (Portfolio Value / Futures Contract Value).

Formula: Put-Call Parity (PCP)

C + K * e^(-rT) = P + S_0