Chapter 4: Options & Option Strategies

This final chapter covers the fundamentals of options, their payoffs, the put-call parity relationship, and various strategies used for speculation, hedging, and betting on volatility.

1. Core Concepts and Definitions

Call Option: A financial contract that gives the owner the right (but not the obligation) to buy a specific underlying asset (S) at a predetermined price (Strike Price, K) on or before a specific date (Expiration Date, T).

Put Option: A financial contract that gives the owner the right (but not the obligation) to sell a specific underlying asset (S) at a predetermined price (Strike Price, K) on or before a specific date (Expiration Date, T).

American Option: An option that can be exercised at any time before or on the expiration date (T). (e.g., most stock options).

European Option: An option that can be exercised only on the expiration date (T). (e.g., most index and currency options).

Moneyness: Describes the relationship between the current price of the underlying asset (S) and the strike price (K) of the option.

In the Money (ITM): The option has intrinsic value if exercised immediately. (Call: S > K; Put: S < K).
Out of the Money (OTM): The option has no intrinsic value if exercised immediately. (Call: S < K; Put: S > K).
At the Money (ATM): The current price is equal to (or very close to) the strike price. (S ≈ K).

2. Key Formulas and Payoffs

Option Payoffs at Expiration (T)

The payoff is the value of the option at expiration, before accounting for the initial cost (premium) paid to buy it.

Long Call Payoff: max(S_T - K, 0)
Profit = Payoff - Call Premium

Long Put Payoff: max(K - S_T, 0)
Profit = Payoff - Put Premium

Put-Call Parity

A fundamental pricing relationship between European call and put options with the same strike price (K) and expiration date (T) on the same underlying asset.

Put-Call Parity Equation:
P + S = C + PV(K)
Where P is the Put price, S is the Stock price, C is the Call price, and PV(K) is the present value of a risk-free bond paying K at expiration.

3. Comparative Analyses of Intersecting Terms

Long Call vs. Short (Write) Call

Feature	Long Call (Buyer)	Short Call (Writer/Seller)
Market View	Bullish (Expects S to rise significantly above K).	Neutral to Bearish (Expects S to stay below or near K).
Maximum Profit	Unlimited (as S can rise indefinitely).	Limited to the premium received upfront.
Maximum Loss	Limited to the premium paid upfront.	Unlimited (if S rises sharply, the writer must still sell at K).

Straddle vs. Butterfly Spread

Feature	Straddle (Long)	Butterfly Spread (Long)
Strategy Construction	Buy 1 ATM Call + Buy 1 ATM Put (same K and T).	Buy 1 ITM Call, Sell 2 ATM Calls, Buy 1 OTM Call.
Market View (Volatility)	Bet on high volatility. Expects a large price move in either direction.	Bet on low volatility. Expects the price to stay near the ATM strike.
Cost & Risk	Expensive (paying two premiums). Loss is limited to premiums paid if S stays near K.	Cheaper (selling 2 ATM calls offsets costs). Loss is strictly limited, but maximum profit is also capped.

4. Common Option Strategies

Portfolio Insurance (Protective Put): Buy the underlying stock + Buy an OTM Put. Limits downside risk while preserving upside potential. (Equivalent to buying a Call + a Risk-Free Bond via Put-Call Parity).
Synthetic Short: Buy an ATM Put + Short an ATM Call + Borrow PV(K). Used when shorting the actual stock is difficult or expensive (e.g., GameStop squeeze).
Bull Spread: Buy an ITM Call (K₁) + Sell an OTM Call (K₂). A conservative bet that the stock will rise, but not beyond K₂. Cheaper than buying a naked call, but caps maximum profit.
Bear Spread: Buy an ITM Put (K₂) + Sell an OTM Put (K₁). A conservative bet that the stock will fall, but not below K₁.
Collar: Hold the stock + Buy an OTM Put (protection) + Sell an OTM Call (to finance the put). Creates a "band" of returns, capping both maximum loss and maximum gain.

This concludes the Asset Management Guide. I will now compile all chapters into a single, comprehensive document for your final review.