Overview
Put options are financial contracts granting the right, but not obligation, to sell a stock by a certain date. Unlike call options (right to buy), put options profit when the underlying stock price declines.
Put Options Definition
- Financial contract giving holder the right to sell a stock by a specified expiration date.
- Holder is not obligated to exercise the option; it's a choice, not a requirement.
- Identical to call option definition except "sell" replaces "buy" in the action.
- Long put position: investor owns the option and wants stock price to decline.
- Short put position: investor sells the option and receives a premium upfront.
Long Put Options
- Investor purchases a put option by paying a premium to the seller.
- Profits when the underlying stock price falls below the strike price.
- Maximum loss is limited to the premium paid for the option contract.
- Formula for put option value: P = max(0, X - S) where X is strike price, S is stock price.
- Profit calculation: value of put option minus premium paid initially.
- Example: strike price $100, premium $10; breakeven point occurs at $90 stock price.
- At $80 stock price: put value is $20, profit is $10 ($20 - $10 premium).
- Maximum profit equals strike price minus premium if stock price falls to zero.
- At $0 stock price with $100 strike: put worth $100, profit $90 after premium.
Short Put Options
- Investor sells a put option and receives the premium immediately as income.
- Profits when stock price stays at or above the strike price.
- Maximum profit is limited to the premium received from selling the option.
- Profit formula: premium received minus value of the put option at expiration.
- Uses same put value formula: P = max(0, X - S) as long position.
- Example: strike price $100, premium $10; investor starts up $10 from premium received.
- Breakeven point at $90 stock price: put value $10 equals premium received.
- At $80 stock price: investor loses $10 because put value is $20 minus $10 premium.
- Maximum loss equals strike price minus premium if stock price drops to zero.
- At $0 stock price: potential loss of $90 ($100 strike minus $10 premium).
Key Terms & Definitions
- Put Option (P): Contract value calculated as max(0, X - S).
- Strike Price (X): Price at which option holder can sell the stock.
- Stock Price (S): Current market price of the underlying asset.
- Premium: Upfront cost paid (long) or received (short) for the option contract.
- Breakeven Point: Stock price where profit equals zero after accounting for premium.
- Long Put: Owning a put option; profits from stock price decline.
- Short Put: Selling a put option; profits from stock price stability or increase.
Payoff Comparison
| Position | Initial Cash Flow | Maximum Profit | Maximum Loss | Breakeven Price |
|---|
| Long Put | -$10 (premium paid) | $90 (if stock → $0) | $10 (premium) | $90 |
| Short Put | +$10 (premium received) | $10 (premium) | $90 (if stock → $0) | $90 |