trading strategies

Option

A contract that gives the holder the right (but not the obligation) to buy or sell an asset (usually a stock) at a set exercise (strike) price (K) on or before a specific date (expiration date T).

Call option

Right to buy stock at K.

Premium

The current price of the option, denoted by C for calls, P for puts.

Current call price (C)

The price of the call option at the current time.

Current put price (P)

The price of the put option at the current time.

Current stock price (S₀)

The price of the stock at the current time.

Stock price at expiration (Sₜ)

The price of the stock at the expiration date.

Exercise (strike) price (K or X)

The price at which the holder can buy or sell the underlying asset.

Time to expiration (T)

The time remaining until the option expires.

Number of shares of stock (Nₛ)

The quantity of shares of stock involved in the option.

Number of call options (N꜀)

The quantity of call options involved.

Number of put options (Nₚ)

The quantity of put options involved.

Profit (P)

The financial gain from a strategy.

Buy Stock Profit Formula

P = Sₜ - S₀

Max profit from buying stock

∞ (if price rises forever).

Max loss from buying stock

-S₀ (if stock goes to 0).

Sell Short Stock Profit Formula

P = -Sₜ + S₀

Max profit from selling short stock

S₀ (if stock goes to 0).

Max loss from selling short stock

∞ (if stock price soars).

Buy a Call (Long Call) Profit Formula

P = max(0, Sₜ - K) - C

Max profit from buying a call

∞.

Max loss from buying a call

-C.

Write a Call (Short Call) Profit Formula

P = -max(0, Sₜ - K) + C

Max profit from writing a call

+C.

Max loss from writing a call

∞ (if stock skyrockets).

Buy a Put (Long Put) Profit Formula

P = max(0, K - Sₜ) - P

Max profit from buying a put

K - P (if stock → 0).

Max loss from buying a put

-P.

Write a Put (Short Put) Profit Formula

P = -max(0, K - Sₜ) + P

Max profit from writing a put

+P.

Max loss from writing a put

-K + P (if stock → 0).

Covered Call

Own stock and sell a call on it.

Protective Put

Own stock + buy a put = 'insurance'.

Synthetic Put

Long Call + Short Stock + Bond.

Synthetic Call

Long Put + Long Stock + Borrowing.

Black-Scholes-Merton (BSM) model

Used to find the current fair value of an option before expiration.

Theta decay

The time value part of an option that decays as expiration approaches.