Options Pricing: Put/Call Parity

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Here you can see the same for put option payoff. And here the same for short call position the inverse of long call. Buying a call option is the simplest of option trades. A call option gives you the right, but not obligation, to buy the underlying security at the given strike price. Below the strike, the payoff chart is constant and negative the trade is a loss.

For example, if underlying price is Same as scenario 1 in fact. Finally, this is the scenario which a call option holder is hoping for. Because the option gives you the right to buy the underlying at strike price If you bought call option and put option formula option at 2. You can also see this in the payoff diagram where underlying price X-axis is Initial cash flow is constant — the same under all scenarios. It is a product of three things:. Of course, with a long call position the initial cash flow is negative, as you are buying the options in the beginning.

The second component of a call option payoff, cash flow at expiration, varies depending on underlying price. That said, it is actually quite simple and you can construct it from the scenarios discussed above. If underlying price is below than or equal to strike price, the cash flow at expiration is always zero, as you just let the option expire and do nothing.

If underlying price is above the strike price, you exercise the option and you can immediately sell it on the market at the call option and put option formula underlying price. Therefore the cash flow is the difference between underlying price and strike price, times number of shares. Putting all the scenarios together, we can say that the cash flow at expiration is equal to the greater of:. It is the same formula.

The screenshot below illustrates call option payoff calculation in Excel. Besides the MAX function, which is very simple, it is all basic arithmetics. One other thing you may want to calculate is the exact underlying price where your long call position starts to be profitable. If you don't agree with any part of this Agreement, please leave the website now. All information is for educational purposes only and may be inaccurate, incomplete, outdated or plain wrong.

Macroption is not liable for any damages resulting from using the content. No financial, investment or trading advice is given at any time. Home Calculators Tutorials About Contact. Tutorial 1 Tutorial 2 Tutorial 3 Call option and put option formula 4.

We will look at: Call Option Payoff Diagram Buying a call option is the simplest of option trades. The key variables are: Strike price 45 in call option and put option formula example above Initial price at which you have bought the option 2. Call Option Scenarios and Profit or Loss Three things can generally happen when you are long a call option. Underlying price is higher than strike price Finally, this is the scenario which a call option holder is hoping for.

Call Option Payoff Formula The total call option and put option formula or loss from a long call trade is always a sum of two things: Initial cash flow Cash flow at expiration Initial cash flow Initial cash flow is constant — the same under all scenarios. It is a product of three things: Cash flow at expiration The second component of a call option payoff, cash flow at expiration, varies depending on underlying price.

Call Option Break-Even Point Calculation One other thing you may want to calculate is the exact underlying price where your long call position starts to be profitable. It is very simple. It is the sum of strike price and initial option price.

Long Call Option Payoff Summary A long call option position is bullish, with limited risk and call option and put option formula upside. Maximum possible loss is equal to initial cost of the option and applies for underlying price below call option and put option formula or equal to the strike price. With underlying price above the strike, the payoff rises in proportion with underlying price. The position turns profitable at break-even underlying price equal to the sum of strike price and initial option price.

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This page explains the Black-Scholes formulas for d1, d2, call option price, put option price, and formulas for the most common option Greeks delta, gamma, theta, vega, and rho. In many resources you can find different symbols for some of these parameters.

For example, strike price is often denoted K here I use X , underlying price is often denoted S without the zero , and time to expiration is often denoted T — t difference between expiration and now.

Call option C and put option P prices are calculated using the following formulas:. Below you can find formulas for the most commonly used option Greeks. Some of the Greeks gamma and vega are the same for calls and puts. Other Greeks delta, theta, and rho are different. The difference between the formulas for calls and puts are often very small — usually a minus sign here and there.

It is very easy to make a mistake. If you want to use the Black-Scholes formulas in Excel and create an option pricing spreadsheet, see detailed guide here:. Option Greeks Excel Formulas. If you don't agree with any part of this Agreement, please leave the website now. All information is for educational purposes only and may be inaccurate, incomplete, outdated or plain wrong. Macroption is not liable for any damages resulting from using the content.

No financial, investment or trading advice is given at any time. Home Calculators Tutorials About Contact. Tutorial 1 Tutorial 2 Tutorial 3 Tutorial 4. The formulas for d1 and d2 are: In several formulas you can see the term: Delta Gamma Theta … where T is the number of days per year calendar or trading days, depending on what you are using.