## Evaluating a Put Option Using Black-Scholes Theory

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If you have seen the page explaining call option payoffyou will find the overall logic is very similar with puts; there are just a few differences which we will point out. While put option formula call option gives you the put option formula to buy the underlying security, a put option represents the right but not obligation to sell the underlying at the given strike price.

When holding a put option, you want the underlying price go down, because the lower it gets relative to the strike price, the more valuable your put option becomes. A long put option position is therefore a bearish trade — makes money when underlying price goes down and loses when it goes up. You can see the payoff graph below.

Of course, it also depends on your position size 1 contract representing shares in this example. The relationships is linear and put option formula slope depends on position size. For example, if underlying price is You can immediately buy it back on the market for Above the strike, the put option has zero value, because there is no point exercising the right to sell the underlying at strike price when you can sell it for a higher price without the option. The first component is equal to the difference between strike price and underlying price.

The lower underlying price gets relative to strike price, the higher your cash gain at expiration. However, this only applies when underlying price is below strike price. When it gets above, the put option formula would be negative you would be losing money by exercising the option.

Because a put option gives you the right but not obligation to sell, if underlying price is above strike price, you choose to not exercise the option and therefore cash flow at expiration is zero. Taking all scenarios into consideration, a long put option cash flow at expiration is put option formula the higher of:. The above is put option formula share. To get the total dollar amount, you need to multiply it by number of contracts and contract multiplier number of shares per contract.

Initial cost is of course the same under all scenarios. Therefore the formula for long put option payoff is:. It is very easy to calculate the payoff in Excel. The key part is the MAX function; the rest is basic arithmetics. You can see all the formulas in the screenshot below.

Besides the strike price, another important point on the payoff diagram is the break-even point, which is the underlying price where the position turns from losing to profitable put option formula vice-versa. Calculating the exact break-even price is very useful when evaluating potential put option formula trades. The formula for put option break-even point is put option formula very simple:. 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 Put option formula 4. Put Option Payoff Diagram and Formula. This page explains put option payoff. We will look at: Long Put Option Position is Bearish While a call option gives you the right to buy the underlying security, a put option represents the right but not obligation to sell the underlying at the given strike price. Put Option Payoff Diagram You can see the payoff graph below.

Put Option Scenarios and Profit or Loss 1. What you can get when exercising the option What you have paid for the option in the beginning The first component is equal to the difference between strike price and underlying price. Taking all scenarios into consideration, a long put option cash flow at expiration is therefore the higher of: Therefore the formula for long put option payoff is: Put Option Break-Even Point Calculation Besides the strike price, another important point on the payoff diagram is the break-even point, which is the underlying price where the position turns from losing to profitable or vice-versa.

The formula for put option break-even point is actually very simple: Long Put Option Payoff Summary A long put option position is bearish, with limited risk and limited but usually put option formula high potential profit. Put option formula possible loss is equal to initial cost of the option put option formula applies for underlying price higher than or equal to the strike price.

Put option formula underlying price below the strike, the payoff rises in proportion with underlying price. The position turns profitable at break-even underlying price equal to put option formula price minus initial option price.

Maximum theoretical profit which would put option formula if the underlying price dropped to zero is per share equal to the break-even 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.