# Call and put options formula

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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: 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 the 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 result 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 therefore the higher of:. The above is per 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.

The term "call" comes from the fact that the owner has the right to "call the stock away" from the seller.

Option values vary with the value of the underlying instrument over time. The price of the call contract must reflect the "likelihood" or chance of the call finishing in-the-money. The call contract price generally will be higher when the contract has more time to expire except in cases when a significant dividend is present and when the underlying financial instrument shows more volatility. Determining this value is one of the central functions of financial mathematics.

The most common method used is the Black—Scholes formula. Importantly, the Black-Scholes formula provides an estimate of the price of European-style options. Adjustment to Call Option: When a call option is in-the-money i. Some of them are as follows:.