## Call and Put Options

Options are a bit complex, but a very popular trading vehicle for traders. Options are financial derivatives that give traders the right, but not the obligation, to buy or sell an underlying asset at an agreed-upon price and date. Investors can use options to earn income, speculate, and hedge risk. In other words, Options form a base for complex trading strategies and to leverage their portfolios.

**Call Option**

When an investor predicts a rise in the price of an underlying asset within a specified time period, he would lock in the price of that security by buying a call option. A call option gives the buyer, the right, but not the obligation to purchase the underlying security at a predetermined price, also known as the strike price, on the expiry of the contract.

**Put Option**

When an investor predicts a fall in the price of an underlying asset within a specified time period, he would lock in the price of that security by selling a call option

A put option is a contract that gives the buyer, the right but not the obligation to sell a particular underlying security at a predetermined price, which is known as the strike price, on the expiration of the contract.

Each contract has two parties, every Call buyer has a call seller and similarly, every put buyer has a put seller.

## Option Calculation

Let us understand some terms before going through calculations for options - Call & Put

*Strike Price:*** **A strike price is a predetermined price at which a derivative contract can be bought or sold when it is exercised.

*Spot Price: *The price of the underlying asset on the expiry or maturity of the contract is known as the Spot Price.

*Premium:*** **The current market price of an option contract is the option's premium.

**Call Option Profit Formula**

__In a Long Call Option (Right to buy)__

**Case 1:**

Strike Price = 100, Premium Paid = 10, Spot Price = 90

As you locked in the security at a strike price of Rs.100, the call buyer has a right to buy at Rs.100, but the market price of the security instead falls to Rs.90 on the expiry date of the contract, the call buyer would not buy the option at 100, hence the premium paid by the trader is the maximum loss incurred, i.e. Rs.10

**Case 2:**

Strike Price = 300, Premium Paid = 30, Spot Price = 450

In this case, you have the right to buy at Rs.300 whereas the market price is 450, (Spot Price- Strike Price), a benefit of Rs.150. But Premium Paid was Rs.30. Hence the net profit is 150-30 = Rs.120.

__In a Short Call Option (Right to sell)__

Strike Price = 100, Premium Received = 10, Spot Price = 150

In the short call option, the trader has an obligation to sell the security at Rs.100, but on the expiry of the contract, the security rises to Rs.150, the trader had recovered a premium of Rs.10 and hence would incur a loss of Rs.40 in this trade.

**Put Option Profit Formula**

__In a Short Put Option (Right to Sell)__

Strike Price = 200, Premium Received = 40, Spot Price = 230

In the Put Option, the strike price is Rs.200 but the market price of the same security is Rs.230 on the expiry of the contract, so a trader would not exercise the option to sell it at Rs.200. Hence, the Premium paid Rs.40 is the maximum loss incurred in this trade.

__In a Long Put Option (Right to Buy)__

Strike Price = 500, Premium paid = 30, Spot Price = 490

In the Long Put, the trader has a right to sell at the strike price of Rs.500 which is higher than the market price RS.490. So, the trader can sell the security at Rs.500 and earn a profit of Rs.10, but he has already paid a premium of Rs.30) = Therefore, the Net loss is Rs.20.

Here, on the other hand, the Short Put Buyer would gain a profit of Rs.20

## Option Premium Calculation

The Premium of option consist of two attributes - Time Value, Intrinsic Value. The sum of the time value and the intrinsic value represents the market price of an option.

*Time Value:*

The value of Rs.100 today might be more than three years down the line. Time Value is simply the value of security measured in ratio to its expiry date. The more time left for an option to expire, the more value does it hold as we can use it to generate returns while we hold it. It is important to understand the time value as a part of an option’s premium. Time value is calculated as the difference between the Option’s Price and the Intrinsic Value.

`Time Value = Option Premium - Intrinsic Value. `

When an investor purchases an OTM or ATM option, whose premium is equal to its time value, there is a greater risk that the option will be of no value at its expiration date, since it is already out of the money or at the money. Due to the greater risk of the option having no value, OTM and ATM options have lower premiums than ITM options on the same underlying asset.

*Intrinsic Value (IV):*

The Intrinsic value is obtained by calculating the difference between the underlying asset’s strike price and its market price at the expiration of the contract. Every asset has an intrinsic value that measures the worth of that particular asset. ATM options and OTM options do not have any intrinsic value since there is no price advantage for the option in both cases. When the trader is certain about the future price movements in the market, they bet in their prices. As the type of contract changes, the process of calculating also changes. Let’s go through each event:

**Intrinsic Value of Call Option**

For example, Tata Motors trading at Rs.310. If a trader predicts a rise in the price of this security in the future, he would buy a call option of Tata Motors at a strike price, say Rs.340, at a premium of Rs.12. The stock price rises above the strike price, say Rs.360.

`Intrinsic value of call option = Spot Price - Strike Price`

Therefore, Intrinsic value of call option would be = 360 - 340 = 20

If stock price falls below the strike price, say Rs.325

Intrinsic value of call option would be = 325 - 340 = -15

The IV cannot be negative, so the strike price will be considered at Rs.325. Therefore, IV= 0

The option whose strike price is less than the market price has a positive intrinsic value and the Option whose strike price is greater than the market price has zero intrinsic value.

**Intrinsic Value of Put Option**

For example, Tata Motors trading at Rs.310. If a trader predicts a fall in the price of this security in the future, he would buy a put option of Tata Motors at a strike price, say Rs.290, at a premium of Rs.12. The stock price falls below the strike price, say Rs.270.

`Intrinsic value = Strike Price – Spot Price `

Therefore, Intrinsic value of put option would be = 290 - 270 = 20

If stock price goes above the strike price, say Rs.300

Intrinsic value of put option would be = 290 - 300 = -10

The IV cannot be negative, so IV= 0

The option whose strike price is greater than the market price has a positive intrinsic value.

And the Option whose strike price is less than the market price has zero intrinsic value.

*Break Even Point:*

Break Even Point is the level at which security must reach for the buyer of an option to avoid loss. In an event when the spot price rises above the strike price, the loss starts to minimize. The losses keep getting minimized till a point where the trade neither results in a profit or a loss. This is called the break even point.

`Break-Even = Strike Price + Premium Paid`

In our example, Strike Price= 340 and the Premium = 12.

So BE point would be = 340 + 12 = 352

*We can easily understand that how much value is attributable to the future expectations of price movement and how much is for the worth of the asset with the help of Time Value and Intrinsic Value concepts and accordingly keep our strategies in place.*

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