Options Case Study – Long Call

An option is a derivative contract used to do trading in many underlying assets.

Derivatives are financial contracts between two parties that derive their value from underlying assets. Two types of derivatives are traded on exchanges - Forwards and Options.

Options Case Study

These financial instruments are based on underlying securities (the most commonly used security is stocks). Options give the party (or the holder) an option to exercise their financial instrument. 

There are two parties involved in options - the option writer and the option holder. The option holder is the person who is persuaded to engage in the option transaction. 

The option writer, also known as an option grantor, is the person who opens a position for an option transaction. The option writer collects a premium from the option buyer.
In the case of options transactions, the writer can be the buyer or seller. 

There are two types of options - the call option and the put option

The call option is a type of option that allows the buyer to buy the security at a specified (pre-defined) time. However, he has the option to not go ahead with the deal. The only payment he needs to do is a premium payment to the option writer. 

The call option usually takes place between two parties of opposing views. Generally, the buyer is bullish on the market, and the writer or the seller is bearish on the market.  

The other type of option is the put option. A put option works opposite a call option. In the case of a put option, the seller has the option to sell the underlying security. However, the seller can withdraw the transaction and only has to pay the option writer a premium amount. 

Before going deep into the types of options, let us understand the basic terms used in option contracts. 

  1. Strike Price: The final price at which the contract is exercised at the date of expiration.
  2. Volume: This metric indicates the liquidity of the options contract.
  3. Time Value: Since we know the time has a money value, time value is the additional amount charged at the expiration date on the initial value. 
  4. Intrinsic Value: The actual worth of options in terms of money.
  5. American style: These are the types of contracts that can be exercised any time before the expiration date
  6. European style: European-style contracts can be exercised only at the date of expiration.

options case study: Types of options

Now let us understand the call and put options and their subclasses:

Types of options

1. Call options:

As we saw above, a call option gives the right, but not the requirement, to purchase a stock at the strike price at the option's expiration. Since the buyer has the option, he needs to pay the writer or the seller for this right in terms of premium. 

Generally, the buyer of the call option is bullish on the market outlook. There are two ways of selling a call option. During the implementation of the option transaction, the seller can buy the underlying asset on the spot, or he can buy it later, depending on his views. 

However, if they buy the underlying security, sell the option at a later specified date, and the price of the stock rises, then they will be covered and won't have to buy the stock at a higher price. This is called a covered call option. 

The profit of the seller will be limited to the stock rise of the options strike price. 

The second way of selling a call option is the seller buys the stock later at the expiration date instead of the initiation date. This way, the reward for the seller won't be limited by the rise in stock price, but there won't be a cap on the potential loss. 

This strategy is called the naked call option. 

In this case, the difference between the current market price and the strike price is the loss to the seller. 

2. Put Option:

As we saw above, similar to a call option, we have a put option - a derivative contract between two parties. However, their functionalities/rights to exercise are totally different. 

The right to exercise or to sell is given to the seller. However, a buyer, in this case doesn't have any option. Generally, the seller of a put option is bearish on the stock market. However, the views change according to various options trading strategies. 

Below are some terms that are used in options trading strategies, especially for hedging purposes. 

  1. At the money: At the money, a situation arises when the stock price is equal to the strike price. 
  2. In the money: This is the case when an option contract has its own intrinsic value, i.e., the stock price is greater than the proposed strike price for an in-the-money call option. For an in-the-money put option, the stock market price is lower than the strike price. 
  3. Out of the money: This situation arises when there is no advantage to using the derivatives contract. The stock market price and the strike price favor direct transactions in terms of stocks instead of derivative contracts. 

In the case of out-of-the-money call options, the strike price is greater than the stock market price, and for out-of-the-money put options, the strike price is lower than the stock market price. 

Pricing models

There are various ways of calculating the options price; some take into consideration factors such as initial value, time, etc., and some are based on a probability approach.

This theoretical value of the option is the estimate of the approximate value of the options taking into consideration all the inputs. These values determine the trading strategy used.

Pricing models

Let us have a look at a few of the pricing models:

1. Black-Scholes Model: 

Black-Scholes Model or Black-Scholes-Merton Model is used to mathematically estimate the value of the option (or any derivative). It takes into consideration the impact of time and risk factors. 

Variables taken into consideration for pricing are Strike price, time to expire, risk-free rate, volatility, and current stock price. Since American options can be exercised before the expiration date, the BS model works only on European options. 

2. Monte-Carlo Model:

Monte-Carlo simulation is one of the most volatile concepts in mathematics. Monte-Carlo simulation uses the concept of random walk to determine the probability of various outcomes. This pricing model takes into consideration risk factors. 

The price taken is discounted expected value (risk-neutral and rational price). A large number of random walks or paths are generated to predict the underlying value. 

The associated exercise value is calculated for each path, taken as an average, and then discounted to get a value for today's option price.

3. ARIMA Model: 

ARIMA stands for Auto-regressive Integrated Moving Average model. This is a time series model. The model is trained on historical data, and we try to compare the predicted value from the model with the strike price. 

These two metrics help make investment decisions.

4. Binomial Model:

This model is used for valuing American-style option contracts. The time is divided into a fixed amount of points. Each node is used as a binomial tree. 

Going from one node to the other increases the number of price calculations since there are two possible outcomes for each node in time: move up or down. 

Options trading strategies

Let us have a look at some of the commonly used Options Trading strategies.

Buy -> Going Long, these terms are used interchangeably in trading

Sell -> Going Short, these two terms are also used interchangeably.

Options trading strategies

Let us start with some of the basic strategies:

Buying Calls:

This is a simple directional strategy. If an investor is bullish on the market, they will go long or buy the call option.

Buying puts:

Similar to buying calls, this strategy is based on the general view of the investor. In this case, the buyer is bearish on the market. 

Selling Calls:

The selling call strategy is a directional strategy and is used when the seller is not so bullish on the market and aims to collect a premium on the contract from speculators (buyers).

Selling Puts:

The selling put strategy is a directional strategy and is used when the seller is bullish and aims to collect a premium from the buyer. 

We have seen a lot of directional strategies. Now, let us look at a non-directional strategy that uses arbitrage over large movements in the market. It can move up or move down. 

Straddle (Buy/Sell):

This strategy involves buying calls as well as put options. This way, profits can be made in either direction of movement. The drawdown or the loss has an upper circuit of the premium paid in buying the options. The case is the same for the Selling Straddle strategy.

There are two breakevens in the straddle strategy. 

Lower breakeven = Strike Price - net premium paid

Higher Breakeven = Strike price + net premium paid.

Synthetic: The synthetic strategy is of two types, long synthetic, and short synthetic. The synthetic strategy doesn't have a maximum possible risk since this is also a directional strategy. 

When the buyer is bullish on the market, he buys a call option and sells the put option; both the option contracts have the same strike price.  

Similarly, for the short synthetic strategy, the investor buys the put option and sells the call option (notice the difference between short and long synthetic). Short synthetic is used when the view on the market is bearish. Again, there is no hedge on the risk involved. 


Backspread, also known as a reverse ratio spread, is similar to a ratio spread strategy that is based on the vertical spread. There are two types of backspread strategies - Call Backspread and Put Backspread. This strategy looks at the direction of the market trends as well as the volatility.

Direction or the trendline is required in order to decide on call or put options. 


Hence, unlike the ratio spread strategy, in this strategy, one needs to be bullish or bearish on the market. This strategy doesn't involve any hedge using call and put options together. Instead, it only focuses on a call option or put option - one at a time.  

This strategy involves money options and out-of-the-money options. In the case of call Backspread, the money call option is sold while two lots of out-of-the-money call options are bought. 

The risk is limited = strike price of short call - strike price of long call +/- net premium paid/received. While the reward is unlimited on the upper side, the lower side has limited rewards.

Similar to all the mentioned strategies, this strategy also involves contracts with the same underlying security and expiration date. 

In put backspread, in-the-money put options are sold, while two lots of out-of-the-money put options are bought. The risk is limited = strike price of short put - strike price of long put +/- net premium paid/received. While the reward is unlimited on the upper side, the lower side has limited rewards.


Strangle strategy is of two types - long strangle and short strangle. 

In the case of a long strategy, the out-of-the-money call option is bought along with the out-of-the-money put option, with the same underlying asset/security and expiration date. 

The risk is limited to the net premium paid. However, the reward is unlimited. For long strangle, the upper breakeven point is buy call strike price + net premium paid, and the lower breakeven point is put strike price - net premium paid. This strategy is used to hedge against risk. 

Similarly, for short strangle, out-of-the-money call options and out-of-the-money put options are sold. However, in this case, the reward is limited, and the risk is unlimited. 

For this, upper breakeven = sell call strike price + net premium received and lower breakeven = sell put strike price - net premium received.


This is one of the hedging strategies. Its utilization is during a bullish view on market direction and volatility. In this strategy, two lots of at-the-money call options and one lot of at-the-money put options are bought. 

This way, the risk is limited to the net premium paid, while the reward is unlimited. The upper breakeven point is strike price + net premium paid/2, and the lower breakeven point is at strike price - net premium paid.


This strategy is similar to the Strap strategy. The only difference is instead of two lots at the money call option, one lot is bought, and instead of one at the money put option, two at the money put options are bought. 

Again, in this case, the risk is limited to the net premium paid, and the reward is unlimited. However, the upper breakeven = strike price + net premium paid and lower breakeven = strike Price - (net premium paid)/2

Many other strategies include Call Ladder, Put Ladder, Call Condor, Call Butterfly, and Collar.

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Researched and authored by Punit Manjani | LinkedIn

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