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- The basics of call option
- The Option Jargons
- Call Option - Buying
- Call option -Selling/Writting
- Buying the Put Option
- Selling the Put option
- Call & Put Option - Summary
- Option contract - Moneyness concept
- Delta - 'The option Greek' Section -1
- Delta - Section 2
- Delta - Section 3
- Gamma - Section 1
- Gamma - Section 2
- Concept of 'Theta"
- The Basics of Volatility
- Calculation of Volatility (Historical )
- A study to Volatility and Normal Distribution
- Application of Volatility
- Vega - Basics
- Understanding the Greek Interaction
- A Guide to 'Greek Calculator'
- Re-calling Call & Put Option
- Bringing to a conclusion
- Physical Settlement

We have already covered the structure and context of a call option. This chapter will outline how we think about the call option, and give us a solid understanding of both selling and buying it. Let's recap what we learned in the first chapter before we get started in this chapter.

- If you anticipate the underlying price will rise, it makes sense to buy a call option.
- The buyer of the call option is liable for any decrease or stagnation in the underlying price.
- The amount of money that the buyer of the option call would lose is equal to the premium (agreement fee) that the buyer pays to the seller/writer of a call option

These three points will be used as a guideline and we will try to understand the call option better.

There are many market situations that justify the purchase of call options. This is one I discovered as I was writing this chapter. I thought it would be a good example to use in our discussions. Take a look at this chart.

(IMAGE 1)

Bajaj Auto Limited is the stock under consideration. Bajaj Auto Limited is one of India's largest manufacturers of two-wheelers. The stock is currently trading at its 52-week low price due to a variety of reasons. There may be an opportunity here to trade. These are my thoughts on this trade.

- Bajaj Auto is a high-quality fundamental stock.
- I believe the stock has been so severely beaten that it may have been an overreaction against volatility in Bajaj Autos’ business cycle
- I believe the stock price will stop falling soon and rise eventually.
- I don't want to purchase the stock for delivery yet, as I am concerned about the stock's future decline.
- To add to the above, I am unable to buy Bajaj Auto futures because of the fear of M2M losses.
- However, I do not want to miss the opportunity for a sharp decline in stock prices.

To summarise, I am optimistic about Bajaj Auto's stock price (the stock will eventually rise), but I am unsure about the stock's immediate outlook. This uncertainty stems mainly from the possibility of severe losses in the near term if the stock continues to fall. Although the likelihood of losing money is very low, it still exists. What should I do?

You will see that I am in the same situation as Ajay. (Remember the Ajay-Venu example from chapter 1). This is a classic example of an options trade.

Bajaj Auto's call options make sense in my situation. I will shortly explain why. Below is a snapshot from Bajaj Auto's options chain.

(image 2

The stock trades at Rs.2026.9 (highlighted blue). I will pay a premium of Rs.6.35/ if I want to purchase the 2050 strike option (highlighted in the red box, red arrow). It is possible you are wondering why I chose the 2050 strike price when there are many other strike prices (highlighted in red). The process of selecting the strike price is an extensive topic, and we will eventually get to that in this module. But for now, let's just say that 2050 is the best strike price to trade.

What happens to the call option when the expiry date is only 15 days away? There are three scenarios that could happen, which you probably already know about.

Scenario 1: The stock price rises above the strike price, 2080

Scenario 2: The stock price falls below the strike price, say 2030

Scenario 3: The stock price remains at 2050

These scenarios are very similar in nature to those we looked at in Chapter 1. I assume you are familiar with P&L calculations at the specific spot value in the scenarios. If not, I suggest you go back through Chapter 1.

This is the idea that I am interested in exploring right now:

- There are three broad scenarios that Bajaj Auto's price movement can be classified (upon expiry). The price increases, decreases or remains flat.
- What about all the prices in between? Scenario 1 states that the price will be 2080, which is higher than the strike of 2050. What about other strike price options such as 2055 or 2060? 2065 or 2070? Is it possible to generalize here in relation to the P&L
- Scenario 2: The price is at 2030, which is lower than the strike of 2050. What about other strike prices like 2045, 2040, and 2035? Is it possible to generalize here in relation to the P&L

What would happen to the P&L at different prices of spot (upon expiry)? I would like these points to be called the "Possible Values of the spot on expiry". This would allow me to generalize the P&L understanding for the call option.

To do this, I will first discuss ( **in part, and not the whole concept**) the notion of the intrinsic value for the option upon expiry'.

The **call option, for now,** is the **non-negative value** that the option buyer would receive if he exercised the call option. This is the intrinsic value (IV). Simply put, ask yourself (assuming that you are the buyer) how much money would you receive upon expiry if your call option is profitable. It is mathematically defined as:

**IV = Strike Price - Spot Price**

If Bajaj Auto is trading at 2068 in the spot market on the day of expiry, the intrinsic value of the 2050 Call option would be -

= 2068-2050

= 18

Similar, if Bajaj Auto trades at 2025 on expiry day, the intrinsic value would be -

= 2025-2050

= -25

Remember that IV of an option, regardless of whether it is a call or put, is a non-negative number. Therefore we leave the IV at 2025

= **0**

Our objective now is to keep the intrinsic value of the option in context, to determine how much money will I make at each possible expiry value for Bajaj Auto, and to make generalizations about the P&L of call option buyers.

Let's keep the idea of the intrinsic value of an option in mind. Let us now build a table to help us determine how much money I, the buyer of the Bajaj Auto 2050 call option, would make under various spot value changes by Bajaj Auto (in the spot market), upon expiry. Remember that the premium for this option is Rs. 6.35/-. No matter how spot values change, the fact that Rs.6.35/= remains the same. This is how much I paid to purchase the 2050 Call Option. Let's keep this in mind and calculate the P&L table.

*The negative sign preceding the premium paid is a cash flow from my trading accounts.*

*(chart*

**What do you see? Two strong observations are made by the table.**

- Even if Bajaj Auto's price drops (below 2050 strike price), the maximum loss appears to be Rs.6.35/.
**Generalization 1**A loss is a price change that occurs below the strike price for a call option buyer. The loss for the call option buyer is**limited**to the amount he has paid in premium

- As soon as Bajaj Auto moves above 2050, the profit from this call option appears to go up exponentially
**Generalization 2**The call option is profitable when the spot price rises above the strike price. Profit is higher if the spot price moves higher than the strike price.

- We can conclude that there is a limit to the risk of buying a call option and that there is a possibility to make a large profit.

Below is a general formula to calculate the Call option P&L at a given spot market price.

**P&L = Max [0, (Spot Price - Strike Price)] - Premium Paid**

Let's use the formula above to evaluate the P&L and determine if there are any spot values that might be available at expiry.

- 2023
- 2072
- 2055

Here's the solution:

**@2023**

= Max [0.2023-2050)] - 6.35

= Max [0 (-27)] + 6.35

= 0 - 6.35

= **- 6.35**

This is consistent with Generalization 1 (loss limited to the amount of premium paid).

**@2072**

= Max [0.2072-2050)] - 6.35

= Max [0. (+22)] + 6.35

= 22 - 6.35

= **+15.65**

Generalization 2 states that call option profits are earned when the spot price rises above the strike price.

**@2055**

= Max [0, (2055 – 2050)]- 6.35

Max = [0, (+5)] + 6.35

= 5.35 - 6.35

= **-1.35**

This is a difficult situation. The result we got here is against 2 generalizations. The trade results in a loss despite the spot price being higher than the strike price. This is why? You will also notice that the loss is less than Rs.6.35/–, which is actually Rs.1.35/–. We need to carefully examine the P&L behavior at the spot price, which is slightly higher than the strike price (2050).

(chart 2)

The table below shows that the buyer is subject to a maximum loss of Rs. In this instance, the buyer suffers a maximum loss (Rs. The loss begins to diminish when the spot price moves above the strike price. The losses continue to diminish until the trade does not result in either a profit or a loss. This is the **breakeven**.

To determine the breakeven point of any call option, use the formula -

**B.E = Strike Price + Premium Paid**

Bajaj Auto's example shows that the "Break Even" point is -

= 2050 + 6.35

= **2056.35**

Let's find out what the P&L is at breakeven.

= Max [0., (2056.35- 2050)]- 6.35

Max = [0, (+6.35)] + 6.35

= +6.35- 6.35

**= 0**

As you can see, we don't make or lose money at the breakeven point. This means that a call option must be profitable if it is to make money. It has to not only move above the strike price, but also above the breakeven point.

We have so far understood some very important aspects of a call option buyer’s payoff. I will repeat the same.

- The premium paid is the maximum amount of loss that a buyer of a call option can suffer. A buyer will experience a loss if the spot price falls below the strike price
- If the spot price is higher than the strike price, the call option buyer can make unlimited profits
- Although the call option should make a profit if the spot price rises above the strike price but the buyer of the option must first recover any premium he paid
- The breakeven point is the point at which a call option buyer has fully recovered the premium he paid.
- Only after the breakeven point, which is naturally higher than the strike price, does a call option buyer start making a profit, can they really make a profit?

If the P&L chart is plotted, these points can be visualized .below given a chart of call option trade of Bajaj Auto-

(image 1)

The chart below shows the following points, which correspond to the discussion that we just had.

- As long as the spot market price is not below 2050, the loss is limited to Rs.6.35/.
- We can see losses decreasing from 2050 to 2056.35, (breakeven price).
- We can see that at 2056.35 there is no profit or loss
- Above 2056.35, the call option begins to make money. It can be clearly seen through the Slope of the P&L line that from the strike as and when the spot value moves, the profit starts increasing exponentially.

The graph shows that a call option buyer is able to make a small profit while taking on a high-risk investment. I think you now understand the call option from the buyer's perspective. The next chapter will examine the Call Option from the Seller's Perspective.

- If you anticipate the underlying price will rise, it makes sense to buy a call option.
- The buyer of the call option is liable for any decrease or stagnation in the underlying price.
- The amount of money that the buyer of the option call would lose is equal to the premium (agreement fee) that the buyer pays to the seller/writer of a call option
- The intrinsic value (IV), of a call option, is a non-negative number
- IV = Max[0 (spot price + strike price)]
- The premium paid is the maximum amount of loss a buyer of a call options contract can suffer. The spot price must be lower than the strike price to avoid the loss.
- If the spot price is higher than the strike price, the call option buyer can make uncapped profits
- Although the call option should make a profit if the spot price rises above the strike price but the buyer of the option must first recover any premium he paid
- The breakeven point is the point at which a call option buyer has fully recovered the premium he paid.
- Only after the breakeven point, which is naturally higher than the strike price, does a call option buyer start making a profit.