Options
• Basics of call options
• Basics of options jargon
• How to buy a call option
• How to buy/sell call option
• Buying put option
• Selling put option
• Call & put options
• Greeks & calculator
• Option contract
• The option greeks
• Delta
• Gamma
• Theta
• All volatility
• Vega
3.1 – Buying call option
In the preceding chapters, we examined the call option’s fundamental construction and learned the general circumstances in which buying a call option makes sense. We will formally organize our ideas about the call option in this chapter and have a solid understanding of both the purchasing and selling of the call option. Here is a quick summary of everything we learned in the first chapter before continuing with this one:
- When you anticipate that the underlying price will rise, it makes sense to purchase a call option.
- The buyer of the call option loses money if the underlying price declines or remains unchanged.
- The premium (agreement fees) that the buyer pays to the seller/writer of the call option is equal to the amount of money that the buyer of the call option would lose.
We shall keep the aforementioned three considerations in mind (which act as fundamental principles) and gain a deeper understanding of the call option.
3.2 – Building a case for a call option
The purchase of a call option is in a variety of market circumstances. Here is one that I just learned about as I was writing this chapter and thought would be a good fit for our conversations.
Bajaj Auto Limited’s stock is being . They are one of India’s largest two-wheeler manufacturers, as you may know. The stock has been severely undervalued in the market for a number of reasons and is currently trading at its 52-week low. I think there might be a chance to start a trade here. I have the following opinions about this trade:
- There is no disputing that Bajaj Auto is a stock with strong fundamentals.
Because of how much the stock has fallen, I think the market may have overreacted to the business cycle instability of Bajaj Auto.
I anticipate that the stock price will finally cease declining and stop short.
But because I’m concerned that the stock will continue to decrease, I don’t want to purchase the stock for delivery (yet).
Extending the previous point, I am unable to purchase Bajaj Auto’s futures due to my concern for M2M losses.
At the same time, I don’t want to pass up a chance for a significant stock price reversal.
In conclusion, I have high hopes for the stock price of Bajaj Auto (which I believe will rise eventually), but I have some trepidation regarding the stock’s near-term prospects. The major source of uncertainty is the potential severity of my short-term losses in the event that the stock’s decline continues. However, based on my estimation, the likelihood of the loss is minimal, but it is still possible. So what do I need to do?
As you can see, I’m in a situation that Ajay was in at the same time (recall the Ajay – Venu example from chapter 1). This kind of situation sets up a classic example of an options transaction.
In light of my predicament, purchasing a call option on Bajaj Auto makes sense for the reasons I’ll discuss in a moment.
As shown, the stock is currently trading at Rs. 2026.9. (highlighted in blue). With a premium of Rs. 6.35, I’ll decide to purchase a call option with a strike price of 2050. (highlighted in the red box and red arrow). You might be wondering why, since there are so many other strike prices available (highlighted in green), I chose the 2050 strike price. We will ultimately cover the process of choosing a strike price in this module, but for now, let’s assume that 2050 is the appropriate strike price to trade.
3.3 – Intrinsic value of a call option (upon expiry)
What transpires with the call option now that the expiration is 15 days away? In general, there are three possibilities that could occur, which I assume you are already aware of:
The stock price rises above the strike price, say 2080, in scenario one.
Scenario 2: The stock price declines to 2030, which is below the strike price.
The stock price remains at 2050 in scenario three.
I’ll also presume that you are familiar with the P&L calculation at the precise value of the spot in the three scenarios above as they are fairly similar to the ones we looked at in chapter 1. (if not, I would suggest you read through Chapter 1 again).
The concept I’m presently interested in investigating is this:
- You will concur that there are just three major categories in which the price movement of Bajaj Auto may be (following expiration), namely, the price either rises, falls, or remains unchanged.
- What about all the other prices in between, though? For instance, in Scenario 1, the price is set at 2080, which is higher than the striking price of 2050. What about further strike prices like 2055, 2060, 2065, 2070, etc.? Can we draw any conclusions about the P&L from this?
- In scenario 2, the price is anticipated to be around 2030, which is less than the 2050 strike. How about more strike prices like 2045, 2040, 2035, etc.? Having said that, anything here with respect to the P&L?
I would want to refer to these points as the “Conceivable values of the spot on expiry” in order to generalize the P&L knowledge of the call option. What would happen to the P&L at various possible spot prices (upon expiry)?
To start, I’d like to discuss the concept of the “intrinsic value of the option at expiry” (in part, not the complete concept).
The non-negative value that the option buyer would be to if he were to exercise the call option is known as the intrinsic value (IV) of the option upon expiration (particularly a call option for now). Simply put, determine how much cash you would receive at expiration if the call option you own were profitable (assuming you are the buyer of the call option). It is in mathematics as –
IV = Strike Price – Spot Price
Therefore, the 2050 Call option’s intrinsic value would be if Bajaj Auto is trading at 2068 on the day of expiration (in the spot market).
= 2068 – 2050
= 18
Likewise, the intrinsic value of the option would be – if Bajaj Auto is trading at 2025 on the expiry day.
= 2025 – 2050
= -25
But keep in mind that the IV of an option is always a positive figure, whether it is a call or a put.
= 0
Now, our goal is to keep the notion of the option’s intrinsic worth in perspective, determine how much money I will make at each potential Bajaj Auto expiration value, and use that information to draw some broad conclusions about the P&L of call option buyers.
3.4 – Generalizing the P&L for a call option buyer
Now that we’ve kept the idea of an option’s intrinsic value in the back of our minds, let’s work to create a table that will show us how much money I, as the buyer of Bajaj Auto’s 2050 call option, would earn under the various potential spot value changes of Bajaj Auto (in the spot market) on expiration. Keep in mind that Rs 6.35 was as the premium for this choice. The fact that I Rs.6.35 remains intact, regardless of how the spot value fluctuates. This is the expense I incurred to purchase the 2050 Call Option.
What then do you notice? The table above reveals two notable observations:
- The most that might be, even if Bajaj Auto’s price drops (below the strike price of 2050), appears to be just Rs. 6.35/-
1. Generalization 1: When the spot price declines below the strike price, the buyer of a call option suffers a loss. However, the call option buyer’s loss is only as great as the premium he has .
2. When Bajaj Auto begins to rise over the 2050 strike price, the profit from this call option appears to grow rapidly.
- Generalization 2: When the spot price rises above the strike price, the call option is lucrative. The profit increases as the difference between the strike price and the current price rises.
3. The buyer of the call option has a restricted risk and the potential to earn a limitless profit, according to the aforementioned two generalizations.
The Call option P&L for a specific spot price can be using the following generic formula:
Max [0, (Spot Price – Strike Price)] = P&L – Premium
Let’s examine the P&L for a few potential spot values on expiry using the formula above:
2023 \s2072 \s2055
The answer is as follows:
@2023
= Max [0, (2023 – 2050)] – 6.35
= Max [0, (-27)] – 6.35
= 0 – 6.35
= – 6.35
The resolution fits Generalization 1 (loss restricted to the extent of the premium ).
@2072
= Max [0, (2072 – 2050)] – 6.35
= Max [0, (+22)] – 6.35
= 22 – 6.35
= +15.65
The solution fits Generalization 2. (Call option gets profitable as and when the spot price moves over and above the strike price).
@2055
= Max [0, (2055 – 2050)] – 6.35
= Max [0, (+5)] – 6.35
= 5 – 6.35
= -1.35
This presents a challenging circumstance because the outcome goes against the second generalization. The trade is losing money even though the spot price is higher than the strike price! What causes this? Furthermore, the actual loss is substantially lower than the maximum loss of Rs. 6.35/-; it is just Rs. 1.35/-. We need carefully examine the P&L activity surrounding the spot value, which is marginally over the strike price, to ascertain why this is occurring (2050 in this case).
As you can see from the table above, until the spot price reaches the strike price, the buyer incurs a maximum loss (in this example, Rs. 6.35). The loss begins to diminish, though, once the spot price begins to rise above the strike price. Up until a moment where neither a profit nor a loss is from the trade, the losses are continuously. The breakeven point is what we refer to as.
Any call option’s breakeven point can be using the following formula:
B.E. = Strike Price Plus Premium
The “Break Even” point for the Bajaj Auto example is –
= 2050 + 6.35
= 2056.35
Let’s actually determine the P&L at the breakeven point.
= Max [0, (2056.35 – 2050)] – 6.35
= Max [0, (+6.35)] – 6.35
= +6.35 – 6.35
= 0
As you can see, at the breakeven point, we are in the negative financially. In other words, for the call option to become profitable, it must move above both the strike price and the breakeven point.
3.5 – Call option buyer’s payoff
We have already discussed a few crucial aspects of a call option buyer’s payment, so let me restate them here:
- The greatest loss a call option buyer can incur is equal to the premium amount. As long as the spot price is lower than the strike price, the buyer loses money.
- If the current price rises over the strike price, the buyer of the call option could benefit indefinitely.
- Even though the call option is meant to provide income when the spot price rises above the strike price, the buyer must first recoup the premium he has already paid.
The breakeven point is the point at which the buyer of a call option fully recoups the premium he has paid.
Only after passing the breakeven mark does the call option buyer actually begin to benefit (which naturally is above the strike price)
The following points, which are consistent with our recent discussion, can be seen in the graphic above:
- As long as the spot price is trading at any price below the strike of 2050, the loss is limited to Rs. 6.35.
- Losses can be shown to decrease from 2050 to 2056.35 (breakeven price).
- We can see that there is no profit or loss at 2056.35.
- The call option starts to profit above 2056.35. In reality, the P&L line’s slope plainly shows that when the spot value moves away from the strike, the profits begin to rise exponentially.
One thing is clear from the graph once more: A call option buyer has low risk but unlimited profit potential. And with that, I hope you have a better understanding of the call option from the standpoint of the buyer. We shall examine the Call Option from the seller’s standpoint in the following chapter.
CONCLUSION
- When you anticipate that the underlying price will rise, it makes sense to purchase a call option.
- The buyer of the call option loses money if the underlying price declines or remains unchanged.
- The premium (agreement fees) that the buyer pays to the seller/writer of the call option is equal to the amount of money that the buyer of the call option would lose.
- A call option’s intrinsic value (IV) is a non-negative number.
- IV = Max[0, strike price minus spot price]
- The maximum loss a call option buyer can incur is equal to the premium they paid. As long as the spot price is lower than the strike price, a loss is incurred.
If the current price rises over the strike price, the buyer of the call option could benefit indefinitely.
Even though the call option is meant to provide income when the spot price rises above the strike price, the buyer must first recoup the premium he has already paid.
The breakeven point is the point at which the buyer of a call option fully recoups the premium he has paid.
Only after passing the breakeven mark does the call option buyer actually begin to benefit (which naturally is above the strike price).