Value of a call option spread

Question

In this example:

An options trader believes that XYZ stock trading at $42 is going to rally soon and enters a bull call spread by buying a JUL 40 call for $300 and writing a JUL 45 call for $100. The net investment required to put on the spread is a debit of $200.

The stock price of XYZ begins to rise and closes at $46 on expiration date. Both options expire in-the-money with the JUL 40 call having an intrinsic value of $600 and the JUL 45 call having an intrinsic value of $100. This means that the spread is now worth $500 at expiration. Since the trader had a debit of $200 when he bought the spread, his net profit is $300.

If the price of XYZ had declined to $38 instead, both options expire worthless. The trader will lose his entire investment of $200, which is also his maximum possible loss.

I don't understand this part:

the JUL 45 call having an intrinsic value of $100. This means that the spread is now worth $500 at expiration.

Why is the value computed by subtracting 600 - 100?

If I am selling 45 Call that means:

• As a writer: I want stock price to go down or stay at strike.
• As a buyer: I want stock price to go up.

Answer 1

On expiry, with the underlying share price at $46, we have :

• the $45 call has an intrinsic value $1 which equates to $100 = 100 x $1.00
• the $40 call has an intrinsic value $6 which equates to $600 = 100 x $6.00

You ask :

How come they substract 600-100. Why ?

Because you have sold the $45 call to open you position, you must now buy it back to close your position. This will cost you $100, so you are debited for $100 and this debit is being represented as a negative (subtracted); i.e., -$100

Because you have purchased the $40 call to open your position, you must now sell it to close your position. Upon selling this option you will receive $600, so you are credited with $600 and this credit is represented as a positive (added) ; i.e., +$600.

Therefore, upon settlement, closing your position will get you $600-$100 = $500. This is the first point you are questioning.

(However, you should also note that this is the value of the spread at settlement and it does not include the costs of opening the spread position, which are given as $200, so you net profit is $500-$200 = $300.)

You then comment :

I know I am selling 45 Call that means : As a writer: I want stock price to go down or stay at strike. As a buyer: I want stock price to go up.

Here, note that for every penny that the underlying share price rises above $45, the money you will pay to buy back your short $45 call option will be offset by the money you will receive by selling the long $40 call option. Your $40 call option is covering the losses on your short $45 call option. No matter how high the underlying price settles above $45, you will receive the same $500 net credit on settlement. For example, if the underlying price settles at $50, then you will receive a credit of $1000 for selling your $40 call, but you will incur a debit of $500 against for buying back your short $45 call. The net being $500 = $1000-$500. This point is made in response to your comments posted under Dr. Jones answer.

Answer 2

I think you're missing the fact that the trader bought the $40 call but wrote the $45 call -- i.e. someone else bought the $45 call from him. That's why you have to subtract 600-100. At expiration, the following happens:

• he exercises the $40 call (buys 100 sh @ $40) and (presumably) sells 100 sh @ $46 = $4600 - $4000 = $600 profit
• his counterparty exercises the $45 call against him (buys 100 sh from him @ $45), so he has to get hold of 100 sh (@ $46) = $4500 - $4600 = -$100 profit

So $600 + -$100 = $500 total profit.

Note: In reality he would probably use the shares he gets from the first call to satisfy the shares he owes on the second call, so the math is even simpler:

• exercises the $40 call (buys 100 sh @ $40), then satisfies the $45 call (sells 100 sh @ $45) = $4500 - $4000 = $500

Answer 3

You have to look at the real price of the share to calculate the value of the spread.

42$ at the start, 46$ at the end. Think of it this way:

When price was 42$
the call 45$ was out of the money, worth 100$ of time value only=100
the call 40$ was in the money and worth 200$ of intrinsic + 100 time value=300
the difference was 200$

Now that price is 46$
the call 45$ is worth 100$ in the money, real or intrinsic value
the call 40$ is worth 600$ in the money, real or intrinsic value
the difference is 500$

NOTE: 1. Commission fees are not included. 2. Time value of 100$ on both calls when price is 42$ is incorrect and for teaching purpose only.

Answer 4

The Explanation is correct. The Traders buys the 1st call and profits linearly form 40$ onwards. At at 45 the short call kick in and neutralizes any further profit on the first call.