Payoff in derivatives

CFA Level I Derivatives
#1

Hello Everyone,

What is the meaning of no option can sell for less than zero otherwise seller has to pay buyer?

I agree with the first half what is the meaning of second half in bold?

Thanks

#2

It is saying that if you want to enter into a long position of an option, the premium must be at least greater than zero.

If the premium is less than zero (or equal to zero), then the writer (short/seller) of the option, must pay the buyer (long) to enter into teh contract. OBviously this makes no sense, or eveyone would enter into long option contract positions because there would be no associated downside (which is usually the premium paid by the long) and only upise potential if the option expires in-the-money.

#3

Thanks a lot :slight_smile:

That means is this premium acts like a marginal money or the cost price for the right to exercise ?

I mean this premium went to writer or clearing house?

and why we don’t include this in the calculation of payoff of option?

For Eg: The underlying is stock priced at $40. A call option with strike price $40 is selling for $7 . I buy the stock and sell the call option. What will be payoff at the expiration if stock is trading at 1) 52 and 2) 38

The answers are :-

  1. 52 -Max(0, 52-48) = 52 2) 38 - Max(0,38-40) = 38

My confusion is in regards of premium =$7 and Is the S(t)-X term in both solution is for the call long position?

Thanks

#4

There is a difference between the payoff of an option, and the profit.

The premium is not determined in the ‘max’ equation because the premium is a sunk cost, so it does not get factored into the decision to exercise the option.

For example: Suppose you have a call option that you paid a premium of $5 for with a strike price of $50. At expiration, the value of the underlying is $53.

So the payoff is max(0,$53-$50) = $3. The profit however, is max(0,$53-$50) - $5 = -$2.

If you did not exercise the option when it had a positive payoff (in-the-money), the profit would have been -$5. So because the premium is a sunk cost, it is not relevant to determine the payoff of the option, and wheter or not to exercise the option.

#5

So in general, for a call option (long position):

payoff = max(0,S-X)

profit = max(0,S-X) - c

#6

Ok, and when we are saying before expiration option always has positive value to the buyer and negative value to seller that means we are talking about right to exercise when the payoff = Max(0,S-X)

thanks

#7

^ Correct.

And as far as where the option premium goes in practice, I am not 100% sure.

The option premium belongs to the writer of the option. If it is an exchange traded option, I imagine that the option premium will be deposited in the option writer’s margin account at the clearinghouse to reduce credit risk from the option writer. If it is an OTC option, the option premium will go directly to the option writer. As far as the CFA L1 material, you will not need to know this.

Someone correct me if this is not accurate.

#8

Hi Dwheats,

Initial Margin is paid by short as well as long position where options premium is not paid upfront.

#9

^ In any case, it is not necessary to know those dynamics.

It is only necessary to know that the premium belongs to the writer of the option.