Who is good with options? Would like help

CFA Level III Derivatives
#1

Options = not my strong suit. But this is very much bugging me:

You are bullish about an underlying that is currently trading at a price of $80. You choose to go long one call option on the underlying with an exercise price of $75 and selling at $10, and go short one call option on the underlying with an exercise price of $85 and selling at $2. Both the calls expire in three months.

The price of the underlying at expiration is $78. What is the value at expiration?

Answer:

Long call: max (0, 78 - 75) = 3. So far so good.

Short call: max (0, 78 - 85) = 0. Heres my problem. Doesn’t a short call profit when the underlying declines?

VT=max(0,ST−X1)−max(0,ST−X2)=max(0,78−75)−max(0,78−85)=3−0=3

T=max(0,ST−X1)−max(0,ST−X2)

=max(0,78−75)−max(0,78−85)=3−0

VT=max(0,ST−X1)−max(0,ST−X2)=max(0,78−75)−max(0,78−85)=3−0=3VT=max(0,ST−X1)−max(0,ST−X2)=max(0,78−75)−max(0,78−85)=3−0=3

VT=max(0,ST−X1)−max(0,ST−X2)=max(0,78−75)−max(0,78−85)=3−0=3

#2

The only profit from a short call is the premium you collect. You must pay out when the spot price is above the strike price at expiration. The call in your example is out of the money so it is worthless. Payoff for a short call is just -MAX(0, S - X).

Note also that in the bull spread question you posted above that once the spot price rises above $85 you have both a short and long position on the same underlying which offset each other. The best way to understand options is to look at payoff diagrams and map out each spread in your head. You will have a tough time remembering the equations but if you know all the components individually you can piece it together.

#3

because you sell the call, think about it from the buyer’s perespective and you wont get tripped up. the buyer has a long call with x @ 85. the underlying at expiration is 78. So the buyer has the irght to buy at 85, but since the stock is lower than that, they would not benefit by doing so, so the option’s value is 0. So add the values: 3 + 0 = 3. then add the premiums to get the overall profit: 3 + -10 + 2. profit = -5

#4

also another thing to keep in mind is value vs profit

#5

as above

#6

Thanks MGurn! I was not looking at the short call logically.

#7

value is always the sum of the values of all of the options used. profit then adjusts value for premium paid/received.

do value first, then profit

#8

thanks

#9

Makes sense, helpful to think from buyers perspective.