Question

Important Red All Tags... 1.13. Suppose that a March call option on a stock with a strike price of $50 costs $2.50 and is held until March. Under what circumstances will the holder of the option make a gain? Under what circumstances will the option be exercised? Draw a diagram showing how the profit on a long position in the option depends on the stock price at the maturity of the option

Answer 1

The option will be exercised if the stock price at expiration is higher than the option strike price of $50. This is because if the stock price at expiration is higher than the option strike price, it is profitable for the option holder to exercise the option and buy the stock at a price lower than the market price.

The option holder will make a gain if the stock price at expiration is higher than (strike price + premium paid to buy call option). Therefore, breakeven point =  strike price + premium paid to buy call option.

Algebraically, this is expressed as :

Payoff of a long call option = Max[S-X, 0] - P

S = underlying price at expiry,

X = strike price

P = premium paid to buy call option

ДА В Payoffs Stock price at Long Call 2 expiryl($50) $40 ($2.50) $41 ($2.50) $42 ($2.50) $43 ($2.50) $44 ($2.50) $45 ($2.50) $46 ($2.50) $47 ($2.50) $48 ($2.50) $49 ($2.50) $50 ($2.50) $51 ($1.50) $52 ($0.50) $53 $0.50 $54 $1.50 $2.50 $56 $3.50 $4.50 $58 $5.50 $59 $6.50 $60 $7.50 $55 $57

А Payoffs Stock price at 2 expiry 3 40 4 41 12 49 13 50 14 51 15 52 Long Call ($50) =MAX(A3-50,0)-2.5 =MAX(A4-50,0)-2.5 =MAX(A5-50,0)-2.5 =MAX(A6-50,0)-2.5 =MAX(A7-50,0)-2.5 =MAX(A8-50,0)-2.5 =MAX(A9-50,0)-2.5 =MAX(A10-50,0)-2.5 =MAX(A11-50,0)-2.5 =MAX(A12-50,0)-2.5 =MAX(A13-50,0)-2.5 =MAX(A14-50,0)-2.5 =MAX(A15-50,0)-2.5 =MAX(A16-50,0)-2.5 =MAX(A17-50,0)-2.5 =MAX(A18-50,0)-2.5 =MAX(A19-50,0)-2.5 =MAX(A20-50,0)-2.5 =MAX(A21-50,0)-2.5 =MAX(A22-50,0)-2.5 =MAX(A23-50,0)-2.5 17154 18 55 21 58 22 59 23 60

Payoffs + $40 $41 $42 $43 $44 545 546 547 $48 $49 $50 $51 52 $53 $54 $55 $56 $57 $58 $59 $60 7