Answer:
<em>$1006 </em>
Explanation:
A long butterfly is created by following these steps
- Long 1 call option for strike X ( highest premium say C)
- Short 2 call option for Strike Y (premium =C-6.67 )
- Long 1 call option for strike Z (premium = C-6.67 - 5.03 = C-11.70
where X<Y<Z
Here, Y-X = Z-Y =$11.70
<u>i) whenever the price at maturity goes below the price of x ( no call option is executed )</u>
payoff = 2*(C-6.67) -C-(C-11.7) = - 13.34 + 11.70 = - 1.64
<u>ii) when the price at maturity is between X and Y, only call with strike X is executed </u>
hence payoff = -1.64 +(P-X) where P is the Price at maturity
p - x = y-x = 11.70
hence maximum payoff = - 1.64 + 11.70 = $10.06
<u>iii) When the price is between Y and Z , only call with strike X and Y are executed.</u>
hence, payoff = -1.64 + (P-X) -2* (P-Y) = -1.64 +( 2Y - X - P) and this value decreases as P increases
the minimum payoff occurs when P=Z
So, maximum payoff = -1.64 + (Z-X) - 2*(Z-Y) = -1.64 + 23.4 - 2*11.7 = -$1.64
<u>iv) When the price at maturity is more than Z , all calls are executed</u>
hence, payoff = -1.64 +(P-X) -2* (P-Y) + (P-Z) = -1.64+(2Y-X-Z)
= -1.64+(Y-X -(Z-Y)) = -1.64+(11.7 - 11.70)
= -$1.64
the maximum payoff occurs when P=Y
considering the four options traded the maximum payoff = $10.06
<em>Finally determine the maximum net gain when 400 options are traded</em>
<em>= 10.06 * 400 / 4 </em>
<em>= 10.06 * 100 = $1006 </em>
