A trader creates a long butterfly spread from call options with strike prices of $160, $170, and $180 per share by trading a total of 40 option contracts (10 contracts at $160, 20 contracts at $170 and 10 contracts at $180). Each contract is written on 100 shares of stock. The options are worth $20, $24, and $30 per share of stock.
What is the value of the butterfly spread at maturity as a function of the then stock price?
What is the profit of the butterfly spread at maturity as a function of the then stock price?
At maturity, let stock price be S
Value of long call with X = 160
max(0, (10*160 - 10 *S)) - 20*10
Value of short call with X = 170
-(2 *(170*10 - 10*S)) + 20*24
Value of long call with X = 180
max(0,(10*180 - 10*S)) - 30 *10
The total value of the strategy ( for 100 stocks )
= (max(0, (10*S - 10 *160)) - 20*10 -(2 *(170*10 - 10*S)) + 20*24 + max(0,(10*S - 10*180)) - 30 *10) * 100
Profit for the strategy =
Case 1
If S < 160
= (0 - 20*10 - 0 + 20*24 + 0 - 30 *10) * 100
Case 2
If 160 < S < 170
= ((10*S - 10 *160) - 20*10 + 20*24 + 0 - 30 *10) * 100
Case 3
If 170 < S < 180
= ((10*S - 10 *160) - 20*10 -(2 *(170*10 - 10*S)) + 20*24 + 0 - 30 *10) * 100
Case 4
If 180 < S
= ((10*S - 10 *160) - 20*10 -(2 *(170*10 - 10*S)) + 20*24 + (10*S - 10*180) - 30 *10) * 100
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