Question

Trading strategy called profitmania is created by taking below calls in the table

calls	strike price	premium
2 long call	k1	c1
1 short put	k2	p2
1 long put	k3	p3

K1 < k2 < k3 is the strike price condition

Please express the break-even stock prices using and

Answer 1

Profit from long call=MAX(stockprice-strike price,0)-call premium

Profit from short put=-MAX(strike price-stock price,0)+put premium

Profit from long put=MAX(strike price-stock price,0)-put premium

Profit=2*MAX(St-K1,0)-2*C1-MAX(K2-St,0)+P2+MAX(K3-St,0)-P3

St<K1: Profit=-2*C1-K2+St+P2+K3-St-P3=-2C1-K2+P2+K3-P3
k1<St<k2: Profit=2St-2K1-2C1-K2+P2+K3-P3
k2<St<K3: Profit=St-2K1-2C1+P2+K3-P3
St>K3: Profit=2St-2K1-2C1+P2-P3

At breakeven: Profit is equal to zero

Hence,
1.
-2C1-K2+P2+K3-P3=0

2.
2St-2K1-2C1-K2+P2+K3-P3=0
=>St=K1+C1+(K2-P2-K3+P3)/2

3.
St-2K1-2C1+P2+K3-P3=0
=>St=2K1+2C1-P2-K3+P3

4.
2St-2K1-2C1+P2-P3=0
=>St=K1+C1+(-P2+P3)/2