Question

Use the two-state put-option value in this problem. So = $100; X = $120, the two possibilities for ST are $150 and $80. The range of P across the two states is , and the hedge ratio is_ Select one A. $0 and $50; +4/7 B. $0 and $40; -4/7 O C. $0 and $50; -4/7 D. $20 and $40; +1/2 o E. $0 and $40; +4/7 When St = $150; P = $0; when ST = $80: P = $40; ($0 - $40)/($150 - $80) =-4/7. When ST = $150; P = $0; when ST = $80: P = $40; ($0 - $40)/($150 - $80)=-4/7. The correct answer is: $0 and $40; -4/7

Why St=150, P=0?

St=80,p=40?

What's the function?

Answer 1

Value of put option = Excercise price-Spot rate  
  
If Spot rate is more than Excercise price, put option will not be excercised. Value shall be nil. in this case loss will be equal to premium paid.   
So minimum payoff on put option is 0. it cannot be negative  
Reason behind this is that put option is right to sell the stock at Strike price. if spot rate on Expiration is less than Strike price, we will excercise the option and sell against the option.  
If spot rate at Expiration is more than strike price, then we can sell at high rate in Market. then why we will excecise the option and sell at lower rate. We will not excercise option. So Value of option is 0  
So function = Excercise or strike price - Spot rate at Expiration  
Subject to 0