Need explnation. How is it 0-75 and what is the formula they are using? Can\'t u

Question

Need explnation. How is it 0-75 and what is the formula they are using? Can't understand anything.

56. The stock price of Bravo Corp. is currently $100. The stock price a year from now will be either $160 or $60 with equal probabilities. The interest rate at which investors invest in riskless assets at is 6%. Using the binomial OPM, the value of a put option with an exercise price of $135 and an expiration date one year from now should be worth today. A. $34.09 B. $37.50 $38.21 D. $45.45 0-75 H-75 160-60 Selling the stock and buying a 1-year discounted note with a $160 face value will give the same payoff as investing in (1/.75) puts P .75 160 -100)=3821 1+.06

Explanation / Answer

Su=160
Sd=60
Value of put=max(strike price-stock price,0)

Hedge ratio=(Pu-Pd)/(Su-Sd)
(Value of put when Stock price is 160-Value of Put when stock price is 60)/(160-60)=(max(135-160,0)-max(135-60,0))/(160-60)=-0.75

1 stock is bought
1/0.75 put is bought
Investment required=P/0.75+100
As we have created a hedge, the payoff in both up and downstates must be the same.
Payoff in upstate=160
Payoff in downstate=60+1/0.75*75=160

Hence, investment must be the present value of payoff
Hence,
P/0.75+100=160/1.06
=>P=38.21

YOu can refer the below link
https://faculty.darden.virginia.edu/conroyb/derivatives/binomial%20option%20pricing%20_f-0943_.pdf

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