Question

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 is 6%. Using the binomial OPM, the value of a put option with an exercise price of $135 and an expiration date 1 year from now should be worth __________ today.
$34.09

$37.50

$38.21

$45.45

I know the answer should be 38.21.

Answer 1

Answer:

correct option is $38.21

Explanation:

given data

stock price = $100

stock price =  either $160 or $60

interest rate = 6%

exercise price = $135

solution

we get here Hedge ratio that is express as

Hedge ratio = (Pay off in case price appreciates - Pay off in case price depreciates) ÷ (Appreciated price - Depreciated price)     ..................1

put here value we get

Hedge ratio = ( Max [$135 - $160, $0] - Max[$135 - $60, $0]) ÷ ($160 - $60)

Hedge ratio = $\frac{ 0 - 75}{ 100}$

Hedge ratio = - 0.75

so here Price of Put option is

Price of Put option = -Hedge ratio × {Appreciated price ÷ (1 + risk free rate) - Present stock price}

Price of Put option =  -(-0.75)  × $\frac{160}{1+0.06} - 100$

Price of Put option = $38.21

so here correct option is $38.21