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A call option with an exercise price of $30 and four months to expiration has a price of $4.10. The stock is currently priced at $29.80, and the risk-free rate is 4 percent per year, compounded continuously. What is the price of a put option with the same exercise price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Respuesta :

Answer:

price is $3.90

Explanation:

given data

exercise price = $30

four months to expiration price = $4.10

stock  currently priced = $29.80

risk free rate = 4 % per year

to find out

What is the price of a put option with the same exercise price

solution

we know that put call parity  that is express as

S + P = C + E × [tex]e^{-rt}[/tex]         ........................1

here S is stock price and P is put price and R is risk free rate and C is call price and t is time to  maturity and E is exercise price

so put here all these value in equation 1  we get

P = C + E × [tex]e^{-rt}[/tex] - S

P = 4.10 + 30 × [tex]e^{-0.04*\frac{4}{12}}[/tex] - 29.80

P = 3.90

so price is $3.90

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