uestion4 An.at the money 3-month call option on the XYZ stock is currently tradi

Question

uestion4 An.at the money 3-month call option on the XYZ stock is currently trading at $52.82 on CBOE. An investor w put is also at the money (i.e. currently the price of the stock is exactls.the same as the exercise price of the option written on this stock.) Take the volatility of the return on SPX to be 15% and the risk-free rate to be 6%. Find the price of the put option. k. Suppose, the a. Find the price of the put option, using put call parity b. Find the price of the put option using Black Sholes option pricing formula for puts

Explanation / Answer

1a) Formula for Put Call Parity:

C+Xe-rt=S+P

Where C=call price

             X=strike price

            S= stock price

            P= put price

Let’s assume the stock price and strike price to be 50 (at the money option)

Therefore, Put Price:

P= 52.82+50e-0.06×0.25-50

=52.82+49.2556-50

=$ 52.0756

1b) The value of put option using the Black Scholes model is:

P= Xe-rt× N(-d2)S0× N(-d1)… (1)

d1= (ln(S0/X)+(r+(2/2)t)/(t)

d2=d1-t

Given Information:

S0=50 (assumed)

X=50 (assumed)

r=0.06

t=0.25

=0.15

First lets find out d1 and d2:

d1= ((ln(50/50)+(0.06+(0.152)/2)0.25))/0.150.25)= 0.2375= 0.24 (rounded)

Therefore, N(d1) in the Z table (look up 0.24)=0.5948

Therefore N(-d1)= 1- N(d1)=1-0.5948=0.4052

  

d2=0.24-0.150.25

    = 0.165 (rounding to 0.16)

Therefore, N(d2) in the Z table (look up 0.16)=0.5636

Therefore N(-d2)= 1- N(d2)=1-0.5636=0.4364

Now simply plugging in values in equation 1 we get the value of the put option:

50e-0.06(0.25) × 0.4364-50×0.4052

=21.49514-20.26

=$ 1.235143

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