Question

Consider the following European plain vanilla options: (1) a call with strike price K = 160, (2)
a put with strike price K = 160, (3) a call with strike price Kc = 165, and (4) a put with strike
price Kp = 155. All options have the same non-dividend-paying underlying stock and mature
after one year.
a) Assuming current stock price 160, stock price volatility 22%, and continuously compounded
risk-free interest rate 0.49%, compute the prices of options (1)–(4) using the
Black–Scholes–Merton formula showing clearly all your computations.

Answer 1

The B-S model formula for find the price of call option is given by

  ...................1

  

Where:

• C is the call option price;
• S_t is the current stock (or other underlying) price;
• K is the strike price;
• r is the risk-free interest rate; and
• t is the time to maturity.
• N denotes a normal distribution.
• =represents the underlying volatility (a standard deviation of log returns

Here,S=160,  =.22, r=0.49,t=1

Now

(1)call with stike price K=160

we will calculate

or,

d1=0.2423 approx=0.24

Now

d2=0.0223

Now from the standard normal distribution table we find the value of

N(d1)=N(0.24)=0.5948

and

N(d2)=N(0.02)=0.5080

C=95.168-81.686

C=13.4816

Call option =13.4816 answer.

(2)To find put with strike price K=160

We can use pull-call parity to calculate the value of put

where P=put price,C=call price calculated above

by putting the values

P=14.16 answer

(3) Call with strike price K=165

by putting in the formula 1,we get

d1=-0.1153=-0.11(approx)

d2=-0.3353=.33(Approx)

Now from the standard deviation table we find the value of

N(d1)=N(-0.11)=0.4562

N(d2)=N(-0.33)=0.3707

now the value of C is

C=11.527 answer.

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