Question

A. What is Price of a European Put option?

B. Price of a European Call option?

Spot price = $60

Strike Price = $44

Time to expiration = 6 months

Risk Free rate = 3%

Variance = 22% (use for volatility)

Show steps/formula

Answer 1

(A)

Given,

T=6/12

S=$60

X=$44

R=3%

Sigma^2=0.22

Sigma=route of 0.22=0.4690

D1=(ln(s/x)+(sigma^2/2+rf)*t)/Sigma*route t

Ln-Natural log

Sigma^2=Variance

Rf=Risk free rate

D1=(Ln($60/$44)+(0.22/2+0.03)*6/12)/0.4690*route of 6/12

D1=0.1363+0.07/0.3316

D1=0.622

D2=d1-sigma*route t

D2=0.622-0.4690*route of 6/12

D2=0.290

NT(d1)=Normal table value of 0.622

NT(d2)=Normal table value of 0.290

(https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf)

NT(0.622)=0.733026

NT(0.290)=0.61409

N(d1)=0.5+-NT(d1)

If NT(d1)&NT(d2) are +ve then add 0.5 if -ve then deduct from 0.5

N(d1)=0.5+0.733026=1.233026

N(d2)=0.5+0.61409=1.11409

N(-d1)=1-0.622=0.378

N(-d2)=1-0.290=0.71

Value of call

Spot price*N(d1)-N(d2)*Strike price * e^-trf

e^-trf=e^-6/12*3%

e^-0.015=1/1.01511=0.98511

Value of call=$60*1.233026-$44*0.98511*1.11409

=73.98156-48.2900

=25.6915

Value of put

Strike price * e^-trf*(N(-d2))-Spot price*(N(-d1))

44*0.98511*0.71-60*0.378

30.774-22.68

=8.094