Respuesta :
a) The price of European call is $2.52
b) The price of American call is $ 2.53
c) the price of European put is $ 1.05
d) [tex]p+s=c+[/tex][tex]Ke^{-rt}[/tex]
as given in the question,
the case stock price is [tex]S_0[/tex]= $30
the exercise price is K=$29
the rate of interest r = 0.05
the volatility is [tex]\sigma[/tex] = 0.25
the maturity period is T = 4/12
now ,
[tex]d_1=\frac{ln\frac{30}{29}+(0.05+\frac{0.25^2}{2} \times \frac{4}{12} }{0.25\sqrt{03333} }[/tex]
=> 0.4225
[tex]d_2=\frac{ln\frac{30}{29}+(0.05-\frac{0.25^2}{2} \times \frac{4}{12} }{0.25\sqrt{03333} }[/tex]
=> 0.2782
N(0.4225) =0.6637
N(0.2782)=0.6096
N(-0.4225)=0.3363
N(-0.2782)=03904
for calculating the European call price,
=> [tex]30\times 0.6637-29e^{(-0.05)\times\frac{4}{12} }\times 0.6096[/tex]
=> 2.52
thus European call price is $2.52
American call price will be same as the European call price i.e $2.52
The European put price is calculated as follows
=>[tex]30\times 0.6637-29e^{(-0.05)\times\frac{4}{12} }\times -0.3904-30\times 0.3363[/tex]
=>$1.05
put-call parity states that
[tex]p+s=c+Ke^{-rT}[/tex]
in this case c=2.52, [tex]S_0[/tex]=30,K=29,p=1.05 and [tex]e^{-rT}[/tex] =0.9835
so , therefore
it is easy to say that the relationship is satisfied
To learn more about non- dividend distribution:
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