Question

Cassiopeia inc. is currently trading at $100 per share. After examining the stock of Cassiopeia, you have determined that in each 3 month period its price will either increase to 25% or decrease by 20%. The interest rate is 3% every 3 months. Verify that put-call parity holds.

Answer 1

Standard Inputs :

S= stock price = 100

E= exercise price = 90

u =1.25

d = 0.8

us =100*1.25 =125

ds = 100*0.80 = 80

R = 1.03

p = risk neutral probability = ( R -d) / ( u -d) = ( 1.03 - 0.8) /( 1.25 -0.8 ) = 0.5111

1- p = 1 - 0.5111 = 0.4889

value of call option

Expected payoff in upmove = 125 -90=35

expected payoff in downmove = 0

Value of call option = 35*0.5111+0*0.4889 = 17.37

value of put option

expected payoff in upmove = 0

expected payoff in downmove = 90 -80 = 10

value of put option =( 0*0.5111 + 10*0.4889) / 1.03 = 4.37

forward = spot rate * ( 1+int rate ) = 100*1.03 = 103

As per the put call parity

value of call option + strike price = value of call option + forward

value of call option + strike price = 17.37 + 90 = 107.37

value of call option + forward rate = 4.37+ 103= 107.37

Put call parity holds .