Put call parity formula
PHLX contract is 5.42 cents per pound at a strike price of $1.81. The 180-day interest rate is 4.22% in London and 2.45% in New York. If the current spot rate is 1 pound sterling = $1.6720 and the put=call parity holds, what is the put premium on a December 25 PHLX pound contract with an exercise price of $1.81?
C= Call premium = 0.0542
P= Put option premium = ?
S = Spot rate = $1.6720
t = 180 days = 0.5 years
X = strike price = 1.81
rf = 4.22%
rh = 2.45%
b(t,T) = e-r(T-t)
f1 = e0*[(1+rh)/(1+rf)] = $1.6720*(1.0211/1.0123) = 1.6866
C = (f1-x)/(1+rh) + P
0.0542 = (1.6866 â?" 1.81) / (1+2.45%*0.5) + P =>
0.0542 = -0.16866 / 1.0123 + P = -0.1218887 + P =>
P = 0.0542 â?" (-0.1218887) = 0.1760887