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put call parity formula

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Please help with the following problem.

On June 25, the call premium on a December 25 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 (-0.1218887) = 0.1760887.

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https://brainmass.com/economics/contracts/put-call-parity-formula-381166

Solution Preview

You have assumed the rate to be 360 rate and then taken the rate for 180 days. The rate is given as 180 days ...

Solution Summary

The put call parity formula is applied in the solution.

$2.19