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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