Put-call parity for European options

Put-call parity for European options with the same strike price and time to expiration is

Call - put = present value of (forward price - strike price)

Equation for put-call parity:
C(K, T) - P(K, T) = PV_0,T(F_0,T - K) = e^-rT(F_0,T - K)

Meaning of variables:

K = strike price of the options

T = time to expiration of the options

C(K, T) = price of a European call with strike price K and time to expiration T.

P(K, T) = price of a European put with strike price K and time to expiration T.

F_0,T = forward price for the underlying asset.

PV_0,T = the present value over the life of the options.

e^-rT*F_0,T = prepaid forward price for the asset.

e^-rT*K= prepaid forward price for the strike.

r = the continuously compounded interest rate.

Source: McDonald, R.L., Derivatives Markets (Second Edition), Addison Wesley, 2006, Ch. 9, p. 282.

MFE question from SOA's Sample question

 Company A is a U.S. international company, and Company B is a Japanese local
company.  Company A is negotiating with Company B to sell its operation in
Tokyo to Company B.  The deal will be settled in Japanese yen.  To avoid a loss at
the time when the deal is closed due to a sudden devaluation of yen relative to
dollar, Company A has decided to buy at-the-money dollar-denominated yen put of
the European type to hedge this risk.
 You are given the following information:
(i) The deal will be closed 3 months from now.
(ii) The sale price of the Tokyo operation has been settled at 120 billion Japanese
yen.
(iii) The continuously compounded risk-free interest rate in the U.S. is 3.5%.
(iv) The continuously compounded risk-free interest rate in Japan is 1.5%.
(v) The current exchange rate is 1 U.S. dollar = 120 Japanese yen.
(vi) The natural logarithm of the yen per dollar exchange rate is an arithmetic
Brownian motion with daily volatility 0.261712%.
(vii)  1 year = 365 days; 3 months = ¼ year.
 Calculate Company A’s option cost.

My Exam

 3 days to my Actuarial exam(MFE), I have studied hundreds of hours for this one.
I really deserve to pass.

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