Parity of Options on Currencies: Practice Problems and Solutions

The Actuary's Free Study Guide for Exam 3F / Exam MFE - Section 4

This section of sample problems and solutions is a part of The Actuary's Free Study Guide for Exam 3F / Exam MFE, authored by Mr. Stolyarov.

This is Section 4 of the Study Guide. See Section 1 here. See Section 2 here. See Section 3 here.

The formula for parity of options on currencies is

C(K, T) - P(K, T) = x₀e^-uT - Ke^-rT

Explanation 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.

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

r = the continuously compounded interest rate, denominated in dollars or the currency of one's choice

u = the continuously compounded interest rate, denominated in euros or some other currency of one's choice

x₀ = the current exchange rate, denominated in dollars/euro or in [currency 1]/[currency 2].

F_0,T = forward price for the underlying asset.

Source: McDonald, R.L., Derivatives Markets (Second Edition), Addison Wesley, 2006, Ch. 9, p. 286.

Original Practice Problems and Solutions from the Actuary's Free Study Guide:

Problem POC1. One euro currently trades for 1.4831 U.S. dollars. The annual dollar-denominated interest rate is 0.01% (due to the Federal Reserve's incessant artificial credit expansions and manipulations of the money supply), while the annual euro-denominated interest rate is 3%. Both interest rates are on a continuously compounded basis. A euro call option with strike price $1.34 has price $0.34. What is the price a euro put option with the same strike price? Both options expire in one year.

Solution POC1. We use the equation C(K, T) - P(K, T) = x₀e^-uT - Ke^-rT

and rearrange it as follows: P(K, T) = C(K, T) - x₀e^-uT + Ke^-rT

Here, C(K, T) = 0.34, K = 1.34, r = 0.0001, u = 0.03, x₀ = 1.4831, T = 1.

Thus, P(K, T) = 0.34 - 1.4831*e^-0.03 + 1.34e^-0.0001 = P(K, T) = 0.2405982359