Binomial Pricing for Currency Options: Practice Problems and Solutions

The Actuary's Free Study Guide for Exam 3F / Exam MFE - Section 21

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 21 of the Study Guide. See Section 1 here. See Section 2 here. See Section 3 here. See Section 4 here. See Section 5 here. See Section 6 here. See Section 7 here. See Section 8 here. See Section 9 here. See Section 10

here. See Section 11 here. See Section 12 here. See Section 13 here. See Section 14 here. See Section 15 here. See Section 16 here. See Section 17 here. See Section 18 here. See Section 19 here. See Section 20 here.

A binomial model can be constructed to price options on currencies, using the following equations:

F_0,h = x₀e^(r-f)h

ux = xe^{(r-f)h + σ√(h)}

dx = xe^{(r-f)h - σ√(h)}

p* = (e^(r-f)h - d)/(u - d)

Δdxe^fh + Be^rh = C_d

Δuxe^fh + Be^rh = C_u

Definitions of variables:

r = annual continuously-compounded risk-free interest rate for currency 1 (the "domestic" currency or the currency in terms of which the option prices are denominated).

f = annual continuously-compounded risk-free interest rate for currency 2 (the "foreign" currency).

x₀ = spot price of "foreign" currency in terms of "domestic" currency.

u = 1 + rate of capital gain on stock if "foreign" currency price increases.

d = 1 + rate of capital loss on stock if "foreign" currency price decreases.

σ = the annualized standard deviation of the continuously compounded return on the "foreign" currency.

p* = the risk-neutral probability of an increase in the "foreign" currency's price.

h = one time period in the binomial model.

F_0,h = the time-h forward price for the currency.

∆ (delta) = the number of units of the "foreign" currency contained in the replicating portfolio for the option.

B = the number of dollars lent out in the replicating portfolio for the option.

Source: McDonald, R.L., Derivatives Markets (Second Edition), Addison Wesley, 2006, Ch. 10, p. 332.

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