A binomial tree with three-month time steps is used to value a currency option.The domestic and foreign risk-free rates are 4% and 6% respectively.The volatility of the exchange rate is 12%.What is the probability of an up movement?
A) 0.4435
B) 0.5267
C) 0.5565
D) 0.5771

Question

Quizplus · Accepted Answer

The probability of an up movement is given by the formula:p = (e^(r_d - r_f) * t + sqrt((e^(r_d - r_f) * t)^2 + (sigma^2 * t))) / (2 * e^(sigma^2 * t))where:r_d is the domestic risk-free rater_f is the foreign risk-free ratet is the time stepsigma is the volatility of the exchange ratePlugging in the given values, we get:p = (e^(0.04 - 0.06) * 0.25 + sqrt((e^(0.04 - 0.06) * 0.25)^2 + (0.12^2 * 0.25))) / (2 * e^(0.12^2 * 0.25))= 0.5565Therefore, the correct answer is C.

A Binomial Tree with Three-Month Time Steps Is Used to Value