Question

You are required to price a one-year, yen-denominated currency option on the USD. The exchange rate over the next year is modeled using a forward binomial tree with the number of periods equal to 4. Assume that the volatility of the exchange rate equals 0.1. The continuously compounded risk-free interest rate for the yen equals 0.05, while the continuously compounded risk-free interest rate for the USD equals 0.02. What is the value of the so-called up factor u in the resulting forward binomial tree

Answer 1

The value of the so-called up factor is

`u = 1.1618`

Explanation:

From the question we are told that

The number of period is n = 4

The volatility of the exchange rate is
`v = 0.1`

The continuously compounded risk-free interest rate for the yen is r = 0.05

The continuously compounded risk-free interest rate for the USD is R = 0.02

Generally the so-called up factor u is mathematically represented as

`u = e^(v + r)`

=>
`u =  e^(0.1 + 0.05)`

=>
`u =  e^(0.15)`

=>
`u = 1.1618`