Deck 18: Binomial Trees in Practice

Question 1

A stock price is initially $30 and a dividend of $2 is expected at the end of 1.5 months. The volatility is 30% per year. In a two step tree with each step equal to one month, what is the stock price on the middle node at the end of the tree? Give two decimal places.) _ _ _ _ _ _

Answer 1

$28.00

Question 2

An exchange rate has a volatility of 12% per year. The domestic and foreign risk-free interest rates are both 4% per annum continuously compounded). The time step on a binomial tree is three months.
i) What are the $p$ , $u$ and $d$ parameters for a Cox-Ross-Rubinstein tree? Give four decimal places.)
u =_ _ _ _ _ _ d = _ _ _ _ _ _ p = _ _ _ _ _ _

Answer 2

i) $u = 1.0618$
ii) $d = 0.9418$
iii) p=0.4850

Question 3

A stock price is initially $30 and u in the Cox-Ross-Rubinstein tree is 1.1. What are the stock prices at the end of two time steps? Give two decimal places.)
_ _ _ _ _ _ and _ _ _ _ _ _ and _ _ _ _ _ _

Answer 3

36.30 and 30.00 and 24.79

Question 4

A binomial tree prices an American option at $3.12 and the corresponding European option at $3.04. The Black-Scholes price of the European option is $2.98. What is the control variate price of the American option?
_ _ _ _ _ _

Question 5

Which of the following cannot be calculated directly from a binomial tree? choose two)

A) vega
B) delta
C) rho
D) gamma
E) theta