Question

Finance Question - Corporate Finance II - FINC2012 (Option Question)

8. Security LAL has an annual standard deviation of 30%. The current stock price is $16 and annual risk-free rate is 4%. What is the price of a European put option on LAL with an exercise price of $18 expiring in 3 months. Use the binomial pricing method. A. 2.11 B. 2.08 C. 1.82 D. 2.05 A. a=1.01, u=1.1618, d=0.8607, prob up=0.4958, prob down=0.5042, price up = 18.59, price down=13.77. How to get 2.11? And How to get price up & up and a & u & d? Thanks!!!

Answer 1

u: up factor

d: down factor

e: natural exponent

r: risk free rate = 4%

s: annual st dev = 30%

K exercise price = 18

t: time to maturity in years = 3months = 3/12 = 0.25years

u = = e^(0.3*0.5) = 1.162

d = 1/u = 0.861

p: probability of up movement

q: probability of down movement = 1 - p = 0.505

At t = 3 months

If stock price is up = 16 * u = 16 * 1.162 = 18.592

Pay off put = max(K - S, 0) = max (18 - 18.59 , 0) = 0

If stock prie is down = 16 * d = 16 * 0.861 = 13.776

Pay off put = max(K - S, 0) = max (18 - 13.77 , 0) = 4.23

Value of put option = discount factor * (expected pay-off)

expected pay-off is calculated using probabilities

discount factor used to find present value of pay off

Value of put option = e^(-r*t) * (0.495*0 + 0.505*4.23)

= e^(-0.04*.25) * (0.505*4.23) = 2.115