FNCE 30007 DERIVATIVE SECURITIES The Binomial Model
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FNCE 30007 DERIVATIVE SECURITIES
Tutorial Questions
The Binomial Model (Part I)
QUESTION 1
Assume you roll a pair of fair dice. Let X be the random variable whose value
represents the sum of numbers rolled. Let Y be the random variable whose
value represents the square of the sum of the numbers rolled.
(i) What is the set of possible values of X ?
(ii) What is the probability of rolling a "seven" ?
(iii) Plot the probability function of X
(iv) What is the expected value of X ?
(v) What is the expected value of Y ?
QUESTION 2
Consider a two period binomial model. Let j be the random variable whose
value measures the number of up movements in the stock price at maturity.
(i) What is the set of possible values of j ?
(ii) Plot the probability function of j assuming the probability of the stock
price increasing each period is 50%
(iii) Repeat parts (i) and (ii) for a three period binomial model.
(A three period model can be considered to be a series of three x one period
models).
QUESTION 3
In the derivation of the one period model it was stated that implies that where . Prove this result.
QUESTION 4
Assume:
· current stock price = $20
· stock price changes by +/-10% each 3 months with equal probability
· European put option, strike $21, maturity 3 months
· constant riskfree rate of 12% p.a.
Use a one period model to calculate the current value of the put.
QUESTION 5
Use a two period binomial model to value the option in question 4 assuming the
stock price changes by +/- 5% each 1.5 months with equal probability.
QUESTION 6
Assume the current price of a stock is $100. Each month, the stock price is
expected to increase by 2% (with 40% probability) or fall by 1% (with 60%
probability). Consider a 2 month European call option on the stock with a strike
of $100 and assume the riskfree interest rate is constant at 12% p.a.
(i) Use a two period binomial model to value the option.
(ii) Assume the stock price rises in the first month. What is the value of the
option at that time ?
(iii) Assume the stock price falls in the first month. What is the value of the
option at that time ?
(iv) Use your answers in parts (ii) and (iii) in combination with a one period
binomial model (with month) to value the option.
(v) Is this a realistic model for movements in the underlying stock price?
2022-09-09