How can I use binomial model to answer to the following questions?
Consider the stock with the current price of $20. It pays no dividends.
1) Maturity: in 4 months
Volatility = 30% per annum
Risk-free rate: 10%
What's the value of European call option?
2) What would be the value of option in 1), if you expect volatility over the next 4 month to be 20%?
3) Given the information in 1) and the expectation declared in 2), what option priced position should we take on?
4) Given that volatility = 30% per annum, what would be the replicating portfolio for the option?
5) What's the price of European put using put-call parity and volatility = 30% per annum?
What's the price of American put using put-call parity and volatility = 30% per annum?
Please see attachment.
1) To be able to solve this problem, and the subsequent ones, we must first set up the problem with the data we are given. We have the following situation:
The binomial tree shown above can be used to calculate the price of the option today. We will use the following terminology:
C = Value of the call option today
X = Exercise price = $20
T = Time period for which the option is active = 4 months = 4/12 years
R = Risk-free interest rate = 10%
S = Price of the stock today = $20
Su = Price of the stock after one year in the up state
Sd = Price of the stock after one year in the down state
Cu = Value of the option after one year in the up state
Cd = Value of the option after one year in the down state
u = Stock return in the up state
d = Stock return in the down state
Pr = Risk-neutral probability of a stock movement in the up state
(1 - Pr) = Risk-neutral probability of a stock movement in the down state
We will use the following formulas using binomial risk-neutral option pricing:
First we calculate the stock returns in both states:
Su = S*1.30 = ...
The expert examines binomial models for current price.