Binomial Model
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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
Strike price:$20
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?
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Solution Summary
The expert examines binomial models for current price.
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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:
(1)
(2)
First we calculate the stock returns in both states:
Su = S*1.30 = ...
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