(A)
To Compute:
What will be the payoff to the put,
Introduction:
The payoff to the put,

Explanation of Solution
Valuation of one year European put option using the two-state approach is described as
follows:
The put price for increase factor of 1.1,
decrease factor of 0.95,
$110.
Calculate the probable value of put, in case stock price increases (
(B)
To Compute:
What will be the payoff,
Introduction:
The payoff,

Explanation of Solution
The hedge ratio at this point can be calculated by using the following formula:
Substitute the value to calculate hedge ratio as follows:
Hence, the hedge ratio is
The final stock price of the portfolio that will be worth $121 at expiry regardless of the final stock price is as follows:
The portfolio must have a current market value equal to the present value of 4121 defined by the following equation:
Calculate the value of put in case stock price decreases
The put price for increase factor of 1.1,
decrease factor of 0.95,
$110
Calculation of the hedge ratio:
The hedge ratio at this point can be calculated by using the following formula:
Therefore, the hedge ratio is -1.0
The final stock price of the portfolio that will be worth $110 at expiry is as follows:
The portfolio must have a current market value equal to the present value of $110,which is defined by the following equation:
Hence, the value of put in case stock price decrease is $9.762.
Calculate P using the values of
The put can increase to a value of
Initial value.
The put can fall to a value of
Initial value.
Calculate hedge ratio at this point as follows:
Thus, the payoff,
(C)
To Compute:
Value the put option using the risk-neutral shortcut described in the box. Confirm that your answer matches the value you get using the two-state approach.
Introduction:

Explanation of Solution
The portfolio will be worth $60.53 at expiry irrespective of the final stock price as follows:
The portfolio must have a market value equal to the present value of $60.53 which is defined by the following equation:
Hence, the value of put option binomial model option pricing is $4.208
Valuation of put option using risk neutral shortcut is described as follows:
Formula for risk neutral probability is as follows:
Here,
u is factor by which stock increases
d is factor by which stock increases
Calculate the risk neutral probability that the stock price will increase as follows:
Calculate the expected cash flows at expiration and discount it by the risk free rate to find
and
Calculate
Calculate
Calculate the expected cash flow in 6 months and discount the E(CF) by the 6 month risk free
Rate as follows:
Hence, the value of put option using risk neutral shortcut is $4.208
Therefore, the value of put option through two state approach and risk neutral shortcut is same, that is, $4.208.
Therefore, the value of put option through two state approach and risk neutral shortcut is same, that is, $4.208.
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Chapter 16 Solutions
ESSEN OF INVESTMENTS CONNECT AC
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