PLEASE PROVIDE THE ANSWERS WITH SOLUTION AND EXPLANATION. THANK YOU!

A.) Over the coming year, Stock X price will decrease to $80 from its current level of $100 or it will rise to $125. The one-year interest rate is 2.5%. Consider a one-year put option on stock X with a strike price of $118.

(a) To replicate this put, find the number of shares to be purchased or sold and the units of ZCB with face value of $1 to be purchased or sold.

Number of shares _____?

Units of ZCB _____?

(b) Use the replicating-portfolio method to value this put.

Value of this put ____?

(c) In a risk-neutral world, what is the probability that stock X will rise in price?

Probability that stock will rise in price _____?

(d) Use the risk-neutral method to check your valuation of the put. (Show calculation and formula)

B.) Stock X price is $100 and could go up by 17% or down by 15% in each six-month period. A one-year put option on stock X has an exercise price of $98. The interest rate is 2.5% a year. (PLEASE Show formula and calculation)

(a) Find a equivalent standard deviation of returns of stock X.

(b) What is the value of the put?

C.) You own a one-year option to buy one acre of San Diego real estate. The exercise price is $2 million, and the current, appraised market value of the land is $1.7 million. The land is currently used as a parking lot, generating just enough money to cover real estate taxes. The annual standard deviation is 15% and the interest rate 12%. How much is your option worth? Use the Black-Scholes-Merton formula.

Formula for Call option:

c=So N(d1 )-PV (K) N(d2 )

d1=(ln(S/PV(K))+(^2/2)T)/(T) and d2=d1-T

D. Use the Black-Scholes formula to find the value of the following PUT option.

(a) Time to expiration 1 year

(b) Standard deviation 20% per year

(c) Exercise price $100

(d) Stock price $100

(e) Interest rate 3%

Formula for PUT option:

p = PV(K) N(-d2 )-SN(-d1 )