QUESTION

The stock price of ABC changes only once a month: either it goes up by $20\%$ or it falls by $16\mathrm{.}7\%.$ Its price is now $$40.$ The interest rate is $12\mathrm{.}7\%$ per year, or about $1\%$ per month. Required:

a$)$ Suppose a one$-$month call option on this stock has an exercist price of $40.$ What is the option delta?

b$)$ Show how the payoffs of this call option can be replicated by buying ABCs stock and borrowing.

c$)$ Using the risk$-$neutral method, calculate the value of a one$-$month call option with an exercise price of $40.$

d$)$ Construct a two$-$month binomial tree. What is the value of a two$-$month call option with an exercise price of $40?$

e$)$ Using put$-$call parity, what is the price for a one$-$month put with the same exercise price? And a two$-$month pur with the same exercise price?