Problem $1(50$ points$)$

Suppose the current value of a $($non$-$dividend$-$paying$)$ stock is $$10,000,$ and the annual continuously

compounded riskless rate of interest is $4\%.$ Based on the example provided on pp$.9-14$ from the

"Derivatives Theory, Part $1"$ lecture note, solve parts A and B below.

A$.(25$ points$)$ What is the "arbitrage$-$free" price for a forward contract on this stock which matures

$1$ year from today?

B$.(25$ points$)$ Suppose the forward price is $$10,400.$ Describe a profitable zero risk, zero net

investment trading strategy involving the forward contract and its replicating portfolio. If you

implement such a strategy, how much profit will you earn?

Problem $2(50$ points$)$

The price of a share of Zoom stock is currently $$250.$ It is known that at the end of $1$ year, the

Zoom share price will be either $$312\mathrm{.}50$ or $$200.$ The riskless interest rate is $2\%$ per year.

A$.(10$ points$)$ Calculate the price of a $1-$year European call option on Zoom stock with an exercise

price of $$250$ by applying the replicating portfolio approach.

B$.(10$ points$)$ Calculate the price of a $1-$year European call option on Zoom stock with an exercise

price of $$250$ by applying the risk neutral valuation approach.

C$.(10$ points$)$ Calculate the price of a $1-$year European put option on Zoom stock with an exercise

price of $$250.$

D$.(20$ points$)$ Next, add another $1-$year timestep; i$.$e$.,$ it is known that at the end of $2$ years,

the Zoom share price will be $$390\mathrm{.}63,$$$250,$ or $$160.$ Calculate the price of a $2-$year European

call option on Zoom stock with an exercise price of $$250.$ Also calculate the price of a $2-$year

European put option on Zoom stock with an exercise price of $$250.$