Your client wants you to design a 3 year investment product that provides the same exposure as owning a Share of JPM stock and 2 European Put options on the stock. The JPM stock trades at $100 and 3 year European Put and Call options are available with a strike rate of $100.

The options are valued using the binominal model with annual time steps. Assume the stock can increase 25% at each node or drop 20%. The risk free rate is 5% and there are no dividends. Assume annual compounding.

a)You decide to dynamically replicate this investment product using a mix of Cash and JPM Stock. Assume you can trade any fractional shares of stock or options. What does that replicating portfolio look like at inception?

b)If the stock increases by 25% by the end of the first year, compute the value of your replicating portfolio?

c)As you rebalance your replicated portfolio for Year 2 you decide to shift to a mix of Cash and Call Options. What would that portfolio look like?