Binomial Options [4]

Consider a case where the stock price S follows a binomial process. Currently, the stock price is So = 100. Each period, the stock price either moves down 10% or up 15%. The (one period) risk free interest rate is 2.5%.

Consider a one-period call option with exercise price X = 100.

1. If you own one stock, how many call options do you need to buy at time 0 for the cashflows in period 1 to be riskless?

2. If you own one call, how many units of the underlying do you need to buy at time 0 for the cashflows in period 1 to be riskless?

Consider now a two period American Call option, with exercise price X = 100.

3. If you own one stock, how many of the two period call options do you need to buy at time 0 for the cashflows in period 1 to be riskless?