Consider the stock of Caruana Inc, trading at the moment for $100. This asset can either go up by 42.86%, or down by 30% each month. Caruana Inc. is a very volatile stock, analysts claim that its annual volatility is around 120%. While Caruana does not pay dividends, analysts are raving about it: everyone expects the stock to do very well over the next three months. One particular analysts suggests this bullish behavior implies a probability of the stock moving up each move (by 42.86%) on the order of 70% (so the stock goes down only with a 30% probability). Assume that the annual risk-free rate is 5%.

(a) What would you say is a fair price for a call option with a strike of $100 on Caruanas stock with a three-month maturity date?

(b) What would be the replicating strategy for such a call option? Please be specific (see next part of this problem for an example) regarding the amounts of Caruanas stock and/or cash you would like to hold at each point in time as a function of what happens to Caruanas stock.