uestion B.1 a. An option trader has built a portfolio of three different call options on the same underlying with the same maturity. The trader has bought one call with a strike of 20 and also bought a call with a strike of 50. The trader has sold two calls with a strike of 35 . The current underlying price is 35. Tabulate, plot and describe the total payoffs from this portfolio. Given your payoff profile, what must be true about the cost of building this portfolio? (10 marks) b. You wish to price three month options on an underlying that pays no dividends. The continuously compounded interest rate is 5%. The current underlying price is $150. You believe that over the course of quarter the underlying will either fall to $120 or rise to $165. Use riskneutral valuation to compute the price of a three month, at-the-money call. Use put-call parity to derive the price of a put with the same strike. (10 marks) c. Calculate the delta of the call option and, from this, construct the replicating portfolio for the call, showing that the portfolio does indeed replicate the payoff of the option. (10 marks) d. Briefly explain why you would pay more for a European call option on a (non-dividend paying) stock which has an annual return volatility of 50% than for a European call on a (non-dividend paying) stock that has annual volatility of 10% (assuming that all other variables that affect option prices are the same for the two options.)