(a) Discuss whether puts and calls in both long and short positions can be considered as insurance when investing in a stock. (6 marks) (b) A non-dividend paying stock is currently priced at $50. John buys a 1-year European call option on this stock with a strike price of $50 for $5 and Joe sells a 1-year European put on this stock with a strike price of $45 for $4. (i) Sketch the profit diagrams of John and Joe at expiration in the same figure and determine the break-even stock price for each of them. (4 marks) (ii) Determine the range of stock price that will give Joe a higher profit than John. (2 marks) (c) Consider an underlying stock with a current spot price of $18. The term structure is flat, with all risk-free interest rate (continuous compounding) being 10%. (i) A European put on the underlying stock expires in three months with a strike price of $18 and has a price of $1. Calculate the price of a European call option that expires in three months and has a strike price of $18. (3 marks) (ii) A European call on the underlying stock expires in six months with a strike price of $20 and has a price $2. In addition, a dividend of $0.30 is expected in the second and fourth months. Calculate the price of a European put option that expires in six months and has a strike price of $20