a. Consider a non-dividend paying stock with current price $50. In one period the price will either rise or fall by 20%. The one-period risk free rate is 10%. i. Derive the price of an at-the-money European call option with one period to maturity. Explain the steps in your pricing analysis as you perform them. (20 marks) ii. How would you expect the call price to change if the strike price was to fall? Give some intuition and some calculations to justify your response. (20 marks) iii. How would you expect the call price to change if the magnitude of the rises and falls in the underlying price were to decrease (e.g. instead of rising or falling 20%, how would the option price change if the underlying was to rise or fall 10%)? Give some intuition and some numerical justification for your views. (20 marks) iv. How would your answers to (ii) and (iii) change if one was considering a put option rather than a call option? Give some intuition for your responses.