Q 1) Suppose that there are three options which differ only in their strike prices such that: K1 2C2(S.T K2) b) Assume an investor writes one call (01) and one call (C3) and buys two call options (C2). 1. il. Draw a diagram of the profit profile for this strategy Using the proof in part a), show that it will always yield a net inflow at the time the position is taken. If this strategy yielded a net outflow when the position was taken, what could an investor do? When might an investor use the strategy described in part 1)? iv 2) A stock price is currently 50. Its annual volatility is 20% The risk free interest rate is 10%. Consider a European call option written on the stock with a maturity of 1 year and a strike price of 49 a) Construct a 2-step Binomial tree using the methodology of Cox, Ross, and Rubinstein and value the European call b) Explicitly construct the replicating portfolio for the European call c) What is the value of a European put with the same strike price and maturity? 3) Suppose that the price of AB company stock is 40 per share on January 20. Three call options are traded on the stock with an exercise price of 50 and maturity dates of April 20, July 20 and October 20. If the standard deviation of the stock is 33% pa and the risk free rate is 10% p.o., value these options using the Black-Scholes model A Q 1) Suppose that there are three options which differ only in their strike prices such that: K1 2C2(S.T K2) b) Assume an investor writes one call (01) and one call (C3) and buys two call options (C2). 1. il. Draw a diagram of the profit profile for this strategy Using the proof in part a), show that it will always yield a net inflow at the time the position is taken. If this strategy yielded a net outflow when the position was taken, what could an investor do? When might an investor use the strategy described in part 1)? iv 2) A stock price is currently 50. Its annual volatility is 20% The risk free interest rate is 10%. Consider a European call option written on the stock with a maturity of 1 year and a strike price of 49 a) Construct a 2-step Binomial tree using the methodology of Cox, Ross, and Rubinstein and value the European call b) Explicitly construct the replicating portfolio for the European call c) What is the value of a European put with the same strike price and maturity? 3) Suppose that the price of AB company stock is 40 per share on January 20. Three call options are traded on the stock with an exercise price of 50 and maturity dates of April 20, July 20 and October 20. If the standard deviation of the stock is 33% pa and the risk free rate is 10% p.o., value these options using the Black-Scholes model A