1. Accelerated Return Notes provide payoffs at maturity that depend on the value of an under- lying stock and the notional N . Assume the stock pays no dividends. If the ending value of the underlying is below or at the starting value the note will pay N ending value /starting value. If the ending value is greater than the starting value then the payoff is given by min[N 1.2, N + N 2 (ending value - starting value) / starting value] . (a) Draw the payoff diagram for the Accelerated Return Note and explain the payoff profile in your own words. Use a notional of N = 100 and an initial value of the underlying of $50. The maturity of the note is in one year. [ 8 marks ] (b) If the only options traded on the underlying are European calls, how would you replicate the payoff? [ 6 marks ] (c) How would you replicate the note if only European puts were available? [ 4 marks ] (d) Now assume that the underlying stock has a volatility of 35% and the (continuously compounded) risk-free rate is given by r = 1%. What is the price of the note in the Black-Scholes-Merton model? [ 4 marks ] (e) Note: If you need values for any other parameters to answer the questions below, make reasonable assumptions and justify these. Simulate the payoff of the Accelerated Return Note in the Black-Scholes-Merton model. Use at least 10,000 simulations of the stock price. What is the average return of investing in the note, as well as the standard deviation of the returns.

[ 15 marks ]

(f) Using your simulation output, is it more risky to invest into the note than to invest into the stock itself? Justify your answer using your simulation output. [ 4 marks ] (g) Using your simulation output, what is the probability that the return of the note is 20%. [ 4 marks ]