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 Nx ending value starting value If the ending value is greater than the starting value then the payoff is given by min Nx 1.2, N + Nx 2x 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] (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] 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 Nx ending value starting value If the ending value is greater than the starting value then the payoff is given by min Nx 1.2, N + Nx 2x 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] (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]
