Consider a two-period binomial model (t = {0, 1, 2}), with a risky non-dividend paying stock, BP, which is currently trading for £2.90. In the first period the stock can go up by 30% or down by 10%. The same behaviour is also exhibited in the second period. The risk-free rate is 2% in the first period and 3% in the second period.

(i) Using the risk-neutral pricing method what is the value today of a European call option on BP stock with maturity date t = 2 and exercise price £2? [5 marks]

(ii) Consider a new option in the market which is path-dependent, with underlying stock BP. The new option has the following payoff function at the maturity date t = 2, max (ST Smin, 0) where ST is the price of BP at the maturity date t = 2 and Smin is the minimum stock price BP takes during the life of the option i.e., the minimum stock price BP realises on the path from t = 0 to t = 2.The option is European so can only be exercised at the maturity date. Explain intuitively whether you expect this new option to have a value today higher, equal, or lower than the option in part (i)? What is the value today of this option?