Based on an in-depth analysis of the banking industry, Alva Jones strongly believes that, over the next 6 months, the stock price of ANZ will drop significantly. ANZ is currently trading on the ASX for $30 per share. Alva, therefore, recommends her clients to hedge their portfolios by purchasing American put options on ANZ stock with a strike of $25. Since Alvas firm will write the puts to their clients, she needs to assess the puts premium to charge the clients. To this end, Alva predicts ANZ stock volatility to be 25% p.a. for the next 4 months and to decrease to 20% p.a. afterwards. Also, she expects a dividend of $2.8 per share to be paid in 3 months from today and a dividend of $3.0 to be paid in 7 months from today. The risk free rate is currently 1.3% p.a. with continuous compounding

a) If Alva relies on a three-step binomial tree to price the options, what would the calculated premium be? Round u and d to 6 decimal digits at each step. For all other calculations, round to 4 decimal digits. Please show all your workings.

b) What are the upper-bound and lower-bound to the value of an otherwise equivalent American call option, based on put-call parity? Round to 4 decimal digits. Please show all your workings.

c) Without recalculating the option price, estimate the change in option price if the stock price decrease by $1 instantly. Round to 4 decimal digits. Please show all your workings.