You are required to price aputoption on the stock ofXYZwithan exercise price of $50and six months to expiration.

The current stock priceofXYZis $52, the risk free rate is10% p.a. (c.c.)and the volatility of the stock priceofXYZis 30% p.a..XYZwill pay adividend of $1 in exactlyfourmonths' time.

This put option is to be priced using a two-period binomial option pricing model, with three months in each period.

(a)Draw the two-period tree diagram for theadjustedstock price (that recognizes the impact of the dividend)ofXYZ. Show the expiration date payoffs from theputoption.

(b)Compare an American put option with an otherwise identical European put option on the stockofXYZ.What is the value of the righttoexercisethe put option before expiry?