Hi David, 1. could you explain why the difference between an American call and an American put (C–P) is bounded by the inequality on p86: S - K <= C - P <= S - K*exp(-rT) ? Also does this inequality imply C>=P for American option? 2. is it true that An American option on a dividend paying stock may be worth less than its European analogue? 3, on p87, "An American option should never be exercised early in the absence of dividends. In the case of a dividend-paying stock, it would only be optimal to exercise immediately before the stock goes exdividend. Specifically, early exercise would remain sub-optimal if the following inequality applied:" Does this paragraph only refer to call, but not put? 4. Could you also pls explain the dividend effects on lower/upper bounds of European and American put/call options? Many thanks.