Suppose the price of a stock today is 1000. ITM put and OTM call options are traded on this stock with (current) moneyness of 1.2 for the puts and 5/6 for the calls. The options mature in 24 months. Both European and American options are traded. The monthly volatility of the rate of return on the stock is 11.55%. The discount risk-free rate is 1.5% per quarter. Use the binomial option pricing approach with a time step of 12 months to value European and American call and put options on the stock. Show your workings.