A 1977 paper by Phelim Boyle pioneered Monte Carlo methods for valuing these things, which are optimal to use when there are multiple sources of uncertainty. William Sharpe proposed a binomial tree model for the price of these things which under the CRR method sets u (15[1])as (-5[1])“e raised to sigma square root delta t” and d as the inverse of u. A model originally for these things makes (-5[1])four assumptions about the market, including no arbitrage (-5[1])and no transaction (15[1])costs. The (*) American type of these things (10[1])can be exercised at any time, (10[1])in contrast (10[1])to the European type of these things, (10[1])whose price can be calculated using the (10[1])Black-Scholes (-5[1])formula. (10[1])For 10 points, name these derivatives whose main varieties are (10[1])called puts and calls (10[2]-5[1])and give (10[1])the holder (-5[1])the sell and purchase (10[1])rights (-5[1])for an underlying (-5[1])asset. ■END■ (10[3]0[7])