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 (-5[1])the price of these things (-5[1])which under the CRR method sets u (15[1])as “e raised to sigma square root delta t” and d as the inverse of u. A model originally for these things makes four assumptions about the market, including no arbitrage and no transaction (15[1])costs. (-5[1])The (*) American type of these things (10[1])can be exercised (10[1])at any time, (10[1])in contrast to the European type of these things, (10[1])whose price can be calculated using (10[1])the Black-Scholes (-5[1])formula. For 10 points, name these derivatives whose main varieties are called puts and calls (10[2]-5[1])and give (10[1])the holder (-5[1])the sell and purchase (10[1])rights for an underlying (-5[1])asset. ■END■ (10[2]0[6])