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LOS d: Calculate prices of interest rate options and options on assets using one- and two-period binomial models. LOS e: Explain how the binomial model value converges as time periods are added. 这个LOS可理解成，当binomial model的区间划分的越来越小的时候，binomial model得到的期权价格趋向于同一个价格，换句话说，划分500个区间与划分1000个区间得到的期权价格很接近。见下面这个图有个直观的了解 LOS f: Explain the assumptions underlying the Black-Scholes-Merton model. BSM模型有六个假设，分别是， 基础资产的价格遵循自然对数正态分布，注意，是价格遵循自然对数正态分别，收益遵循的是正态分布。 无风险利率已知且不变。 基础资产的波动率已知且不变 无税收和交易成本 在期权寿命期间，基础资产不会产生现金流 BSM模型只适用与定价European options The following key assumptions underlie the Black-Scholes-Merton Model: ?1.?The underlying price follows a lognormal probability distribution as it advances through time. Log returns are also referred to as continuously compounded returns. If this return follows a normal distribution, it is log normally distributed. ?2.?The risk-free rate is known and invariable, or constant 。the model does not allow interest rates to be random. ?3.?The volatility of the underlying asset is known and invariable 。volatility is both known, and assumed not to changeover time. This is the most critical assumption of the model. Of course, volatility in reality is not constant. ?4.?There are no taxes or transaction costs. ?5.There are no cash flows on the underlying asset. ?6.The model is generally only used to value European options. A binomial model with a great number of time periods is better to value American options. LOS h: Explain how an option price, as represented by the Black-Scholes-Merton model, is affected by each of the input values (the option Greeks). 这个LOS讲了，如何利用BSM公式，来知道期权价格与输入量之间的关系。对于call来说，可以用这个公式帮助记忆，，变形为，从这个公式可知，价格与现价成正相关，与X成负相关，与R成正相关，与时间t成正相关。另外，波动率增加，会增加卖权与买权的价值，这个要另外记忆了。 *There is an exception to this, the general rule that the theta of a European put is positive. An increase in time to expiration can decrease the value of a European put, when the price decrease from discounting the exercise price at a higher rate out