5.6计算标的资产价值
使用欧式看涨期权评估模型，将相关数据输入，得出期权价值为27217.1百万美元。高于收益法2倍以上，主要原因在于收益法排斥波动，而期权法将其波动视为一种资产，从而更加合理的评估了区块价值。
例：若将成本设置为70美元/桶，此时使用收益法将会得出净现值为-17533.77百万美元，即该地块并不存在投资价值。其主要原因在于现值的石油价值等因素均处于不断的变化之中，而收益法忽略了区块产权所有者所拥有的推迟开发、扩大产量、缩减产量等基本权利。如使用期权评价法，其价值达到20643。
6百万美元。可见期权法将会比收益法高估一项资产的价值。
6两资产彩虹估价模型
在具有伴生产品的矿产定价中，可以采用两资产彩虹期权模型进行估价。其中，彩虹期权的定价模型采用的是两资产最优看涨期权。意味着产权所有者可以在两个资产中达到最大价值那个进行开发。其计算方法如同单资产模型。其A资产、B资产的价格均为其折现现金流收入；其敲定价格为开发总成本。需要注意的是相关性的计算，其值的大小、正负将会大幅影响到期权的价值。相关性的计算以价格变动的相关性为主，以两产品的互补或替代率，需求的交叉变动率等因素加以充分考虑。
总结：在进行自然资源的评估定价中，使用期权方法进行估价将会更科学和合理，也更能够反映出标的资产的处置灵活性。在评价单一自然资源时，要充分考虑到其价格变动、储量变动、汇率变动等因素；在评价具有伴生资源的区块中，需要尤为注意两资产的价值相关性系数的计算。
英文原文 1.彩虹期权定义
Rainbow option is a derivative exposed to two or more sources of uncertainty,[1] as opposed to a simple option that is exposed to one source of uncertainty, such as the price of underlying asset. Rainbow options are usually calls or puts on the best or worst of n underlying assets, or options which pay the best or worst of n assets. The number of assets underlying the
option is called the number of colours of the rainbow.[2] The options are often considered a correlation trade since the value of the option is sensitive to the correlation between the various basket components.
Rainbow options are used, for example, to value natural resources deposits. Such assets are exposed to two uncertainties—price and quantity.
Some simple options can be transformed into more complex instruments if the underlying risk model that the option reflected does not match a future reality. In particular, derivatives in the currency and mortgage markets have been subject to liquidity risk that was not reflected in the pricing of the option when sold.
2.彩虹期权类比
Here's a sports-betting analogy that demonstrates a rainbow option: suppose you're at a baseball tournament with three fields backing one another. One game is halfway through, a second is just starting and a third starts in an hour. A type of bet that's analogous to a rainbow option is one that earns you a profit if you pick all three winners, but gets you nothing if any one team you pick is a loser.
3.彩虹期权的类型
A．Best of n Assets Plus Cash（资产与现金择优期权）
- This type of rainbow effectively has n + 1 payoff possibilities. If we consider a 2 asset \Asset 2, or the predetermined cash amount. There is no strike price and the payoff is given as:
Stulz (1982) presented the first significant paper on rainbow options, and from there, we can find a set of analytical formulae for best of 2 assets plus cash.
Where:
Where N(x) is the cumulative normal distribution and B(a, b, rho) is the bivariate cumulative normal distribution.
is the correlation between the 2
assets, and other variables are defined under the standard notation. The effects of varying the cash amount are shown in the below graph:
b) Better of n Assets
This type of rainbow is similar to the best of n assets plus cash but with the exception that there is no possible cash payoff, and X is set to 0. With this in mind, a better of 2 assets rainbow is essentially a two-asset call option, with a payoff being: