John Hull 書中的 IVF 和底層證券的隱含分佈

約翰赫爾的書中有一個關於未來資產Options, Futures and Other Derivatives 9th page 633之間關係implied volatility function (IVF)的陳述。implied distribution

When it is used in practice the IVF model is recalibrated daily to the prices of plain vanilla options. It is a tool to price exotic options consistently with plain vanilla options. As discussed in Chapter 20 plain vanilla options define the risk-neutral probability distribution of the asset price at all future times. It follows that the IVF model gets the risk-neutral probability distribution of the asset price at all future times correct. This means that options providing payoffs at just one time (e.g., all-or-nothing and asset-or-nothing options) are priced correctly by the IVF model. However, the model does not necessarily get the joint distribution of the asset price at two or more times correct. This means that exotic options such as compound options and barrier options may be priced incorrectly.

我無法理解，IVF 保證模型匹配所有罷工的普通期權的市場價格 $ K $ 和所有的成熟 $ T. $ 並且implied distribution未來時間的資產完全由市場價格決定：

$$ p(S^,t^;K,T) = e^{r(T - t^)}\dfrac{\partial^2 V}{\partial K^2}. $$ 在這裡，市場價值： $ V, $ 到期 $ T, $ 罷工 $ K, $ 資產現貨價格： $ S^, $ 目前時間： $ t^*. $

誰能給我一個明確的解釋？

一個例子：即使你知道所有未來時間 T 的隱含分佈，你對兩個未來時間 T1 和 T2 之間的價格變化一無所知。因此，無法定價取決於從 T1 到 T2 的價格變化的異國情調。

引用自：https://quant.stackexchange.com/questions/36487