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RT，比如说，我们如果知道标的股票的波动率，那么基于该股票的看涨期权的波动率几何？这个期权的波动率能否在复合期权或者高阶期权中得以体现？我在写一篇关于保险定价的文章中就涉及到与之类似的问题。

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关键词：衍生产品 生产品 波动率 复合期权 文章 产品 保险

Dont understand what do you mean by "得以体现" and "波动率几何"? Could you explain it more in detail?

Δ x S x σ (assuming BS model)?

In BS model,

dS = μS dt + σS dX

From Ito's

dV = A dt + Δ dS where A are differentiation terms grouped under dt

dV = A dt + Δ (μS dt + σS dX)

Thus, the coefficient of dX is just Δ x S x σ?

It seems correct intuitively too. The stdev of dS follows σS. Given that dV is more or less ΔdS, the stdev would not be far from ΔσS?

Subject to further discussion.

oddsmaker 发表于 2012-7-9 13:05
Δ x S x σ (assuming BS model)?

In BS model,

what is your point???

Sorry I don't get it.

stoneyl 发表于 2012-7-9 09:12
Dont understand what do you mean by "得以体现" and "波动率几何"? Could you explain it more in detail ...

两者的意思是：复合期权中标的期权的波动率的表达式及其衡量问题

chengzhifu2013 发表于 2012-7-9 18:16
两者的意思是：复合期权中标的期权的波动率的表达式及其衡量问题

I still dont quite understand.

However, on pricing of the exotics options, one thing to make clear first is that how you should hedge the risk (For instance vega here).

Normally vega is hedged with exchange traded options and variance swap(let's forget this for now). this is due to the fact that exchange traded options are liquid, price observable and available with different maturity/strikes so that you can construct a surface to model the vol dynamic to price smile sensitive deals, such as barrier options for instance. That's why we have to fit our implied/local/stochastic or whatever model to the liquid vanilla options then use it to price more complex product whose price might not be avaible from the market.

Does this anwser your question?

stoneyl 发表于 2012-7-9 19:21
I still dont quite understand.

However, on pricing of the exotics options, one thing to make c ...

非常感谢，虽然没完全明白过来你说的什么

chengzhifu2013 发表于 2012-7-10 09:59
非常感谢，虽然没完全明白过来你说的什么

Which part exactly you dont understand?

A very simple example if you want to price a barrier option on s&p500 index. First thing you should to is to determine which model you should use to model the vol dynamics. Since barrier option is smile sensitive, stochastic vol/local stochastic volatility model are normally used. Take the Heston stochastic vol model as example, you first have to fit the model to exchange traded s&p500 options price which is called model calibration. Then you can use the calibrated model to price the OTC barrier option by certain numerical methods.

stoneyl 发表于 2012-7-10 10:03
Which part exactly you dont understand?

主要还是语言障碍，谢谢你了