p****w
发帖数: 21 | 1 Hi,
最近在考虑一个问题volatility option的hedging，如果我假设volatility是可以交易
的资产，服从以下mean-reverting square root process：
dV=a(b-V)dt+sigma sqrt(V)dW
W 是standard Brownian motion.
欧式期权的定价从PDE里可以求出来，有closed-form solution.
我的问题是，如果我用类似于Black-Scholes的方式建一个 hedging portfolio: 买入
voltatility option，卖出delta份volatility，持有B_t份zero-coupon bond， 这样
的portfolio是不是delta-neutral, 是不是self financing?
这里的delta就是定价公式对underlying求一阶偏导。简单的说，如果我们改变
underlying process的假设,我们用类似Black-Scholes建的delta-hedging 是不是
delta-neutral 和 self financi |
p******i
发帖数: 1358 | 2 if the assumption that volatility is a tradable asset is valid, then yeah,
you are right.
anyone verify this assumption? |
p****w
发帖数: 21 | 3 Thanks!
Volatility futures are tradable. I phrased volatility vaguely in my previous
post to make the question simpler.
The CBOE cash volatility index (VIX) is a nonlinear function of SPX options
prices and SPX index. It is not tradable.Then my question follows: if the
underlying is a function of tradable asset prices, is that same hedging
strategy delta neutral and self financing?
【在 p******i 的大作中提到】
: if the assumption that volatility is a tradable asset is valid, then yeah,
: you are right.
: anyone verify this assumption?
|
t********t
发帖数: 1264 | 4 volatility is not tradable, variance is.
refer to the variance swap model, constructed by Madan, Carr, etc.
The VIX index is actually calculated in the same way as the variance swap,
refer to CBOE's documents |
p*****w
发帖数: 82 | 5 你的hedging采用的是replication 策略。而且你用bond，说明你假设这个option的增
长是和bond一样的。但是vol是mean reversion， 说明它的增长不是fisk free rate。
那你怎么能用bond来replicate呢？ |
p******i
发帖数: 1358 | 6 请自行回去复习risk neutral valuation
【在 p*****w 的大作中提到】
: 你的hedging采用的是replication 策略。而且你用bond，说明你假设这个option的增
: 长是和bond一样的。但是vol是mean reversion， 说明它的增长不是fisk free rate。
: 那你怎么能用bond来replicate呢？
|
p*****w
发帖数: 82 | 7 stock在risk neutral probability measure下的growth rate是risk free rate。
volatility 是mean reverting process.， 他的risk neutral probabilty measure底
下你的growth rate 你怎么value 啊？ |
p******i
发帖数: 1358 | 8 I see your point
well, If we take volatility futures as underlying,then I don't think
modeling its real world process is necessary
【在 p*****w 的大作中提到】
: stock在risk neutral probability measure下的growth rate是risk free rate。
: volatility 是mean reverting process.， 他的risk neutral probabilty measure底
: 下你的growth rate 你怎么value 啊？
|
