t*******y
发帖数: 18 | 1 上次发文求建议，收到很多真诚的帮助。想了想可以写篇我对 VIX index 的学习心得
，算是表达感谢吧。
说明一下，我毕竟是个菜鸟新人，这篇也只是综合公开资料再加上我自己对 VIX 的理
解，也就希望对准备学习这个领域的人有所帮助，熟悉volatility trading的内行看了
肯定觉得简单，有不对的地方请多多指正。
废话完毕。
1. Rationale behind VIX
想了解 VIX index 计算方法的依据，必读的文章是
“More than you wanted to know about variance swap".
http://elis.sigmath.es.osaka-u.ac.jp/research/gs-volatility_swa
具体的证明比较繁琐，我总结就是:
In a nut shell, if we can ignore friction, an out-of-money option portfolio
with certain weights could replicate a variance swap, whose payoff = Et [Var
] – Var.
Note: Var is the realized variance between t and t+1, and Et [Var] is its
expectation at time t. t+1 has to be the expiration of your option portfolio.
VIX index就是这个 replication portfolio（of variance swap）的价格，换句话说
，VIX的值应该恒等于一个正好30天后到期的 variance swap 的价格。（当然这个
variance swap 必须是用 S&P 500 return 计算的，因为VIX是用的SPX option 计算的
，underlying必须一致才能挂钩。）
As always，模型和实际不一定是吻合的。需要指出的是，如果我对这篇文章理解正确
的话，这个replication portfolio 非常难构建，需要购买所有out-of-money 的期权
，然后对每个期权的仓位进行动态调整，at every fucking instant！虽然Black-
Schole 公式依据的option replication portfolio也要求动态调整，但那毕竟只在现
金和股票直接转换，可行性高得多，因此用来给option定价，option的价格才不会偏离
replication value 太多。我个人认为VIX as a replication of variance swap is
only possible on paper，我不建议用VIX来判断 variance swap 价格是否偏离合理值
。我没有 variance swap 的价格数据，
如果哪位能证实和VIX脱节，我不会太吃惊。
除此之外，VIX不能直接买卖，还更何况现实中根本不存在一个6月10日12点7分到期（
正好30天）的S&P500 variance swap 来和 今天12点7分的VIX值做比较。 So, sorry,
no arbitrage opportunity here， 哈哈。
2.VIX as a measure of option expensiveness
如果你和我一样对VIX as replication value of variance swap 持怀疑态度，可以用
另外一种理解方法：VIX as a measure of option expensiveness, and in turn as a
measure of implied volatility。撇开模型的证明过程，只看VIX的构造，不就是
weighted average price of options with different strike but all expire in 30
days吗。比如此时此刻的VIX值，应该是反映6月10日12点30分到期（for now, ignore
the fact that these options don’t actually exist）的所有期权的加权平均价格
，5分钟后的VIX值应该是反映6月10日12点35分到期的所有期权的加权平均价格。
不同strike的期权vegga值不同，但用权重统一了，expiration又永远是30天，delta也
是0（这里有个caveat, 一会谈到）那么影响这个weighted option portfolio的价格就
只有implied volatility 了。如果市场预期未来动荡，options 的价格自然会上升，
VIX也就随之升高，反之亦然。我觉得把VIX想成index of option expensiveness (or
implied volatility), 比variance swap price更简单也更准确一些，因为VIX本来就
是 weighted-average price of a basket of options嘛，期权涨价VIX 就涨。
3.Linear interpolation of VIX
细心的人肯定看出上一章节的问题了，SPX option只在特定的日期expire。除了每月的
某一天，绝大部分时间都不会有正好在30天后到期的。现在CBOE的解决办法是linear
interpolation。比如现在正好有10天到期和41天到期的两组option，那么就先计算10
day VIX 和 41 day VIX，然后做线性平均。这个看起来很不靠谱的解决办法其实问题
不大。首先绝大多数时间near term 和 next near term 的VIX 其实差别不大，用非线
性的平均和线性平均几乎没有区别。
最重要的是VIX derivative settle 的那一刻，永远是正好有一组option 在30天后到
期，这一刻的VIX计算（也就是SOQ）也就只用那一组期权，不需要涉及平均问题。换句
话说即使线性平均给VIX计算造成bias，这个bias也不会在任何VIX derivative 交割的
那一刻出现，因此也就不会影响real money transfer。希望我讲清楚了。
4. VIX future and variance swap
接下来重点讲VIX future。先讲一下VIX future 和 variance swap 的区别。可能是我
读得不够多，但我看到网上的很多讨论都认为两者都是volatility trading的工具，只
要注意variance和volatility 之间转换的convexity问题就行了，只是细节不同。其实
两者有很大区别。
在到期交割的时候，variance swap 的settlement value是由过去30天的realized
volatility 决定的，彼时彼刻市场对于未来波动的预期不影响交割价格。VIX future
恰恰相反，是由交割时刻的 VIX决定settlement value，而彼时彼刻的VIX是由市场对
交割日之后未来30天的expected volatility 决定。当然过去的realized volatility
也会因为volatility clustering这个现象影响市场对未来波动的预期，但也只是间接
影响。
用一个理想化例子来做比较：
Scenario A假设你在t=0持有t=30到期的variance swap, 再假设在你持有期间，只在 t
=5 时出现超出预期的大幅波动，其他时间realized volatility = expected
volatility。这导致最终realized volatility高于strike，你的payoff应该为正。现
在考虑Scenario B，把同样的大幅波动从t=5挪到t=25，其他一切不变，t=0 和t=30之
间的总realized volatility也不变。你的payoff有区别吗？没有。两种情况下你
variance swap的payoff显然是相同的，这是由settlement 的计算方式决定的。
如果你是在t=0持有t=30到期的VIX future，Scenario A 和Scenario B 下你的payoff
很可能完全不一样。Scenario B，市场大幅波动发生在t=25，由于volatility
clustering，expected volatility会被推高，在t=30的时候VIX应该仍然处于一个比较
高的位置。反过来看Scenario A，市场大幅波动发生在t=5，那么25天后它对市场的影
响基本上已经消退，到t=30的时候，没有其他shock，VIX应该已经回到正常水平。比较
两种Scenario ，在t=30到期的VIX future 的payoff 很可能非常不同。
总而言之，
variance swap其实是trade【未来30天（1 < t < 31）的realized volatility】和【
现在对其预期：E[Variance between t=1 and t=30] @ t=0】之间的差异。
VIX future 是trade 【30天后（t=30）的早上9点，市场对下一个30天（31 < t < 61
）的volatility 的预期】和【现在对这个预期的预期：
E0[E30[Volatility between t=31 and t=60]]】之间的差异。虽然有correlation，但
其实trade的不是一种东西。
5.What we know about VIX future return
熟悉了VIX future 到底是在trade什么，我们可以开始研究VIX future 的 return了。
我是 Empirical asset pricing 派的，对于find the best model to price VIX
future 的兴趣不高，我更关心的是how to generate alpha。 目前的大量研究，包括
我自己做的，基本上已经可以确定 VIX future on average gives negative return,
statistically and economically significant。换句话说想赚钱应该short VIX
future（Near term为主，远期的也是negative return但liquidity很差）。但这个
return不一定就是alpha，因为还得考虑risk factor。实际上VIX future 确实是
highly negatively correlated with the market，也就是说这个negative return 至
少一部分是对market risk loading的公平回报。第二个现象是variation of VIX
future is predictable，这就意味着有market timing 的可能性：根据一些因变量，
选择性地short/long VIX future，能得到比always shorting更好的回报。
如果有兴趣，我强烈推荐 “VIX future basis trading”
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2094510
两个主要结论：1.VIX future basis 作为a signal of market timing非常有效。2.
用SPX future 作为hedging 可以大大提高sharp ratio（risk 的减少超过excess
return的减少），tail risk也大幅减小。（虽然negative correlation with the
market 还是不能完全消除。）
这也间接证明 negative beta 不能完全解释VIX future的negative return，否则
return应该随correlation同比例减少，sharp ratio 也不会因为混合了SPX future而
提高。我自己做的研究就是以这篇论文为基础，进一步提高signal 和 effective
hedging。
另外提醒一下，即使在使用 SPX future 作为hedging 之后，portfolio的tail risk
仍然很高，碰到2008年那样的肯定wipe out。所以VIX future basis trading with
SPX future as hedging仍然是一种高风险高回报的策略。
6. Volatility trading with simple options
其实volatility trading 不需要依赖于 VIX future 和 variance swap，有option 就
可以。最简单的方法，long straddle 其实就是在 long volatility。不过也有问题。
一是straddle的Vegga 对strike的sensitivity 非常高，一旦straddle 因为市场变动
离开at the money的位置，Vegga会急剧减小。结果就是，假设你long at the money
straddles，并假设你现在的 Vegga 是10。 接下来波动率上升0.1，于是你赚了一块，
但因为市场一移动，你的straddle 不再是at the money，Vegga立刻减少了，如果接下
来波动率再上升0.1，你可能就只再多赚0.05块了，so on and on。而VIX future 和
variance swap 都没有这个问题，Vegga始终是constant的。（但我再次强调，这两
trade的不是一个东西）。
第二个问题是straddle也和VIX future 一样，和市场反向移动，beta为负。很多同学
可能意识到不对了，At the money straddle 的 delta 显然是0啊，怎么会beta为负。
Delta 的定义是 dV / dS ，Delta 为0仅仅意味着在其他parameter （包括implied
volatility）不变的情况下underlying 的价格变动不影响derivative的价格。但是
Implied volatility shock往往伴随着shock of underlying price。Market 下跌的时
候，Implied volatility 几乎100%要抬高，因此Delta为0但Vegga不为0的derivative
的价格基本上肯定要随underlying价格波动，beta也就不为0。
引申一下。如果你的Portfolio 的Vegga不等于0，不要被delta = 0 欺骗，觉得你是
market neutral 的，还是用历史数据跑跑，看realized beta究竟是多少吧。这也是为
什么之前谈到VIX future trading要用 SPX future 来hedge risk， 哪怕VIX 理论上
也是Delta neutral的。
7.Concern with VIX future return calculation
最后说一下一个研究VIX future return 的一个细节，就是VIX future return 计算时
denominator 该用什么。计算 sharp ratio 倒是无所谓，用什么都一样，但如果做
multiple risk factor analysis，return 的denominator选择会直接影响你的alpha大
小，用不公平的denominator计算不同strategy的return，然后直接比较alpha大大的不
妥。
股票return用股票价格做 denominator是因为股票价格就是天然的 VAR(100%)，但VIX
future 的价格绝不是VIX future trading 的VAR(100%)，VIX future 的价格可以从
20 跳到80，如果你是short，VAR(100%)应该远远大于VIX future 的价格，即便你是
long VIX future，我也很怀疑VIX future price 就是准确的VAR(100%)，因为VIX 不
会到0。直接用VIX future 价格做denominator肯定是不对的。
我想了一个办法，用Historical VAR(a%)，比如用Historical VAR(90%) 来做
denominator 计算VIX future 的return。（Generally speaking, historical VAR(
100%) is extremely difficult to measure, so I avoid it.）然后把你用来做比较
的其他option strategy return也做转换，把denominator 统一成Historical VAR(90%
)。这样你用multiple risk factor analysis 跑不同strategy的 alpha 才能公平的比
较。
最后这一点其实是我的一家之言，不一定对，哪位对此有心得的不妨点拨一下。 |
n*****e
发帖数: 6 | 2 想对VIX future和variance swap那部分补充点看法。
的确，在交割期时来看，我同意你的观点，但这里忽视了一个MtM的问题，如果在t=5出
现大的波动，realized和expected var term structure上升，你的swap MtM为正，会
比t=25时出现同样情况的value要高，因为合约即将到期,expected var接近realized，
而且极端的情况下大的exposure会使交易对手会出现funding或者credit risk，这时这
部分风险也会被price到合约价格里。 |
x********o
发帖数: 519 | 3 zan~~
【在 t*******y 的大作中提到】
: 上次发文求建议，收到很多真诚的帮助。想了想可以写篇我对 VIX index 的学习心得
: ，算是表达感谢吧。
: 说明一下，我毕竟是个菜鸟新人，这篇也只是综合公开资料再加上我自己对 VIX 的理
: 解，也就希望对准备学习这个领域的人有所帮助，熟悉volatility trading的内行看了
: 肯定觉得简单，有不对的地方请多多指正。
: 废话完毕。
: 1. Rationale behind VIX
: 想了解 VIX index 计算方法的依据，必读的文章是
: “More than you wanted to know about variance swap".
: http://elis.sigmath.es.osaka-u.ac.jp/research/gs-volatility_swa
|
t*******y
发帖数: 18 | 4 赞补充。之前只谈 hold to settlement 的情况是想尽量简化，把区别讲清楚。在
settlement 之前，考虑 mark to market，一个 unexpected volatility shock 对VIX
future 和 variance swap 价格（假设同时到期）的影响大致取决于两个因素：
1.距离到期的时间T - t
2.市场预期这个shock 会有多长时间的影响。
Variance swap 的价格受 Et[Variance from T-t to T] 的影响， VIX future 价格受
Et[Variance from T to T+30]的影响，这两个expectation 都会受到这个
volatility shock 的冲击，但这两个因素就会决定sensitivity的不同。
【在 n*****e 的大作中提到】
: 想对VIX future和variance swap那部分补充点看法。
: 的确，在交割期时来看，我同意你的观点，但这里忽视了一个MtM的问题，如果在t=5出
: 现大的波动，realized和expected var term structure上升，你的swap MtM为正，会
: 比t=25时出现同样情况的value要高，因为合约即将到期,expected var接近realized，
: 而且极端的情况下大的exposure会使交易对手会出现funding或者credit risk，这时这
: 部分风险也会被price到合约价格里。
|
p********n
发帖数: 1707 | |
w******e
发帖数: 142 | 6 赞内容丰富长文，想补充一点个人的对于vix future看法.虽然大家上课都学的是
future的价钱是未来underlying东东的期待价钱，但是如果大家观察时间足够长就会发
现这个expectation好像和最后实际的vix spot会差距很大。有一篇最近的paper，忘了
名字了，就是测试spot和front month的价钱是否满足expectation hypothesis，这个
就和Fama很多年前研究bond的yield curve的结果有相似之处，就是yield curve
predicts future excess bond returns rather than future yield changes,或者是
it is better at forecasting changes in short-dated yeilds while it is a poor
forecaster of near-term changes in long-dated yields.所以不能完全把vix
future价钱理解为risk neutral里面的期待值。
同时morgan stanley的这个比较老的报告其实也包含了很多有用的信息，大家可以参考。
http://www.scribd.com/doc/128143861/A-Guide-to-VIX-Futures-and-
【在 t*******y 的大作中提到】
: 上次发文求建议，收到很多真诚的帮助。想了想可以写篇我对 VIX index 的学习心得
: ，算是表达感谢吧。
: 说明一下，我毕竟是个菜鸟新人，这篇也只是综合公开资料再加上我自己对 VIX 的理
: 解，也就希望对准备学习这个领域的人有所帮助，熟悉volatility trading的内行看了
: 肯定觉得简单，有不对的地方请多多指正。
: 废话完毕。
: 1. Rationale behind VIX
: 想了解 VIX index 计算方法的依据，必读的文章是
: “More than you wanted to know about variance swap".
: http://elis.sigmath.es.osaka-u.ac.jp/research/gs-volatility_swa
|
s******e
发帖数: 1751 | 7 VIX101: vix spot and vix future are not the same thing. it's not like gold
spot and gold future.
you cannot compare them.
poor
考。
【在 w******e 的大作中提到】
: 赞内容丰富长文，想补充一点个人的对于vix future看法.虽然大家上课都学的是
: future的价钱是未来underlying东东的期待价钱，但是如果大家观察时间足够长就会发
: 现这个expectation好像和最后实际的vix spot会差距很大。有一篇最近的paper，忘了
: 名字了，就是测试spot和front month的价钱是否满足expectation hypothesis，这个
: 就和Fama很多年前研究bond的yield curve的结果有相似之处，就是yield curve
: predicts future excess bond returns rather than future yield changes,或者是
: it is better at forecasting changes in short-dated yeilds while it is a poor
: forecaster of near-term changes in long-dated yields.所以不能完全把vix
: future价钱理解为risk neutral里面的期待值。
: 同时morgan stanley的这个比较老的报告其实也包含了很多有用的信息，大家可以参考。
|
w******e
发帖数: 142 | 8 肯定是不一样的，比如convenience yield就是vix的protection作用，cost就是
insurance premium.每个future都不一样，但是都要在expire的时候converge.而且实
际操作的时候一些传统的commodity的algo都还是一样很有效的，主要是term
structure的persistence很大。
【在 s******e 的大作中提到】
: VIX101: vix spot and vix future are not the same thing. it's not like gold
: spot and gold future.
: you cannot compare them.
:
: poor
: 考。
|
s******e
发帖数: 1751 | 9 what i meant was, today's vix spot and the front month vix future, are not
the same thing, by definition. they only reconcile when the future expires.
【在 w******e 的大作中提到】
: 肯定是不一样的，比如convenience yield就是vix的protection作用，cost就是
: insurance premium.每个future都不一样，但是都要在expire的时候converge.而且实
: 际操作的时候一些传统的commodity的algo都还是一样很有效的，主要是term
: structure的persistence很大。
|
z***e
发帖数: 5600 | 10 1. Replication of variance swap by strip of options is fine at least for SPX
index options. Note that size of a certain option is fixed (proportional
to 1/K^2). In fact, market maker do trade replication strips to close their
VIX positions during the special quote window of the expiring Wednesday.
3. There is also a special case when extrapolation instead of interpolation
is required to calculate VIX index when next monthly SPX option expiration
is five weeks away. Has CBOE started using weekly SPX options yet?
4. There are several VIX futures contracts with different expirations. Each
refers to the forward 30-day volatility of SPX, which is related to the
forward variance swap. Variance swaps do have gamma risk and VIX futures do
not.
5. VIX expensiveness is risk premium. Yes most of the time you make money by
selling vix or variance swaps just like selling puts. However, 2008, Sept
11, 1987, and even 1929 did happen and there is a demand for tail hedges.
Backtest of VIX strategy need to include those "black swan" periods whether
or not historical data are readily available.
6. If you are long variance swap, you are short the market. Market makers
do incorporate that in their model ( which requires something to fit skew )
and manage risk accordingly.
7. Use Pnl instead of return. Sizing is part of the strategy and many times
the most important one.
BTW, it is Vega ...
【在 t*******y 的大作中提到】
: 上次发文求建议，收到很多真诚的帮助。想了想可以写篇我对 VIX index 的学习心得
: ，算是表达感谢吧。
: 说明一下，我毕竟是个菜鸟新人，这篇也只是综合公开资料再加上我自己对 VIX 的理
: 解，也就希望对准备学习这个领域的人有所帮助，熟悉volatility trading的内行看了
: 肯定觉得简单，有不对的地方请多多指正。
: 废话完毕。
: 1. Rationale behind VIX
: 想了解 VIX index 计算方法的依据，必读的文章是
: “More than you wanted to know about variance swap".
: http://elis.sigmath.es.osaka-u.ac.jp/research/gs-volatility_swa
|
|
|
S*******s
发帖数: 13043 | 11 vix future 的settlement price的确定方式楼主为什么不谈谈呀？挺有意思的事。几
年前有人写了文章证明了只要用很小的代价来改变deep otm的期权报价就可以显著影响
vro的最终结算价，之后cboe完全改变了定价方式。
即使现在这个方式结算价也是被明显地操纵着。比如大家可以看看1月份vix future的
结算价12.36，比前一天跌了6.7%，可是相应的vix基本上没有变。为什么呀？我认为是
我那天犯懒有2手合同没有在最后一个交易日清盘。就2手呀，他们就为这个砸盘。 |
s******e
发帖数: 1751 | 12 I highly doubt that's the case.
The contribution for a single contract is dK/K^2 * price.
OTM call does not matter b/c K is too high.
OTM put, say K is 600, dK is 25, how much you need to change price to have a
meaning impact (1 cent) on VIX spot?
that's .01 / (dK/K^2) = 144? that won't work.
【在 S*******s 的大作中提到】
: vix future 的settlement price的确定方式楼主为什么不谈谈呀？挺有意思的事。几
: 年前有人写了文章证明了只要用很小的代价来改变deep otm的期权报价就可以显著影响
: vro的最终结算价，之后cboe完全改变了定价方式。
: 即使现在这个方式结算价也是被明显地操纵着。比如大家可以看看1月份vix future的
: 结算价12.36，比前一天跌了6.7%，可是相应的vix基本上没有变。为什么呀？我认为是
: 我那天犯懒有2手合同没有在最后一个交易日清盘。就2手呀，他们就为这个砸盘。
|
S*******s
发帖数: 13043 | 13 很明显你没看懂
a
【在 s******e 的大作中提到】
: I highly doubt that's the case.
: The contribution for a single contract is dK/K^2 * price.
: OTM call does not matter b/c K is too high.
: OTM put, say K is 600, dK is 25, how much you need to change price to have a
: meaning impact (1 cent) on VIX spot?
: that's .01 / (dK/K^2) = 144? that won't work.
|
a******y
发帖数: 40 | 14 1. VIX future settlement VXS 确实和当天的VIX有较大差距
2. VIX 计算是从中间价来的。有bid-ask spread而且相当大。vxvwa-vxvwb经常有一个
多点。
3. VXS 计算是从成交价来的。一般VXS在VIX bid-ask spread之内。但也有例外
4. VXS option chain的vega 比 vix future settlement的vega要小很多。所以做市不
难。应当也有人在做。 |
s******e
发帖数: 1751 | 15 interesting, move VIX settlement 1 cent, 需要move多少skew 或 OTM vol level?
a quick sketch on the paper, the result was not economical.
【在 a******y 的大作中提到】
: 1. VIX future settlement VXS 确实和当天的VIX有较大差距
: 2. VIX 计算是从中间价来的。有bid-ask spread而且相当大。vxvwa-vxvwb经常有一个
: 多点。
: 3. VXS 计算是从成交价来的。一般VXS在VIX bid-ask spread之内。但也有例外
: 4. VXS option chain的vega 比 vix future settlement的vega要小很多。所以做市不
: 难。应当也有人在做。
|
S*******s
发帖数: 13043 | 16 我不是明确地说了结算价的确定方式有过一个很大的变动吗？在那以前很轻易地改变
deep otm的期权价格就可以达到显著影响，之后这个bug被补上了。你还算个什么劲呀。
?
【在 s******e 的大作中提到】
: interesting, move VIX settlement 1 cent, 需要move多少skew 或 OTM vol level?
: a quick sketch on the paper, the result was not economical.
|
s******e
发帖数: 1751 | 17 when was that?
i was assigned to look into this in 2009, at that time I didn't see anything
we could do to exploit it, although we were already the biggest vix dealer
(and one of the biggest spx dealer).
呀。
【在 S*******s 的大作中提到】
: 我不是明确地说了结算价的确定方式有过一个很大的变动吗？在那以前很轻易地改变
: deep otm的期权价格就可以达到显著影响，之后这个bug被补上了。你还算个什么劲呀。
:
: ?
|
t*******y
发帖数: 18 | 18 Wow, 抛砖引玉了！
感谢大家回帖，趁这里人多，问几个不明白的地方。
@zooie
Yes, it is Vega, WTF with my brain.
Thank you for sharing your experience. I'd like to discuss the issue further
if you have time.
1. I have no doubt that trading strips of options can largely hedge your VIX
position, especially for a short while. My doubt is merely about whether we
can exactly replicate a payoff of variance swap: σ^2 - E(σ^2) with option
portfolios. The position required for each option is actually 1/(T * K^2),
instead of 1/K^2, T is constantly changing. At the beginning of the coverage
period of a variance swap, T is changing slowly, so no big deal. But
towards the expriation, when T is close to 0, the position adjust required
by replication is quite substantial.
My point is VIX may not track the price of variance swap (that covering the
same period of time). But, all after all, variance swaps are (mostly?) OTC,
so we can't really observe how close their price are to VIX.
3. Well, short term VIX, using weekly SPX options, has already come. I'd bet
its popularity will overgrow that of the 30-day VIX.
5. By VIX expensiveness, I assume you mean the general positive returns of
VIX future. Whether its return is merely a compensation-for-risk is an
ultimate question I’d like to answer very much.
I’ve spent a lot of time on risk analysis on VIX future. Initially, he PnL
profile makes we inclined to think it is only compensation for market risk (
negative beta) or tail risk (extreme loss at crisis time). However some
facts might cast doubt on these explanations, at least for the dynamic
trading of VIX future.
Suppose you follow Simon and Campasano's study and buy/sell VIX future based
on basis-difference (see their paper if you are confused here). As shown by
Simon and Campasano, also verified by myself, the bulk of PnL still remains
after you hedge away most of the market risk. So I think it's fair to say
market risk explanation doesn't go very far.
As for the heavy tail of VIX future return. I compare PnL of dynamically
trading VIX future based on basis-difference versus trading VIX future at
random time points. The former offers much better average PnL while the tail
loss is similar or even less. I consider this as a strong evidence that the
abnormal return of dynamically VIX future trading not being explained by
tail risk.
Disclaimer: I have to admit that tail risk is such a pain-in-a$$ in
empirical study. It is hard to quantify and even harder to price. So far I
am not aware of a good model that can price it well (correct me if I am
wrong). So if anyone here have experience in analyzing tail risk, please
share with us.
6. Yes, it should be a common knowledge among market makers.
7. I totally agree with you that “Sizing is part of the strategy and many
times the most important one.” But doesn’t using PnL as a performance
measure totally ignore this aspect of investment? Kinda contrary to your
point.
@ StarVenus @sametime
The change of calculation was in 2003.
For current methodology, it would be a bad idea to try to move VIX
settlement by trading OTM options. The relative weight of each option in VIX
is determined by two factors: dK/K^2 and option price P. Yes, you may
increase 1/K^2 factor by going out of the money, but the decreasing price
will more than offsetting it. Let’s say K is 20% lower, and your first
factor is raised by 1/0.64. But the bid/ask of that out-of-money option is
usually already as low as (0 , 0.05). While at a peaceful settlement
Wednesday, the price of the atm option would be $25-$30. Obviously VIX would
not move much by the price fluctuation of otm options.
*********************Fen Ge Xian*********************
One last question. I am trying to make a model that can predict the change
of spot VIX. My first version is a simple moving window ARMA model. (I know,
it's laughable simple.) ARMA for the obvious mean-reverting property.
Moving-window to account for the regime change of VIX mean. Any suggestions?
Bless you all. |
s******e
发帖数: 1751 | 19 why do you call it a vix future basis when you compare today's vix spot and
front month vix future price.
as i mentioned many times, vix spot and vix future are different things. it'
s not like gold spot and gold future.
In another word, Vix future for May14 and Jun14 are 2 different contracts
covering forward variance (approximately) of different periods. While gold
future (front month and 2nd month) are very close (physical gold).
If you agree with that, then I can argue that VIX spot is the projected vol
from now to 30 days, and vix future is from it's expiry (3rd Wed of the
month) to next SPX option expiry. Given that I doubt that published paper
has much value (I could be wrong).
I wish my explanation makes sense to you.
I don't think it's wise to spend much time on VIX unless you are dedicated
to pursue a profession in option/vol-of-vol market making.
further
VIX
we
option
,
【在 t*******y 的大作中提到】
: Wow, 抛砖引玉了！
: 感谢大家回帖，趁这里人多，问几个不明白的地方。
: @zooie
: Yes, it is Vega, WTF with my brain.
: Thank you for sharing your experience. I'd like to discuss the issue further
: if you have time.
: 1. I have no doubt that trading strips of options can largely hedge your VIX
: position, especially for a short while. My doubt is merely about whether we
: can exactly replicate a payoff of variance swap: σ^2 - E(σ^2) with option
: portfolios. The position required for each option is actually 1/(T * K^2),
|
t*******y
发帖数: 18 | 20 And when did I say VIX and VIX future were the same thing?
and
it'
vol
【在 s******e 的大作中提到】
: why do you call it a vix future basis when you compare today's vix spot and
: front month vix future price.
: as i mentioned many times, vix spot and vix future are different things. it'
: s not like gold spot and gold future.
: In another word, Vix future for May14 and Jun14 are 2 different contracts
: covering forward variance (approximately) of different periods. While gold
: future (front month and 2nd month) are very close (physical gold).
: If you agree with that, then I can argue that VIX spot is the projected vol
: from now to 30 days, and vix future is from it's expiry (3rd Wed of the
: month) to next SPX option expiry. Given that I doubt that published paper
|
|
|
n****e
发帖数: 629 | 21 spot vix is not tradeable
Why bother making a model on something you can't make money from.
【在 t*******y 的大作中提到】
: And when did I say VIX and VIX future were the same thing?
:
: and
: it'
: vol
|
t***l
发帖数: 3644 | 22 Vix is not tradeable. Is this just for some reason CBOE doesnt want to make
it tradeable or some other more sophisticated reason? I know physical
settled annuity and cash settled annuity for a interest rate swap can not be
both tradeable. But why the fuck VIX is not tradeable? This confuses me.
【在 n****e 的大作中提到】
: spot vix is not tradeable
: Why bother making a model on something you can't make money from.
|
t*******y
发帖数: 18 | 23 Maybe check out Citigroup's CVOL?
Or you can just trade strips of near-term options.
make
be
【在 t***l 的大作中提到】
: Vix is not tradeable. Is this just for some reason CBOE doesnt want to make
: it tradeable or some other more sophisticated reason? I know physical
: settled annuity and cash settled annuity for a interest rate swap can not be
: both tradeable. But why the fuck VIX is not tradeable? This confuses me.
|
z***e
发帖数: 5600 | 24 1. No, variance swap replication does not need to worry about shrinking of
T. Variance swap is the term variance throughout the period. Every day
passes by, there are fewer days and lower vega left. Vega goes to zero
instead of going to infinity when it gets close to expiration. Same with
the replicating options hence you do not need to rebalance because of change
of T.
5. Market practioners also use term structure trades as an alternative of
long/short vix. It tends to have lower beta. However, there is also
concerns of size limits, more bid/offer to pay, basis risk, and even more
unpredictable risk of being caught too big. There is decent amount of
similarity between vix and natural gas trading. Remember Amaranth? For
those basis-risks, you never know the 20-stdev move can happen until you get
one...
7. Sizing. Sizing should be part of the trading strategy. Once you
incorporate sizing in your strategy, you can use pnl to analyze the
performance of the strategy, just like how you would have traded an actual
portfolio. Whether you use return or difference or something else of the
instrument is just a choice of sizing strategy (e.g. constant dollar average
vs. contracts etc)
further
VIX
we
option
,
【在 t*******y 的大作中提到】
: Wow, 抛砖引玉了！
: 感谢大家回帖，趁这里人多，问几个不明白的地方。
: @zooie
: Yes, it is Vega, WTF with my brain.
: Thank you for sharing your experience. I'd like to discuss the issue further
: if you have time.
: 1. I have no doubt that trading strips of options can largely hedge your VIX
: position, especially for a short while. My doubt is merely about whether we
: can exactly replicate a payoff of variance swap: σ^2 - E(σ^2) with option
: portfolios. The position required for each option is actually 1/(T * K^2),
|
t*******y
发帖数: 18 | 25 Many thanks.
of
change
【在 z***e 的大作中提到】
: 1. No, variance swap replication does not need to worry about shrinking of
: T. Variance swap is the term variance throughout the period. Every day
: passes by, there are fewer days and lower vega left. Vega goes to zero
: instead of going to infinity when it gets close to expiration. Same with
: the replicating options hence you do not need to rebalance because of change
: of T.
: 5. Market practioners also use term structure trades as an alternative of
: long/short vix. It tends to have lower beta. However, there is also
: concerns of size limits, more bid/offer to pay, basis risk, and even more
: unpredictable risk of being caught too big. There is decent amount of
|
n*****e
发帖数: 6 | 26 重新翻了一下cboe的VIX的white paper，其实他的公式用的是加权的期权价格(公式1)
，里面根本没有implied vol，也就是说VIX反应的是综合期权价格和不是期权中的隐含
波动率。
http://www.cboe.com/micro/vix/vixwhite.pdf
如果这样的话，为什么VIX还能被用作是Variance Swap的fair strike呢？ |
t********t
发帖数: 1264 | 27 期权价格的加权平均理论上可以replicate expected vol^2
【在 n*****e 的大作中提到】
: 重新翻了一下cboe的VIX的white paper，其实他的公式用的是加权的期权价格(公式1)
: ，里面根本没有implied vol，也就是说VIX反应的是综合期权价格和不是期权中的隐含
: 波动率。
: http://www.cboe.com/micro/vix/vixwhite.pdf
: 如果这样的话，为什么VIX还能被用作是Variance Swap的fair strike呢？
|
b******r
发帖数: 1137 | 28 you are basically trading the same thing if you trade a VIX futures expiring
in month X and a 30 day variance swap forward starting on the expiration
day of month X.
【在 t*******y 的大作中提到】
: 上次发文求建议，收到很多真诚的帮助。想了想可以写篇我对 VIX index 的学习心得
: ，算是表达感谢吧。
: 说明一下，我毕竟是个菜鸟新人，这篇也只是综合公开资料再加上我自己对 VIX 的理
: 解，也就希望对准备学习这个领域的人有所帮助，熟悉volatility trading的内行看了
: 肯定觉得简单，有不对的地方请多多指正。
: 废话完毕。
: 1. Rationale behind VIX
: 想了解 VIX index 计算方法的依据，必读的文章是
: “More than you wanted to know about variance swap".
: http://elis.sigmath.es.osaka-u.ac.jp/research/gs-volatility_swa
|
S*******s
发帖数: 13043 | 29 what would you guys say about the almost historical low vix? |
