 BLOBY
Topic Author
Posts: 113
Joined: May 17th, 2004, 5:07 am

### How can you replicate a put on index variance with vanilla equity stock options ?

Hello, I'm wondering if it's possible to replicate a put on index variance with vanilla equity stock options ?Any ideas ? BLOBY
Topic Author
Posts: 113
Joined: May 17th, 2004, 5:07 am

### How can you replicate a put on index variance with vanilla equity stock options ?

Sorry, replicate with vanilla equity index options .... DavidJN
Posts: 1757
Joined: July 14th, 2002, 3:00 am

### How can you replicate a put on index variance with vanilla equity stock options ?

A general property of options that would work against you doing this is that a portfolio of options is worth less than an option on a portfolio. list
Posts: 2041
Joined: October 26th, 2005, 2:08 pm

### How can you replicate a put on index variance with vanilla equity stock options ?

The starting point that would be independent on a quality of theory is to check their dependence. Compute correlation coefficient try write regression equations linear or nonlinear. If you will find out you can look for theoretical background. It is possible that you will find some kind of dependence between Index volatility and volatility ( or mean ) of vanilla equity stock options. I would say that numeric interpretation volatility in modern finance looks has a strong shift from what is well known from statistics. The formulas that used in pricing volatility the volatility if the linear deterministic functions are not 0. The developers attempted to convince that this is a good approximation and introduced some numeric examples that confirm this point. On the other hand as usually happened is how to randomize known data. For example the benchmark that uses closed or open prices as the estimate for a day statistics is the one point and if you use say mid-point between high-low for mean and high -low for volatility exposure is completely different point of view. daveangel
Posts: 17031
Joined: October 20th, 2003, 4:05 pm

### How can you replicate a put on index variance with vanilla equity stock options ?

QuoteThe starting point that would be independent on a quality of theory is to check their dependence. Compute correlation coefficient try write regression equations linear or nonlinear. If you will find out you can look for theoretical background. It is possible that you will find some kind of dependence between Index volatility and volatility ( or mean ) of vanilla equity stock options. I would say that numeric interpretation volatility in modern finance looks has a strong shift from what is well known from statistics. The formulas that used in pricing volatility the volatility if the linear deterministic functions are not 0. The developers attempted to convince that this is a good approximation and introduced some numeric examples that confirm this point. On the other hand as usually happened is how to randomize known data. For example the benchmark that uses closed or open prices as the estimate for a day statistics is the one point and if you use say mid-point between high-low for mean and high -low for volatility exposure is completely different point of view. no offence dude but I found it really hard to understand your point.I think BLOBY's question relates to the replication of puts on variance through options and please feel free to correct me if I am wrong. As is well known, a contract that pays the difference between realised variance and some contracted amounted (the variance swap) can be replicated in the BSM world using a portfolio of calls and puts (see Derman's paper). I think what BLOBY might be referring to is that as we can replicate the swap, can we use soemthing akin to put call parity to replicate just the put on variance using idnex options ? I think it should be possible but I haven't tried to do it yet.thinking about it (hence the edit), I think Carr has published something on pricing options on variance - hence you can use that and replicate the delta of the variance swap using options ....
Last edited by daveangel on May 6th, 2009, 10:00 pm, edited 1 time in total.
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Posts: 110
Joined: September 30th, 2008, 8:35 am

### How can you replicate a put on index variance with vanilla equity stock options ?

I thought we can't replicate option on var with vanilla options because we can't replicate volatility swap with them, is that correct? list
Posts: 2041
Joined: October 26th, 2005, 2:08 pm

### How can you replicate a put on index variance with vanilla equity stock options ?

The notion "replication" did not formalized either in finance or statistics. So one could interpret it broadly as a dependence of 2 random processes or synthetic representation of the price of the instrument as an index.Concerning volatility pricing idea it is much worst than BS pricing that many people still used or studying. The BS theory of pricing is wrong because it prices equally options with different rates of return and equal risk (volatility). This contradicts finance basics regardless derivatives. You do not need to know about derivatives at all to state that.I belief that formula derived Carr and Madan that a payoff could be presented in the form of a linear combination of functions that could be interpreted as call and put payoff and it might or might not make sense to apply for volatility pricing if the volatility price is defined itself. When I look at realized variance formula it looks rather as exotic path dependent derivative. The developers stated it close to statistical variance though their examples stems from their interpretation of volatility that looks insufficient. To highlight the difference in randomization assume that you have to close prices say 0.02 and 0.021. One interpretation you have slow changed data. You can use these or middle point for randomization. On the other hand if you will look at high and low you could see significant volatility that could not be ignored.In the second example the replacement of the statistical volatility by realized could be immature or even wrong.About analytics. The question is we observe the stocks prices and any information is available. Is it possible to define (not calculate) the price of volatility. If not then better to stop because we calculate something undefined. If yes then what it is? Nevertheless assume that volatility could be priced then is that should be a component or correlate with the stock price? St the expected return could be priced too?  