tag:blogger.com,1999:blog-5880610.post110178551300041626..comments2024-01-13T18:57:18.243-05:00Comments on Information Processing: VIX and Black-ScholesSteve Hsuhttp://www.blogger.com/profile/02428333897272913660noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-5880610.post-1101928241526734422004-12-01T14:10:00.000-05:002004-12-01T14:10:00.000-05:00What is striking about the CBOE VIX data that I li...What is striking about the CBOE VIX data that I linked to is not just that the vol changes over long timescales, but that it changes *in response to market moves*. That is, if the SP500 has a rough week (say, it drops 3%) the implied vol shoots up 12% on average. Whereas, if there is a runup of 3%, the vol drops by 12%. This path dependence goes beyond the original skepticism I had over using a Steve Hsuhttps://www.blogger.com/profile/02428333897272913660noreply@blogger.comtag:blogger.com,1999:blog-5880610.post-1101927953434850762004-12-01T14:05:00.000-05:002004-12-01T14:05:00.000-05:00I don't know the details of the GARCH models but t...I don't know the details of the GARCH models but to me it seems like the Black-Scholes equation which is based on a Fokker-Planck type formalism is inherently flawed for long time scales. Probably for a month to two months it's okay but the non-Gaussianity and memory effects become more important as you go longer. I don't know the industry at all of course but I bet that traders are going on Carson C. Chowhttps://www.blogger.com/profile/08464737817585277975noreply@blogger.comtag:blogger.com,1999:blog-5880610.post-1101847914163664852004-11-30T15:51:00.000-05:002004-11-30T15:51:00.000-05:00"detrending"= fitting Black-Scholes drift term? Th..."detrending"= fitting Black-Scholes drift term? This always bothered me as well. They are doing more sophisticated stuff now, like using stochastic vol or these GARCH models which I guess have path dependence.<br /><br />The old way of extracting implied vol was to fit option prices using the Black-Scholes formula. The new way (post 2003 for VIX) is to use the prices to fit an implied probabilitySteve Hsuhttps://www.blogger.com/profile/02428333897272913660noreply@blogger.comtag:blogger.com,1999:blog-5880610.post-1101839586266547902004-11-30T13:33:00.000-05:002004-11-30T13:33:00.000-05:00I've always felt that fixed volatility was a huge ...I've always felt that fixed volatility was a huge weakness in Black-Scholes. I once saw a talk where this person plotted a securities price, arbitrarily detrended it and then fit a Gaussian. I asked him how he decided between fluctuations and trends and he had no idea what I was asking. To my eye there did not seem to be an obvious time scale in the fluctuations to separate the two. You Carson C. Chowhttps://www.blogger.com/profile/08464737817585277975noreply@blogger.com