tag:blogger.com,1999:blog-2182962435875556601.post3148239765318690642..comments2023-09-24T08:04:06.909-04:00Comments on FSK's Guide to Reality: The Black-Scholes Formula is Wrong! - Part 1/12 - Overview and BackgroundFSKhttp://www.blogger.com/profile/11903396202330950362noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-2182962435875556601.post-11240038646565734872011-03-28T16:43:42.159-04:002011-03-28T16:43:42.159-04:00here is an online BS calculatorhere is an online BS calculatorAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2182962435875556601.post-32575596670494243652008-03-29T21:23:00.000-04:002008-03-29T21:23:00.000-04:00Hello,Your article is interesting, as you have obs...Hello,<BR/><BR/>Your article is interesting, as you have observed something most people miss:<BR/><BR/>Provided the stock market outperforms the risk free rate (which tends to be the case), the expected return of calls is significantly above the risk free rate and the expected return of puts is significantly below the risk free rate. This is particularly true of further out of the money puts/calls.<BR/><BR/>This does _NOT_, however, mean that equity options are mispriced. Black-Scholes is based on an arbitrage argument, not directly on the expected return. The relationship you observe:<BR/><BR/>price = exp(-rT) * (Risk-neutral expectation)<BR/><BR/>is a theorem regarding risk-neutral valuation, but not the primary motivation for the Black-Scholes equation.<BR/><BR/>Indeed, if options were priced so that their expected return is zero (I suspect you think this is the "fair" price), then there would in fact be an arbitrage opportunity whereby one could earn more than the risk free rate by buying/selling options and delta hedging them.<BR/><BR/>Also, note that calls and puts are far more leveraged investment vehicles than the underlying instrument itself. If one were to invest by buying calls (or shorting puts), you would indeed outperform the risk free rate provided the underlying did also, but you would do this at the expense of assuming more risk (variance in your returns). Thus you are merely collecting a risk premium. You aren't really getting anything for free. You can verify this yourself by looking at the Sharpe ratio for these investment techniques.<BR/><BR/>JoshAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2182962435875556601.post-15939960382977058282008-02-15T07:55:00.000-05:002008-02-15T07:55:00.000-05:00An economist was giving a series of lectures for s...An economist was giving a series of lectures for small investors in some community center. Now, there weren't many people attending this lectures, so the man was very surprised to find overcrowded room , waiting for lecture on "Problems with Black-Scholes".<BR/>The whole crowd stared at him throgh the lecture, and then left without asking a single question. Only latter did he learn that the publisher of the info leteer for the community center misspeled his lecture as "Problems of Black Schools".<BR/><BR/>for some reason (well, i can think of number of them) , people find cheap socialism far more intresting than concrete economics.Jonatan Krovitskyhttps://www.blogger.com/profile/03755263917070708938noreply@blogger.com