Year to date.... . the close to high (or low) has more varience then close to close.. variance scales with time..... fractal dimension is a way to describe the change of roughness to the size of the stick your using to measure .. a coastline gets longer the shorter the stick you measure it with... so think of stock ddeviations as roughness and time as the measuring stick... take a look at simple moving averages! Average of price variations... the longer the time frame the more you smooth out the spikes you see if you were measuring shorter term time windows.... I don't like when I hear comments heading towards "the market is so efficient you can never find anomalies". There's a cost to selling premium as a net seller of vol your assuming that risk for that price .. a distro gives you stardard devs... a stardard D of 9 can be a standard dev of 1.5 if vol changes abruptly.. no one measures the magnitude of those changes? I am sure they happen in scale! When markets get volatile time speeds up. you might consider roughness/variance to be constant and time is actually varying... time does fly when more things are happening.... idk. There's some tangent in there but bottom like vol isn't priced correctly everywhere all the time...
No, I do mean that you should be getting lower annualized volatility numbers for weekly volatility then for daily. See attached spreadsheet for an example, in this case S&P 500. PS. can't seem to attach an excel file
print screen then paste inside a new file in photoshop or whatever picture editing program you have.. upload to image shack as a png or jpg..
so BSM model uses a square root of the quadratic variation of stock returns.. which is a variation based upon a stochastic/random process.. random being defined by martingales or Brownian motion.. so basically you utilizing this "quadratic variation of stock returns" quadratic variation is just a distribution of the log of stock returns.. if thats right i get it.. but what is the time frame assumption for the stock returns to price an option.. i think its reverse.... the supply and demand for the cumulative options series will dictate the options price... BSM is only for to come up with fair price based on your assumption of historic realized volatility or as they put it stock returns. or BSM can be used to figure out the greeks. The Greeks for Blackââ¬âScholes are given in closed form below. They can be obtained by straightforward differentiation of the Blackââ¬âScholes formula. http://en.wikipedia.org/wiki/Black–Scholes the implied vols you buy is fixed at the rate you buy it at.. the realized vol will be based on how much volatility is realized.. your P/L will be the difference between the two.. so implied is then fixed.. realized is the variable rate going forward.. so if you can scalp more volatility intraday then you have bought you make money.. period end of story.. obviously if you can see that intra day realized vol is higher then close to close and you think there is an edge there you can buy premium and gamma scalp for a profit. Finding the "discrete" time frequency considering commissions is the next step... two variables.. now hedging frequency and weather your bet on realized intraday (or for matter whatever time frame) will be higher then the implied rate you bought it at.. you need to graph where the discrete hedging interval makes the most money considering commssions/costs.. remember thats still historic intraday volatility... that doesn't imply its going to be higher then implied in the future.. please anyone correct anything wrong i say.. i'm still new obviously wiki standard dev for BSM: the volatility of the stock's returns; this is the square root of the quadratic variation of the stock's log price process
My studies on this matter (from about 2 years ago) agreed with TskTsk's conclusion. Daily, weekly, monthly were close (within a vol or two) for index.
That's basically all their making if they are right at that perfect hedging frequency.......one or two vols.. but that's normalized.?. meaning its one or two vols higher intra day compared to closeto close per day? One or two vols a day realized daily compounding could add up no?
Daily and weekly are be about a vol off (daily over) or about 3-5% of daily vol level. If you don't have to do any work to collect this money, it's not a bad deal - e.g. trade weekly variance against daily variance (long daily). The trade-off is that sometimes you have consistent volatile trends which would hurt, however, that is usually offset by higher levels of M/R in the following weeks. Volatility in high frequency space is meaningfully higher, too, though I don't have the data on hand.
How would you do this in practice? Long a daily option / short the weekly? Shouldn't it be the other way round (short daily) in that case?
(Also someone correct me if I'm off) That would be true for a vanilla option in the ideal situation that i. you predicted correctly the volatility when you bought the option ii. you kept the option until expiry iii. you were delta hedging continuously at the vol value you had predicted and proved to be the correct one. If you are gamma scalping then the P&L also depends on the gamma so when your position moves away from ATM then the gamma fades and so does the P&L even if you are right about volatility.