Well? Basically, some time ago i was using black-scholes from online sources since i din't understand almost anything about black-scholes. Then...i started programming black-scholes on my own to be sure that the price is calculated as it has to. Today, I am using my own enhanced version of black-scholes and instead of calculating the CDF of the normal distribution, i am using the CDF of Levy distribution, which gives presumably lower values for options (which is obviously good for the buyer and bad for the seller), but while matching my "levy black-scholes" prices on historical data - it seems closer to the real option prices. Basically...i am thinking now to try even more ambitious approach and try design my own option pricing formula. Of course it all can turn to be a waste of time since after all black-scholes often gives quite closely accurate option prices to the real market price...which...since my strategies don't involve any static arbitrage of say 3-4% yearly return...i am not interested in something so much better than black-scholes. Perhaps i should focus my efforts to some other direction? So...what do you do when pricing your "best" price for the option given the stock price, time and other factors? thanks!
I've been trading options for 20 years and I have never spent 1 minute thinking about this. Is there any way that this will make you money?
Well, at least in my opinion, there is...for example: Today you buy a call option which costs $2. Now you're thinking...: "OK, the stock is now $10 and given the volatility....time and bla, bla, bla - the option ACCORDING to black-scholes should cost $2.2 tomorrow if the price of the stock goes to $12...but is the black-scholes correct...what if the price of the option costs $1.9, since theta is a bitter opponent sometimes ?". Again, I am not saying that one will become a millionaire in no time if they use something better than black-scholes, since it is robust enough - I am just curious how others operate since just like everybody i would like to be ahead of the competition as much as possible .
The key input in the Black-Scholes formula is volatility. Tipically, options are quoted in terms of "implied volatility". Given a cash option price, the volatility value that would produce the current market cash price of an option is actually quoated and is called "implied" volatility. There is very little money that can be made here by reverse-enginering the calculation. There is a (unlikely) possibility that some of the market participants use Black-Scholes with holidays/dividends accounted for differently than other markte participants. This may be a source of arbitrage. What, I understand, the OP is trying to achieve is to produce credible option prices based on historical (asopposed to imnplied) volatility. If this project succeeds, it has a potential for being extremeley profitable.
Exactly, otherwise it will be an oxymoron...that is, it won't make sense to price an option given the implied volatility - since the implied volatility will be the result of an option price. Then again, you have other types of volatility such as: stochastic most notably and hell these days everyone thinks of their own type of volatility (like E.Derman and others...). I am still not sure how much credit should be given to the historical volatility though, after all we all know the gambler's fallacy problem (just because a coin has tossed tail 100 times, there is no reason to believe that head is much more likely to occur). In a similar fashion, just because the volatility is calculated to be 20% over 100 calculations, is there a reason to believe that it will remain like that? It my opinion, it makes no sense to trheat continous values (like volatility) like a discrete values (that is...it doesn't make sense to calculate a mean of something that should last forever...). Speaking of stochastic volatility, assuming that price is random is also a too brave assumption. But these all could turn to be just plain generalizations. Will see...now i gotta take a break and drink some coffee.
How do you use the information your calculate in your trading? How does the extra effort toward making a more precise estimate of price help you? I studied Black-Scholes over 30 years ago as an academic exercise. However, I have never used it in my trading which consists almost exclusively of index options credit spreads. If I recall correctly, the use some make of it is to find options that are priced anomalously and "bet" they will return toward normal. Is that your purpose?
You are correct regarding being suspicious of HV, and not putting too much credit in it. The problem with HV is with the way it's calculated using standard deviation. For example, if we were to choose a 10 day period where the security is constantly tanking or rallying every day at the rate of 3%, HV will register a very low number not reflecting the actual movement or REAL vola. hence its lack of usefulness and practicality in vola. model designed around real world applications geared toward predicting future vola.
imo: Profit/Loss_t1/t2=f(IV;etc.)@t2-f(IV;etc.)@t1 IV=f(OpPrices;Rate;etc.) OpPrice=f(ProjULPrices;Strike;T_Exp;etc.) ProjULPrice=f(HistULPrices;etc.) for some technical traders Depending on what trading model to use, the value of HistV may generally have little direct impact, however for those technical traders, the source of HistV most likely would. Whether practical or not, and how much useful, should be another issue.
A simplified pricing model according to Gallacher (who uses basically no conventional Greeks including Deltas designed for measuring various sensitivties related to OpPrices): OpPriceATM@t=StrikexIVxSqrt(T_Exp/254)x0.4