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It's useless to say that it needs to be rescaled to get the sum of probabilities equal to unity. Masteratwork

+1, there would be no need of options :p .

True . As a practical way to do it, you can estimate implied distribution with at least 3 calls with closed strikes. Assume 3 calls C1 C2 C3 with strikes K1=K2-d and K3=K2+d, with interest rate r, and T the maturity. C1(K2-d) C2(K2) C3(K2+d) Implied distribution at K2 is...

My bad, I thought you wrote "I am pretty sure that I have a decent options system if I didn't have to worry about delta neutrality, but that is not my reality since I don't have access to variance or vola swaps." So where is your problem ? Delta neutrality ? Masteratwork

Hi nitro, As a trader who used to price variance swaps, I don't get it. Since you quote a variance swap, you need a lot of vanilla strikes to construct a portofolio that would replicate the variance payoff. You need to delta hedge your vanilla portofolio to keep a pure volatility...

Are you sure about that ?

Risk neutral distribution is the probability distribution that makes the expected future price be (today) forward price. Because the trend of an underlying doesn't make sense as one prices a derivative (because pricing models are based on a delta hedge strategy), that way, the expected future...

Hi nitro, Why are you comparing risk neutral distribution with real one ? Risk neutral distribution is just a tool to price derivatives. In no way it has to do with real distribution. In fact the real distribution can't be known. The only thing that is known is past prices hence a...

Vol of vol is related to volatility. It just means that vol fluctuates. dvega/dvol is related to the sensitivity of a vega. There is no vega and no dvega/dvol for a S&P future for example, but prices volatility could be variable. If volatility is variable, then there is vol of vol.

Hi Martinghoul, I see your point, but the fact that there are autocorrelation and/or vol of vol doesn't change forward vol. Forward vol is correct just for the moment one derives it. It's a weak way to forecast future volatility but it has to hold since everybody prices volty by the...

'would be nice :)

HI Martinghoul What do you mean with "In the presence of vol of vol, the equation doesn't have to hold" ? The equation is based on the definition of the variance. I May miss something but I don't see where vol of vol is involved ?

Hi, you have a lower boundary for vol2 vol2=vol1*SQRT(T1/T2) There is no way Vol2 be lower that level. If it were, that would tells you that volatility between T1 and T2 gets negative. How would it be ? Masteratwork.

Well, you don't price an option with IV, you quote an option with IV. In some models like BS, you price an option with HV. IV is always unknown. The only thing you could know is 'Black & Scholes pricing model implied volatility'. IV is model dependent. A SABR model would have a different IV for...

I didn't write something about quoting options without pricing model. What I've written is that market doesn't know future. So, it doesn't know future volatility. Again, if I pay $1 to buy a put and a pricing model shows that fair value is $ 0.15, it doesn't mean that I expect higher future...

Hi Mark, happy new year, Sorry, IV has nothing to do with future volatility ! How the market would know it ? IV is just what makes your pricing model match current quotes. Demand and supply for option make the price. And the price has nothing to do with IV. A pricing model does. That why...

Both could be at the money !

OP, You'd have a positive time decay if you trade a spread. The only thing you 'd have to check, is that the option sold is near at the money. Assume the spot is around 100. A call spread 80/100 (you buy the strike 80 and sell the strike 100) has a positive time decay. A put spread 120/100...

Back of the envelope calculation seems to valid your numbers. What matters with those datas ?