



These are the two idealizations - real orders do not come in a fixed block size. They come in a distribution of sizes, and all the evidence I've seen (including that from agent based sims of trading systems) indicates that this is a significant contributor to returns kurtosis / derivations from lognormality. So my first recommendation is to drop the chunking of blocks into 100 shares, that treats large orders as just a large number of 100 share orders, and instead to select order sizes from an empirically fitted order distribution, across all the scales of order sizes actually seen.



The second idealization is that market orders can always be filled without moving the market. You have it easy due to the above idealization, basically - you always have some bid or ask that will truly fill any market order that hits your imagine system, because your block size is just 100 shares. What actually happens is you have bids or asks for up to 1000 shares at X, and a market order for 5000 shares arrives, and blows through that bid or ask immediately, being filled only after the market has moved. Because mechanically the way large market orders are filled is they sweep up all market or limit orders on the other side until they are filled, the price moves to the last required to fill that market order.



In your imagined system, only limit orders result in price movements, but in market reality, large market orders hitting limit orders as the other side / as needed to "fill" that market order, are the main events that move market prices. And volatility spikes precisely when market orders of larger size than the tight limit bids and asks of the ordinary market makers, hit and exhaust those, and push the price in either direction deeper into the limit order books.



So, why recommendation would be - (1) drop the block size simplifications, (2) get block size and limit order sizes from real order books, (3) simulate with those details empirically right, and see if the rest of your analysis then results in power law tails as an emergent result.



I hope this is helpful.



Sincerely,

Jason Cawley The overall idea is quite promising, but I think 2 idealizations made in the process you outline prevent me from accepting your explanation for the observed tail characteristics. Also you put in one power law rather than deriving it from the modeled market clearance dynamics, and if you correct the issues I mention below you might instead derive that one too, instead of putting it in.These are the two idealizations - real orders do not come in a fixed block size. They come in a distribution of sizes, and all the evidence I've seen (including that from agent based sims of trading systems) indicates that this is a significant contributor to returns kurtosis / derivations from lognormality. So my first recommendation is to drop the chunking of blocks into 100 shares, that treats large orders as just a large number of 100 share orders, and instead to select order sizes from an empirically fitted order distribution, across all the scales of order sizes actually seen.The second idealization is that market orders can always be filled without moving the market. You have it easy due to the above idealization, basically - you always have some bid or ask that will truly fill any market order that hits your imagine system, because your block size is just 100 shares. What actually happens is you have bids or asks for up to 1000 shares at X, and a market order for 5000 shares arrives, and blows through that bid or ask immediately, being filled only after the market has moved. Because mechanically the way large market orders are filled is they sweep up all market or limit orders on the other side until they are filled, the price moves to the last required to fill that market order.In your imagined system, only limit orders result in price movements, but in market reality, large market orders hitting limit orders as the other side / as needed to "fill" that market order, are the main events that move market prices. And volatility spikes precisely when market orders of larger size than the tight limit bids and asks of the ordinary market makers, hit and exhaust those, and push the price in either direction deeper into the limit order books.So, why recommendation would be - (1) drop the block size simplifications, (2) get block size and limit order sizes from real order books, (3) simulate with those details empirically right, and see if the rest of your analysis then results in power law tails as an emergent result.I hope this is helpful.Sincerely,Jason Cawley