Starting by mathematically modeling financial markets. We follow the price dynamics of a traded stock. E.g. Bank Leumi stock (LUMI:IT) intraday tick data; specifically, every purchase and sale that is registered on the Tel Aviv exchange per millisecond. Every millisecond a random number of Bank Leumi stocks is being traded. In a research I conducted with the PhD Student Bella Dubrov, , We investigated how long should we wait in order to assume that the price change is completely random. In our research we empirically found that the log-return of the stock is random after time increments of 15 minutes and no forecasting of future stock returns can be done based on historical prices. In other words the market is efficient after time increments of 15 min. And the stock purchase cost premium will determine that time increment. This explains why all free financial data is given in a 15 min delay (E.g stock prices given buy Yahoo Finance and Google Finance). For more profound reading please read Market Efficiency at the Tel-Aviv Stock Exchange written by Bella Dubrov and Gal Zahavi. A further suggested research is to extend this work empirically for 500 stocks traded on the new york stock exchange NYSE, and show that all markets behave similarly.

We extend this research in collaboration with Uri Gil, Electrical Engineer from the Technion. Liquidity in financial markets is defined as the expected time to buy or sell a stock. In order to make the financial instruments more accessible and shorten the transaction time, exchanges employ liquidity providers that hold an inventory and release it to the markets at the best rate according to demand. We present a non-linear autoregressive model to show that we can provide earnings from market liquidity in 90% of the time. In other times, we can forecast that stocks prices will exhibit extreme changes and devise a stop trade strategy. For further reading please look into Online Learning of Informed Market Making.

A further research suggests testing the algorithm for other high frequency exchange traded notes. E.G. options and other structured financial derivatives.

We derive a further forecasting analysis with the investigation of the Interest Rates Yield Curve aiming to forecast recessions. In work done with Economists and Industrial Engineers from the Technion Denis Guidman and Tzachi Perri, we model the forecasting of recessions as the ratio of the aggregated government bonds for long term investment versus short term government bonds.

The result of empirical investigation based on streaming data we conclude that recessions can be forecasted several months in advance depending on central banks liquid government bonds. For further reading please refer to: Forecasting Recessions Using Aggregated Debt Portfolio.

A last research in this empirical series, was conducted in collaboration with Ilan Geller, my master student at the Technion. We developed and empirically substantiated a methodology to find the best Mathematical Pricing model for providing liquidity in derivative markets. Our research shows that for 5 different mathematical

models of option prices, we can uniquely determine the best performing model. We tested our theory by historically simulating returns on a 5-Years traded option prices (all option contracts on the S&P500). We assume that the profits from a hedged market making strategy is the measure of market efficiency. It proves that the better the mathematical model captures the market implied probability, the more profitable providing liquidity of financial assets will be. We found that best performing model was a two dimensional stochastic SABR process which assumes that one variable is the stock price and the other is its implied volatility. We solve it as the solution of a two

dimensional partial differential equation. For further reading please refer to: Hedged Inventory Risk in Market Making of Derivative Markets. In the future, this model selecting mechanism should be implied to any financial market with liquid derivatives.