Not long ago securities were traded by human traders in face-to-face markets. The ecosystem of an open outcry market was well-known, visible to a human eye, and rigidly prescribed. Now trading is increasingly done in anonymous electronic markets where traders do not have designated functions or...

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Understanding the microstructure of the financial market requires the processing of a vast amount of data related to individual trades, and sometimes even multiple levels of quotes. This requires computing resources that are not easily available to financial academics and regulators....

We first develop an efficient algorithm to compute Deltas of interest rate derivatives for a number of standard market models. The computational complexity of the algorithms is shown to be proportional to the number of rates times the number of factors per step. We then show how to extend the...

Research indicates that individual investors trade excessively and underperform the market indices, Barber and Odean 2000). The purpose of this paper is to help explain which behavioral biases, if any, can explain this result using a simulation approach. Results indicate that putting too much...

We set a lower bound on the complexity of options pricing formulae in the lattice metric by proving that no general explicit or closed form (hypergeometric) expression for pricing vanilla European call and put options exists when employing the binomial lattice approach. Our proof follows from...

I prove that if markets are efficient, meaning current prices fully reflect all information available in past prices, then P=NP, meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse by showing how...

Bid and ask sizes at the top of the order book provide information on short-term price moves. Drawing from classical descriptions of the order book in terms of queues and order-arrival rates (Smith et al., 2003), we consider a diffusion model for the evolution of the best bid/ask queues. We...