By Olivier Gueant
This e-book is one of the first to offer the mathematical versions most ordinarily used to unravel optimum execution difficulties and industry making difficulties in finance. The monetary arithmetic of marketplace Liquidity: From optimum Execution to marketplace Making offers a normal modeling framework for optimum execution problems–inspired from the Almgren-Chriss approach–and then demonstrates using that framework throughout quite a lot of areas.
The e-book introduces the classical instruments of optimum execution and industry making, besides their useful use. It additionally demonstrates how the instruments utilized in the optimum execution literature can be utilized to resolve classical and new concerns the place accounting for liquidity is critical. particularly, it offers state of the art study at the pricing of block trades, the pricing and hedging of ideas while liquidity issues, and the administration of advanced percentage buy-back contracts.
What units this ebook except others is that it makes a speciality of particular subject matters which are hardly, or in basic terms in brief, tackled in books facing marketplace microstructure. It is going a ways past current books when it comes to mathematical modeling–bridging the space among optimum execution and different fields of Quantitative Finance.
The e-book contains appendices devoted to the mathematical notions used during the ebook. Appendix A remembers classical recommendations of mathematical economics. Appendix B recollects classical instruments of convex research and optimization, in addition to principal rules and result of the calculus of variations.
This self-contained e-book is offered to somebody with a minimum history in mathematical research, dynamic optimization, and stochastic calculus. protecting post-electronification monetary markets and liquidity matters for pricing, this e-book is a perfect source to assist funding banks and asset managers optimize buying and selling options and increase total chance management.
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Extra info for The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making
Obviously, the hidden part of the iceberg order always has lower priority than any visible order at the same price. Iceberg orders can be seen as an automatic way to split and post orders. However, an iceberg order is more than that, and it is sometimes like real dark liquidity. In effect, a liquidity-taking order arriving 27 Post-trade transparency is another requirement – see for instance  for a thorough analysis of post-trade transparency. Organization of markets 29 at the price of the iceberg order can be matched with the hidden part of the iceberg order if the size of this aggressive order is larger than the total size of visible orders at that price, and if there are no other hidden orders with higher (time) priority at the same price.
However, optimal execution problems only make sense when one considers market frictions such as transaction costs, execution costs, and market impact. Therefore, optimal execution could be seen initially as a new area built on top of market impact and execution cost models, and therefore as an extension of classical topics of market microstructure. At the same time, econophysicists got interested in market impact modeling, and this area ceased to be the prerogative of economists only. However, it is noteworthy that the new entrants were initially more interested in modeling the market impact as the reaction of a physical system to new volume, rather than as the proceed of an (dynamic) equilibrium.
They act indeed as liquidity-providing arbitrageurs across the different platforms quoting the same stock. Therefore, they make it possible for the information to circulate almost instantaneously from one pool to the others. In other words, high-frequency market makers are essential to solve what L. Harris called in  the problem of the “two mostly incompatible competitions”: the competition between traders who buy and sell shares, and 28 Off-market trades have a long history. Historically, large orders were often executed on the upstairs markets in order to reduce market impact.