The financial mathematics of market liquidity: From optimal execution to market making

The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making

Volumn , Issue , 2016, Pages 1-278

  Guéant, Olivier ^a  

^a Ecole Nationale de la Statistique et de l'Administration Economique   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85007303992     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (177)

1. F. Abergel, J.-P. Bouchaud, T. Foucault, C.-A. Lehalle, and M. Rosenbaum. Market Microstructure: Confronting Many Viewpoints. John Wiley & Sons, 2012.
2. F. Abergel and R. Tachet des Combes. A nonlinear partial integrodifferential equation from mathematical finance. Discrete and Continu- ous Dynamical Systems, Series A, 27(3):907-917, 2010.
3. A. Alfonsi, A. Fruth, and A. Schied. Optimal execution strategies in limit order books with general shape functions. Quantitative Finance, 10(2):143-157, 2010.
4. A. Alfonsi and A. Schied. Optimal trade execution and absence of price manipulations in limit order book models. SIAM Journal on Financial Mathematics, 1(1):490-522, 2010.
5. A. Alfonsi, A. Schied, and A. Slynko. Order book resilience, price manipulation, and the positive portfolio problem. SIAM Journal on Financial Mathematics, 3(1):511-533, 2012.
6. R. Almgren. Optimal execution with nonlinear impact functions and trading-enhanced risk. Applied Mathematical Finance, 10(1):1-18, 2003.
7. R. Almgren. Optimal trading with stochastic liquidity and volatility. SIAM Journal on Financial Mathematics, 3(1):163-181, 2012.
8. R. Almgren and N. Chriss. Value under liquidation. Risk, 12(12):61-63, 1999.
9. R. Almgren and N. Chriss. Optimal execution of portfolio transactions. Journal of Risk, 3:5-40, 2001.
10. R. Almgren, C. Thum, E. Hauptmann, and H. Li. Direct estimation of equity market impact. Risk, 18(7):58-62, 2005.
11. M. Avellaneda, A. Levy, and A. Parás. Pricing and hedging derivative securities in markets with uncertain volatilities. Applied Mathematical Finance, 2(2):73-88, 1995.
12. M. Avellaneda, J. Reed, and S. Stoikov. Forecasting prices from level-I quotes in the presence of hidden liquidity. Algorithmic Finance, 1(1):35- 43, 2011.
13. M. Avellaneda and S. Stoikov. High-frequency trading in a limit order book. Quantitative Finance, 8(3):217-224, 2008.
14. L. Bachelier. Théorie de la spéculation. Gauthier-Villars, 1900.
15. E. Bacry, A. Iuga, M. Lasnier, and C.-A. Lehalle. Market impacts and the life cycle of investors orders. Available at SSRN 2532152, 2014.
16. M. Bardi and I. Capuzzo-Dolcetta. Optimal control and viscosity solu- tions of Hamilton-Jacobi-Bellman equations. Springer Science & Business Media, 2008.
17. L. Bargeron, M. Kulchania, and S. Thomas. Accelerated share repurchases. Journal of Financial Economics, 101(1):69-89, 2011.
18. G. Barles and M. Soner. Option pricing with transaction costs and a nonlinear Black-Scholes equation. Finance and Stochastics, 2(4):369- 397, 1998.
19. E. Bayraktar and M. Ludkovski. Liquidation in limit order books with controlled intensity. Mathematical Finance, 24(4):627-650, 2014.
20. N. Bershova and D. Rakhlin. The non-linear market impact of large trades: Evidence from buy-side order flow. Quantitative Finance, 13(11):1759-1778, 2013.
21. D. Bertsimas and A. Lo. Optimal control of execution costs. Journal of Financial Markets, 1(1):1-50, 1998.
22. J. Bia lkowski, S. Darolles, and G. Le Fol. Improving VWAP strategies: A dynamic volume approach. Journal of Banking & Finance, 32(9):1709- 1722, 2008.
23. F. Black. How we came up with the option formula. Journal of Portfolio Management, 15(2):4-8, 1989.
24. F. Black and P. Karasinski. Bond and option pricing when short rates are lognormal. Financial Analysts Journal, 47(4):52-59, 1991.
25. F. Black and R. Litterman. Asset allocation: Combining investor views with market equilibrium. The Journal of Fixed Income, 1(2):7-18, 1991.
26. F. Black and M. Scholes. The pricing of options and corporate liabilities. The Journal of Political Economy, 81(3):637-654, 1973.
27. A. Bladon, E. Moro, and T. Galla. Agent-specific impact of single trades in financial markets. Physical Review E, 85(3):036103, 2012.
28. B. Bouchard and N.-M. Dang. Generalized stochastic target problems for pricing and partial hedging under loss constraints-application in optimal book liquidation. Finance and Stochastics, 17(1):31-72, 2013.
29. B. Bouchard, N.-M. Dang, and C.-A. Lehalle. Optimal control of trading algorithms: A general impulse control approach. SIAM Journal on Financial Mathematics, 2(1):404-438, 2011.
30. B. Bouchard, G. Loeper, and Y. Zou. Almost-sure hedging with permanent price impact. arXiv preprint arXiv:1503.05475, 2015.
31. J.-P. Bouchaud, Y. Gefen, M. Potters, and M. Wyart. Fluctuations and response in financial markets: The subtle nature of random price changes. Quantitative Finance, 4(2):176-190, 2004.
32. J.-P. Bouchaud, J. Kockelkoren, and M. Potters. Random walks, liquidity molasses and critical response in financial markets. Quantitative Finance, 6(2):115-123, 2006.
33. A. Brace, D. Gatarek, and M. Musiela. The market model of interest rate dynamics. Mathematical Finance, 7(2):127-155, 1997.
34. X. Brokmann, J. Kockelkoren, J.-P. Bouchaud, and E. Serie. Slow decay of impact in equity markets. Available at SSRN 2471528, 2014.
35. P. Cannarsa and C. Sinestrari. Semiconcave functions, Hamilton-Jacobi equations, and optimal control, volume 58. Springer Science & Business Media, 2004.
36. A. Carollo, G. Vaglica, F. Lillo, and R. Mantegna. Trading activity and price impact in parallel markets: SETS vs. off-book market at the London Stock Exchange. Quantitative Finance, 12(4):517-530, 2012.
37. Á. Cartea, R. Donnelly, and S. Jaimungal. Algorithmic trading with model uncertainty. Available at SSRN 2310645, 2013.
38. Á. Cartea and S. Jaimungal. Risk metrics and fine tuning of high frequency trading strategies. Mathematical Finance, 25(3):576-611, 2013.
39. Á. Cartea and S. Jaimungal. A closed-form execution strategy to target VWAP. Available at SSRN 2542314, 2014.
40. Á. Cartea and S. Jaimungal. Incorporating order- ow into optimal execution. Available at SSRN 2557457, 2015.
41. Á. Cartea and S. Jaimungal. Optimal execution with limit and market orders. Quantitative Finance, 15(8):1-13, 2015.
42. Á. Cartea and S. Jaimungal. Order- ow and liquidity provision. Avail- able at SSRN 2553154, 2015.
43. Á. Cartea, S. Jaimungal, and D. Kinzebulatov. Algorithmic trading with learning. Available at SSRN 2373196, 2014.
44. Á. Cartea, S. Jaimungal, and J. Penalva. Algorithmic and High- Frequency Trading. Cambridge University Press, 2015.
45. Á. Cartea, S. Jaimungal, and J. Ricci. Buy low, sell high: A high frequency trading perspective. SIAM Journal on Financial Mathematics, 5(1):415-444, 2014.
46. U. Çetin, R. Jarrow, and P. Protter. Liquidity risk and arbitrage pricing theory. Finance and Stochastics, 8(3):311-341, 2004.
47. U. Çetin, M. Soner, and N. Touzi. Option hedging for small investors under liquidity costs. Finance and Stochastics, 14(3):317-341, 2010.
48. L. Chan and J. Lakonishok. The behavior of stock prices around institutional trades. The Journal of Finance, 50(4):1147-1174, 1995.
49. T. Chemmanur, Y. Cheng, and T. Zhang. Why do firms undertake accelerated share repurchase programs? Available at SSRN 1570842, 2010.
50. R. Cont and A. de Larrard. Order book dynamics in liquid markets: Limit theorems and diffusion approximations. Available at SSRN 1757861, 2011.
51. R. Cont and A. Kukanov. Optimal order placement in limit order markets. arXiv preprint arXiv:1210.1625, 2012.
52. R. Cont, A. Kukanov, and S. Stoikov. The price impact of order book events. Journal of Financial Econometrics, 12(1):47-88, 2014.
53. R. Cont and L. Wagalath. Impact of large institutional investors on the dependence structure of asset returns. Working paper, 2013.
54. J. Cox, J. Ingersoll, and S. Ross. A theory of the term structure of interest rates. Econometrica, 53(2):385-407, 1985.
55. J. Cox, S. Ross, and M. Rubinstein. Option pricing: A simplified approach. Journal of Financial Economics, 7(3):229-263, 1979.
56. G. Curato, J. Gatheral, and F. Lillo. Optimal execution with nonlinear transient market impact. Available at SSRN 2539240, 2014.
57. J. Cvitanić, H. Pham, and N. Touzi. A closed-form solution to the problem of super-replication under transaction costs. Finance and Stochas- tics, 3(1):35-54, 1999.
58. K. Dayri and M. Rosenbaum. Large tick assets: Implicit spread and optimal tick size. Market Microstructure and Liquidity, 1(1):1550003, 2015.
59. J. Donier. Market impact with autocorrelated order flow under perfect competition. Available at SSRN 2191660, 2012.
60. J. Donier, J. Bonart, I. Mastromatteo, and J.-P. Bouchaud. A fully consistent, minimal model for non-linear market impact. Quantitative Finance, 15(7):1109-1121, 2015.
61. R. Donnelly. Ambiguity aversion in algorithmic and high frequency trading. Available at SSRN 2527808, 2014.
62. B. Dupire. Pricing with a smile. Risk, 7(1):18-20, 1994.
63. Z. Eisler, J.-P. Bouchaud, and J. Kockelkoren. The price impact of order book events: Market orders, limit orders and cancellations. Quantitative Finance, 12(9):1395-1419, 2012.
64. A. Esser and B. Mönch. The navigation of an iceberg: The optimal use of hidden orders. Finance Research Letters, 4(2):68-81, 2007.
65. J. D. Farmer, A. Gerig, F. Lillo, and S. Mike. Market effciency and the long-memory of supply and demand: Is price impact variable and permanent or fixed and temporary? Quantitative Finance, 6(2):107-112, 2006.
66. J. D. Farmer, A. Gerig, F. Lillo, and H. Waelbroeck. How effciency shapes market impact. Quantitative Finance, 13(11):1743-1758, 2013.
67. J. D. Farmer and F. Lillo. On the origin of power-law tails in price fluctuations. Quantitative Finance, 4(1):7-11, 2004.
68. J. D. Farmer, P. Patelli, and I. Zovko. The predictive power of zero intelligence in financial markets. Proceedings of the National Academy of Sciences of the United States of America, 102(6):2254-2259, 2005.
69. J.-D. Fermanian, O. Guéant, and A. Rachez. Agents behavior on multidealer- to-client bond trading platforms. Working paper, 2015.
70. P. Fodra and H. Pham. High frequency trading in a Markov renewal model. Available at SSRN 2333752, 2013.
71. P. Forsyth, J. Kennedy, S. Tse, and H. Windcliff. Optimal trade execution: A mean quadratic variation approach. Journal of Economic Dynamics and Control, 36(12):1971-1991, 2012.
72. T. Foucault, O. Kadan, and E. Kandel. Liquidity cycles and make/take fees in electronic markets. The Journal of Finance, 68(1):299-341, 2013.
73. C. Frei and N.Westray. Optimal execution of a VWAP order: A stochastic control approach. Mathematical Finance, 25(3):612-639, 2015.
74. J. Gatheral. No-dynamic-arbitrage and market impact. Quantitative Finance, 10(7):749-759, 2010.
75. J. Gatheral and A. Schied. Optimal trade execution under geometric Brownian motion in the Almgren and Chriss framework. International Journal of Theoretical and Applied Finance, 14(03):353-368, 2011.
76. J. Gatheral, A. Schied, and A. Slynko. Transient linear price impact and Fredholm integral equations. Mathematical Finance, 22(3):445-474, 2012.
77. L. Glosten and P. Milgrom. Bid, ask and transaction prices in a specialist market with heterogeneously informed traders. Journal of Financial Economics, 14(1):71-100, 1985.
78. R. Grinold and R. Kahn. Active portfolio management. McGraw Hill New York, 2000.
79. S. Grossman and M. Miller. Liquidity and market structure. The Journal of Finance, 43(3):617-633, 1988.
80. O. Guéant. Permanent market impact can be nonlinear. arXiv preprint arXiv:1305.0413, 2013.
81. O. Guéant. Execution and block trade pricing with optimal constant rate of participation. Journal of Mathematical Finance, 4:255-264, 2014.
82. O. Guéant. Optimal execution and block trade pricing: A general framework. Applied Mathematical Finance, 22(4):336-365, 2015.
83. O. Guéant. Market making on option markets. Working paper, 2016.
84. O. Guéant. Optimal market making. Working paper, 2016.
85. O. Guéant, J.-M. Lasry, and J. Pu. A convex duality method for optimal liquidation with participation constraints. Market Microstructure and Liquidity, 1(1):1550002, 2015.
86. O. Guéant and C.-A. Lehalle. General intensity shapes in optimal liquidation. Mathematical Finance, 25(3):457-495, 2015.
87. O. Guéant, C.-A. Lehalle, and J. Fernandez-Tapia. Optimal portfolio liquidation with limit orders. SIAM Journal on Financial Mathematics, 3(1):740-764, 2012.
88. O. Guéant, C.-A. Lehalle, and J. Fernandez-Tapia. Dealing with the inventory risk: A solution to the market making problem. Mathematics and Financial Economics, 7(4):477-507, 2013.
89. O. Guéant and J. Pu. Option pricing and hedging with execution costs and market impact. To appear in Mathematical Finance, 2016.
90. O. Guéant, J. Pu, and G. Royer. Accelerated share repurchase: Pricing and execution strategy. International Journal of Theoretical and Applied Finance, 18(3):1550019, 2015.
91. O. Guéant and G. Royer. VWAP execution and Guaranteed VWAP. SIAM Journal on Financial Mathematics, 5(1):445-471, 2014.
92. F. Guilbaud and H. Pham. Optimal high-frequency trading with limit and market orders. Quantitative Finance, 13(1):79-94, 2013.
93. J. Guyon. Path-dependent volatility. Risk Technical Paper, September 2014.
94. J. Guyon and P. Henry-Labordère. The smile calibration problem solved. Available at SSRN 1885032, 2011.
95. J. Guyon and P. Henry-Labordère. Nonlinear Option Pricing. CRC Press, 2013.
96. P. Hagan, D. Kumar, A. Lesniewski, and D.Woodward. Managing smile risk. Wilmott, pages 84-108, September 2002.
97. L. Harris. Trading and Exchanges: Market Microstructure for Practi- tioners. Oxford University Press, 2002.
98. L. Harris. Regulated Exchanges: Dynamic Agents of Economic Growth. Oxford University Press, 2010.
99. J. Harrison and D. Kreps. Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20(3):381-408, 1979.
100. J. Harrison and S. Pliska. Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and Their Applica- tions, 11(3):215-260, 1981.
101. D. Heath, R. Jarrow, and A. Morton. Bond pricing and the term structure of interest rates: A discrete time approximation. Journal of Finan- cial and Quantitative Analysis, 25(4):419-440, 1990.
102. D. Heath, R. Jarrow, and A. Morton. Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica, 60(1):77-105, 1992.
103. P. Henry-Labordère. Calibration of local stochastic volatility models to market smiles: A Monte-Carlo approach. Risk Magazine, September 2009.
104. S. Heston. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 6(2):327-343, 1993.
105. T. Ho and H. Stoll. Optimal dealer pricing under transactions and return uncertainty. Journal of Financial Economics, 9(1):47-73, 1981.
106. T. Ho and H. Stoll. The dynamics of dealer markets under competition. The Journal of Finance, 38(4):1053-1074, 1983.
107. C. Hopman. Do supply and demand drive stock prices? Quantitative Finance, 7(1):37-53, 2007.
108. U. Horst and F. Naujokat. When to cross the spread? Trading in two-sided limit order books. SIAM Journal on Financial Mathemat- ics, 5(1):278-315, 2014.
109. G. Huberman and W. Stanzl. Price manipulation and quasi-arbitrage. Econometrica, 72(4):1247-1275, 2004.
110. R. Huitema. Optimal portfolio execution using market and limit orders. Available at SSRN 1977553, 2014.
111. H. Hult and J. Kiessling. Algorithmic trading with Markov chains. Working paper, 2010.
112. M. Humphery-Jenner. Optimal VWAP trading under noisy conditions. Journal of Banking & Finance, 35(9):2319-2329, 2011.
113. S. Jaimungal, D. Kinzebulatov, and D. Rubisov. Optimal accelerated share repurchase. Available at SSRN 2360394, 2013.
114. S. Kakade, M. Kearns, Y. Mansour, and L. Ortiz. Competitive algorithms for VWAP and limit order trading. In Proceedings of the 5th ACM Conference on Electronic Commerce, pages 189-198. ACM, 2004.
115. D. Keim and A. Madhavan. The upstairs market for large-block transactions: Analysis and measurement of price effects. Review of Financial Studies, 9(1):1-36, 1996.
116. F. Klöck, A. Schied, and Y. Sun. Price manipulation in a market impact model with dark pool. Available at SSRN 1785409, 2011.
117. H. Konishi. Optimal slice of a VWAP trade. Journal of Financial Markets, 5(2):197-221, 2002.
118. P. Kovaleva and G. Iori. Optimal trading strategies in a limit order market with imperfect liquidity. Working paper, 2012.
119. P. Kratz and T. Schöneborn. Optimal liquidation in dark pools. Quan- titative Finance, 14(9):1519-1539, 2014.
120. P. Kratz and T. Schöneborn. Portfolio liquidation in dark pools in continuous time. Mathematical Finance, 25(3):496-544, 2015.
121. A. Kyle. Continuous auctions and insider trading. Econometrica: Jour- nal of the Econometric Society, 53(6):1315-1335, 1985.
122. M. Labadie and C.-A. Lehalle. Optimal starting times, stopping times and risk measures for algorithmic trading. The Journal of Investment Strategies, 3(2), 2014.
123. A. Lachapelle, J.-M. Lasry, C.-A. Lehalle, and P.-L. Lions. Effciency of the price formation process in presence of high frequency participants: A mean field game analysis. arXiv preprint arXiv:1305.6323, 2013.
124. S. Laruelle, C.-A. Lehalle, and G. Pagès. Optimal split of orders across liquidity pools: A stochastic algorithm approach. SIAM Journal on Financial Mathematics, 2(1):1042-1076, 2011.
125. C. Lee and M. Ready. Inferring trade direction from intraday data. The Journal of Finance, 46(2):733-746, 1991.
126. C.-A. Lehalle. The impact of liquidity fragmentation on optimal trading. Trading, 2009(1):80-87, 2009.
127. C.-A. Lehalle. Rigorous strategic trading: Balanced portfolio and meanreversion. The Journal of Trading, 4(3):40-46, 2009.
128. C.-A. Lehalle and S. Laruelle. Market Microstructure in Practice. World Scientific Publishing Ltd., 2013.
129. C.-A. Lehalle, M. Lasnier, P. Bessson, H. Harti, W. Huang, N. Joseph, and L. Massoulard. What does the saw-tooth pattern on US markets on 19 July 2012 tell us about the price formation process? Crédit Agricole Cheuvreux Quant Note, 2012.
130. H. Leland. Option pricing and replication with transactions costs. The Journal of Finance, 40(5):1283-1301, 1985.
131. D. Li. On default correlation: A copula function approach. Available at SSRN 187289, 1999.
132. T. Li. Dynamic Programming and Trade Execution. PhD thesis, Princeton University, 2013.
133. T. Li. Optimal limit-versus-market order slicing under a VWAP benchmark-discrete case. Available at SSRN 2318890, 2013.
134. T. Li and R. Almgren. Option hedging with smooth market impact. Working paper, 2015.
135. F. Lillo and J. D. Farmer. The long memory of the effcient market. Studies in Nonlinear Dynamics & Econometrics, 8(3), 2004.
136. F. Lillo, J. D. Farmer, and R. Mantegna. Single curve collapse of the price impact function for the New York Stock Exchange. arXiv preprint cond-mat/0207428, 2002.
137. F. Lillo, J. D. Farmer, and R. Mantegna. Econophysics: Master curve for price-impact function. Nature, 421(6919):129-130, 2003.
138. P.-L. Lions and J.-M. Lasry. Large investor trading impacts on volatility. Annales de l'IHP Analyse non linéaire, 24(2):311-323, 2007.
139. A. Lipton. The vol smile problem. Risk, 15(2):61-66, 2002.
140. J. Lorenz and R. Almgren. Mean-variance optimal adaptive execution. Applied Mathematical Finance, 18(5):395-422, 2011.
141. J. McCulloch. Relative volume as a doubly stochastic binomial point process. Quantitative Finance, 7(1):55-62, 2007.
142. J. McCulloch and V. Kazakov. Optimal VWAP trading strategy and relative volume. Working paper, 2007.
143. J. McCulloch and V. Kazakov. Mean variance optimal VWAP trading. Available at SSRN 1803858, 2012.
144. McKinsey & Company. Corporate bond e-trading: Same game, new playing field. Technical report, 2013.
145. A. Menkveld. High frequency trading and the new market makers. Jour- nal of Financial Markets, 16(4):712-740, 2013.
146. D. Mitchell, J. Bialkowski, and S. Tompaidis. Optimal VWAP tracking. Available at SSRN 2333916, 2013.
147. O. Morgenstern and J. von Neumann. Theory of Games and Economic Behavior. Princeton University Press, 1953.
148. E. Moro, J. Vicente, L. Moyano, A. Gerig, J. D. Farmer, G. Vaglica, F. Lillo, and R. Mantegna. Market impact and trading profile of hidden orders in stock markets. Physical Review E, 80(6), 2009.
149. Y. Nevmyvaka, Y. Feng, and M. Kearns. Reinforcement learning for optimized trade execution. In Proceedings of the 23rd International Conference on Machine Learning, pages 673-680. ACM, 2006.
150. K. Nyström, S. M. Ould Aly, and C. Zhang. Market making and portfolio liquidation under uncertainty. International Journal of Theoretical and Applied Finance, 17(5):1450034, 2014.
151. A. Obizhaeva and J. Wang. Optimal trading strategy and supply/ demand dynamics. Journal of Financial Markets, 16(1):1-32, 2013.
152. E. Platen and M. Schweizer. On feedback effects from hedging derivatives. Mathematical Finance, 8(1):67-84, 1998.
153. V. Plerou, P. Gopikrishnan, X. Gabaix, and H. Stanley. Quantifying stock-price response to demand fluctuations. Physical Review E, 66:027104, 2002.
154. M. Potters and J.-P. Bouchaud. More statistical properties of order books and price impact. Physica A: Statistical Mechanics and Its Ap- plications, 324(1):133-140, 2003.
155. R. Rockafellar. Conjugate convex functions in optimal control and the calculus of variations. Journal of Mathematical Analysis and Applica- tions, 32(1):174-222, 1970.
156. R. Rockafellar. Convex Analysis. Princeton University Press, 1970.
157. R. Rockafellar. Existence and duality theorems for convex problems of Bolza. Transactions of the American Mathematical Society, 159:1-40, 1971.
158. L. Rogers and S. Singh. The cost of illiquidity and its effects on hedging. Mathematical Finance, 20(4):597-615, 2010.
159. S. Ronnie and G. Papanicolaou. General Black-Scholes models accounting for increased market volatility from hedging strategies. Applied Mathematical Finance, 5(1):45-82, 1998.
160. W. Schachermayer and J. Teichmann. How close are the option pricing formulas of Bachelier and Black-Merton-Scholes? Mathematical Finance, 18(1):155-170, 2008.
161. A. Schied and T. Schöneborn. Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets. Finance and Stochastics, 13(2):181-204, 2009.
162. A. Schied, T. Schöneborn, and M. Tehranchi. Optimal basket liquidation for CARA investors is deterministic. Applied Mathematical Finance, 17(6):471-489, 2010.
163. C. Sprenkle. Warrant prices as indicators of expectations and preferences. Yale Economic Essays, 1(2):178-231, 1961.
164. S. Stoikov and M. Sağlam. Option market making under inventory risk. Review of Derivatives Research, 12(1):55-79, 2009.
165. H. Stoll. Inferring the components of the bid-ask spread: Theory and empirical tests. The Journal of Finance, 44(1):115-134, 1989.
166. R. Tachet des Combes. Non-Parametric Model Calibration in Finance. PhD thesis, École Centrale, 2011.
167. B. Tóth, Y. Lemperiere, C. Deremble, J. de Lataillade, J. Kockelkoren, and J.-P. Bouchaud. Anomalous price impact and the critical nature of liquidity in financial markets. Physical Review X, 1(2), 2011.
168. B. Tóth, I. Palit, F. Lillo, and J. D. Farmer. Why is equity order flow so persistent? Journal of Economic Dynamics and Control, 51:218-239, 2015.
169. S. Tse, P. Forsyth, J. Kennedy, and H. Windcliff. Comparison between the mean-variance optimal and the mean-quadratic-variation optimal trading strategies. Applied Mathematical Finance, 20(5):415-449, 2013.
170. O. Vasicek. An equilibrium characterization of the term structure. Jour- nal of Financial Economics, 5(2):177-188, 1977.
171. J. Wald and H. Horrigan. Optimal limit order choice. The Journal of Business, 78(2):597-620, 2005.
172. P. Weber and B. Rosenow. Order book approach to price impact. Quan- titative Finance, 5(4):357-364, 2005.
173. P. Wilmott. Frequently Asked Questions in Quantitative Finance. John Wiley & Sons, 2010.
174. P. Wilmott and P. Schönbucher. The feedback effect of hedging in illiquid markets. SIAM Journal on Applied Mathematics, 61(1):232-272, 2000.
175. A. Wranik. A trading system for flexible VWAP executions as a design artifact. PACIS 2009 Proceedings, 2009.
176. C. Yingsaeree. Algorithmic Trading: Model of Execution Probability and Order Placement Strategy. PhD thesis, University College London, 2012.
177. E. Zarinelli, M. Treccani, J. D. Farmer, and F. Lillo. Beyond the square root: Evidence for logarithmic dependence of market impact on size and participation rate. arXiv preprint arXiv:1412.2152, 2014.