On the microstructural hedging error

SIAM Journal on Financial Mathematics

Volumn 1, Issue 1, 2010, Pages 427-453

  Robert, Christian Y ^a   Rosenbaum, Mathieu ^b  

^a CREST   (France)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

Continuous time processes; Discrete hedging; Endogenous trading times; Limit theorems for martingales; Microstructure noise; Stable convergence in law

Indexed keywords

EID: 79954607942     PISSN: None     EISSN: 1945497X     Source Type: Journal    
DOI: 10.1137/090764578     Document Type: Article

References (28)

1. O. E. Barndorff-Nielsen P. R Hansen A. Lunde and N. Shephard Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise Econometrica 76 (2009) pp. 1481-1536.
2. D. Bertsimas L. Kogan and A. W. Lo When is time continuous? J. Financial Econ. 55 (2000) pp. 173-204.
3. U. Cetin M. Soner and N. Touzi Option hedging for small investors under liquidity costs Finance Stoch. to appear.
4. D. Duffie Dynamic Asset Pricing Theory 3rd ed. Princeton Ser. Finance Princeton University Press Princeton NJ 2002.
5. N. El Karoui M. Jeanblanc-Picqúe and S. Shreve Robustness of the Black and Scholes formula Math. Finance 8 (1998) pp. 93-126.
6. M. Fukasawa Discretization Error of Stochastic Integrals Working paper 2009.
7. C. Geiss and S. Geiss On an approximation problem for stochastic integrals where random time nets do not help Stochastic Process. Appl. 116 (2006) pp. 407-422.
8. S. Geiss Quantitative approximation of certain stochastic integrals Stoch. Stoch. Rep. 73 (2002) pp. 241-270.
9. S. Geiss and A. Toivola Weak convergence of error processes in discretizations of stochastic integrals and Besov spaces Bernoulli 15 (2009) pp. 925-954.
10. V. Genon-Catalot and J. Jacod On estimating the diffusion coefficient for multidimensional processes Ann. Inst. H. Poincaŕe Probab. Statist. 29 (1993) pp. 119-151.
11. E. Gobet and E. Temam Discrete time hedging errors for options with irregular pay-offs Finance Stoch. 5 (2001) pp. 357-367.
12. T. Hayashi and P. A. Mykland Hedging errors: An asymptotic approach Math. Finance 15 (2005) pp. 309-343.
13. J. Jacod Y. Li P. A. Mykland M. Podolskij and M. Vetter Microstructure noise in the continuous case: The pre-averaging approach Stochastic Process. Appl. 119 (2009) pp. 2249-2276.
14. J. Jacod and A. N. Shiryaev Limit Theorems for Stochastic Processes 2nd ed. Springer-Verlag Berlin 2003.
15. E. Jouini and H. Kallal Arbitrage in securities markets with short sales constraints Math. Finance 5 (1995) pp. 197-232.
16. Y. M. Kabanov and G. Last Hedging under transaction costs in currency markets: A continuous-time model Math. Finance 12 (2002) pp. 63-70.
17. Y. M. Kabanov and M. M. Safarian On Leland's strategy of option pricing with transactions costs Finance Stoch. 1 (1997) pp. 239-250.
18. I. Kalnina and O. B. Linton Estimating quadratic variation consistently in the presence of correlated measurement error J. Econometrics 147 (2008) pp. 47-59.
19. P. F. Koehl H. Pham and N. Touzi Hedging in discrete time under transaction costs and continuoustime limit J. Appl. Probab. 36 (1999) pp. 163-178.
20. Y. Li P. A. Mykland E. Renault L. Zhang and X. Zheng Realized Volatility When Sampling Times Are Possibly Endogenous Working paper 2009.
21. D. Revuz and M. Yor Continuous Martingales and Brownian Motion 3rd ed. Springer-Verlag Berlin 1999.
22. C. Y. Robert and M. Rosenbaum A new approach for the dynamics of ultra high frequency data: The model with uncertainty zones J. Financial Econometrics to appear.
23. C. Y. Robert and M. Rosenbaum Volatility and covariation estimation when microstructure noise and trading times are endogenous Math. Finance to appear.
24. R. Roll A simple implicit measure of the effective bid-ask spread in an efficient market J. Finance 39 (2009) pp. 1127-1139.
25. M. Rosenbaum Integrated volatility and round-off error Bernoulli 15 (2009) pp. 687-720.
26. P. Tankov and E. Voltchkova Asymptotic analysis of hedging errors in models with jumps Stochastic Process. Appl. 119 (2009) pp. 2004-2027.
27. L. Zhang Efficient estimation of stochastic volatility using noisy observations: A multi-scale approach Bernoulli 12 (2006) pp. 1019-1043.
28. L. Zhang P. A. Mykland and Y. Aǐt-Sahalia A tale of two time scales: Determining integrated volatility with noisy high-frequency data J. Amer. Statist. Assoc. 100 (2005) pp. 1394-1411.