Inverse Problems and Imaging (IPI)

Data driven recovery of local volatility surfaces
Pages: 799 - 823, Issue 5, October 2017

doi:10.3934/ipi.2017038      Abstract        References        Full text (1873.6K)           Related Articles

Vinicius Albani - Dept. of Mathematics, UFSC, Florianopolis, Brazil (email)
Uri M. Ascher - Dept. of Computer Science, University of British Columbia, Canada (email)
Xu Yang - IMPA, Rio de Janeiro, Brazil (email)
Jorge P. Zubelli - IMPA, Rio de Janeiro, Brazil (email)

1 Y. Achdou and O. Pironneau, Computational Methods for Option Pricing, SIAM, 2005.       
2 Y. Achdou and O. Pironneau, Numerical procedure for calibration of volatility with American options, Applied Mathematical Finance, 12 (2007), 201-241.
3 V. Albani, U. Ascher and J. Zubelli, Local volatility models in commodity markets and online calibration, J. Computational Finance, 2017. Accepted, to appear.
4 V. Albani and J. P. Zubelli, Online local volatility calibration by convex regularization, Appl. Anal. Discrete Math., 8 (2014), 243-268.       
5 U. Ascher, H. Huang and K. van den Doel, Artificial time integration, BIT, 47 (2007), 3-25.       
6 F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Pol. Econ., 81 (1973), 637-654.       
7 P. Boyle and D. Thangaraj, Volatility estimation from observed option prices, Decisions in Economics and Finance, 23 (2000), 31-52.       
8 D. Calvetti, O. Ernst and E. Somersalo, Dynamic updating of numerical model discrepancy using sequential sampling, Inverse Problems, 30 (2014), 114019, 19pp.       
9 A. De Cezaro, O. Scherzer and J. Zubelli, Convex regularization of local volatility models from option prices: convergence analysis and rates, Nonlinear Analysis, 75 (2012), 2398-2415.       
10 A. De Cezaro and J. P. Zubelli, The tangential cone condition for the iterative calibration of local volatility surfaces, IMA Journal of Applied Mathematics, 80 (2015), 212-232.       
11 B. Dupire, Pricing with a smile, Risk, 7 (1994), 18-20.
12 H. Egger and H. Engl, Tikhonov regularization applied to the inverse problem of option pricing: convergence analysis and rates, Inverse Problems, 21 (2005), 1027-1045.       
13 H. W. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems, Kluwer, 1996.       
14 J. Gatheral, The Volatility Surface: A Practitioner's Guide, Wiley Finance. John Wiley & Sons, 2006.
15 J. Granek and E. Haber, Data mining for real mining: A robust algorithm for prospectivity mapping with uncertainties, Proc. SIAM Conference on Data Mining, (2015), 9pp.
16 E. Haber, U. Ascher and D. Oldenburg, Inversion of 3D electromagnetic data in frequency and time domain using an inexact all-at-once approach, Geophysics, 69 (2004), 1216-1228.
17 B. Hofmann and R. Krämer, On maximum entropy regularization for a specific inverse problem of option pricing, J. Inverse Ill-Posed Problems, 13 (2005), 41-63.       
18 B. Hofmann, B. Kaltenbacher, C. Pöschl and O. Scherzer, A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators, Inverse Problems, 23 (2007), 987-1010.       
19 H. Huang and U. Ascher, Fast denoising of surface meshes with intrinsic texture, Inverse Problems, 24 (2008), 034003, 18pp.       
20 M. Iglesias, K. Law and A. Stuart, Ensemble Kalman methods for inverse problems, Inverse Problems, 29 (2013), 045001, 20pp.       
21 R. Jarrow, Y. Kchia and P. Protter, How to detect an asset bubble, SIAM J. Financial Mathematics, 2 (2011), 839-865.       
22 C. Johns and J. Mandel, A two-stage ensemble Kalman filter for smooth data assimilation, Environmental and Ecological Statistics, 15 (2008), 101-110.       
23 N. Kahale, Smile interpolation and calibration of the local volatility model, Risk Magazine, 1 (2005), 637-654.
24 R. Korn and E. Korn, Option Price and Portfolio Optimization: Modern Methods of Mathematical Finance, volume 31 of Graduate Studies in Mathematics, AMS, 2001.       
25 R. Kumar, C. da Silva, O. Aklain, A. Aravkin, H. Mansour, B. Recht and F. Herrmann, Efficient matrix completion for seismic data reconstruction, Geophysics, 80 (2015), 97-114.
26 G. Nakamura and R. Potthast, Inverse Problems. An Introduction to the Theory and Methods of Inverse Problems and Data Assimilation, IOP Publishing, 2015.
27 S. Reich and C. Cotter, Probabilistic Forecasting and Bayesian Data Assimilation, Cambridge, 2015.       
28 F. Roosta-Khorasani, K. van den Doel and U. Ascher, Data completion and stochastic algorithms for PDE inversion problems with many measurements, ETNA, 42 (2014), 177-196.       
29 C. Vogel, Computational Methods for Inverse Problem, SIAM, Philadelphia, 2002.       

Go to top