markov chain approximations
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2019 ◽  
Vol 34 ◽  
pp. 183-201
Author(s):  
Giulio Fella ◽  
Giovanni Gallipoli ◽  
Jutong Pan

2019 ◽  
Vol 12 (2) ◽  
pp. 69
Author(s):  
Dilip B. Madan ◽  
Wim Schoutens

It is argued that the growth in the breadth of option strikes traded after the financial crisis of 2008 poses difficulties for the use of Fourier inversion methodologies in volatility surface calibration. Continuous time Markov chain approximations are proposed as an alternative. They are shown to be adequate, competitive, and stable though slow for the moment. Further research can be devoted to speed enhancements. The Markov chain approximation is general and not constrained to processes with independent increments. Calibrations are illustrated for data on 2695 options across 28 maturities for S P Y as at 8 February 2018.


2018 ◽  
Author(s):  
Giulio Fella ◽  
Giovanni Gallipoli ◽  
Jutong Pan

2015 ◽  
Vol 125 (10) ◽  
pp. 3932-3957 ◽  
Author(s):  
Aleksandar Mijatović ◽  
Matija Vidmar ◽  
Saul Jacka

2015 ◽  
Vol 15 (02) ◽  
pp. 1550009 ◽  
Author(s):  
Jan Gairing ◽  
Michael Högele ◽  
Tetiana Kosenkova ◽  
Alexei Kulik

We introduce the notion of coupling distances on the space of Lévy measures in order to quantify rates of convergence towards a limiting Lévy jump diffusion in terms of its characteristic triplet, in particular in terms of the tail of the Lévy measure. The main result yields an estimate of the Wasserstein–Kantorovich–Rubinstein distance on path space between two Lévy diffusions in terms of the coupling distances. We want to apply this to obtain precise rates of convergence for Markov chain approximations and a statistical goodness-of-fit test for low-dimensional conceptual climate models with paleoclimatic data.


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