Simultaneous Two-Dimensional Continuous-Time Markov Chain Approximation of Two-Dimensional Fully Coupled Markov Diffusion Processes

2019 ◽  
Author(s):  
Yuejuan Xi ◽  
Kailin Ding ◽  
Ning Ning
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Diffusion Processes ◽  
Two Dimensional ◽  
Continuous Time Markov Chain ◽  
Markov Chain Approximation ◽  
Markov Diffusion ◽  
Chain Approximation ◽  
Fully Coupled

scholarly journals Arbitrage Free Approximations to Candidate Volatility Surface Quotations

2019 ◽  
Vol 12 (2) ◽  
pp. 69
Author(s):  
Dilip B. Madan ◽  
Wim Schoutens
Keyword(s):  
Markov Chain ◽  
Continuous Time Markov Chain ◽  
Fourier Inversion ◽  
Markov Chain Approximation ◽  
Independent Increments ◽  
Markov Chain Approximations ◽  
Processes With Independent Increments ◽  
Volatility Surface ◽  
The Moment ◽  
Chain Approximation

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.

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