Distribution of the exit time and value for homogeneous processes with independent increments given on a finite Markov chain

1975 ◽  
Vol 26 (3) ◽  
pp. 239-245
Author(s):  
D. V. Gusak ◽  
S. I. Peresypkina
Keyword(s):  
Markov Chain ◽  
Exit Time ◽  
Finite Markov Chain ◽  
Independent Increments ◽  
Processes With Independent Increments

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.

scholarly journals Global sensitivity analysis for stochastic processes with independent increments

2020 ◽  
Vol 62 ◽  
pp. 103098
Author(s):  
Emeline Gayrard ◽  
Cédric Chauvière ◽  
Hacène Djellout ◽  
Pierre Bonnet ◽  
Don-Pierre Zappa
Keyword(s):  
Sensitivity Analysis ◽  
Stochastic Processes ◽  
Global Sensitivity Analysis ◽  
Global Sensitivity ◽  
Independent Increments ◽  
Processes With Independent Increments
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