Numerical Validation of the Continuous Time Markov Chain Approximation as a Service Level Estimation Method for Heterogeneous Customer Demand Classes

2019 ◽  
Author(s):  
Oguzhan VICIL
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Estimation Method ◽  
Service Level ◽  
Continuous Time Markov Chain ◽  
Customer Demand ◽  
Markov Chain Approximation ◽  
Numerical Validation ◽  
Demand Classes ◽  
Chain Approximation

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.

AN IMPROVED MARKOV CHAIN APPROXIMATION METHODOLOGY: DERIVATIVES PRICING AND MODEL CALIBRATION

2014 ◽  
Vol 17 (07) ◽  
pp. 1450047 ◽  
Author(s):  
CHIA CHUN LO ◽  
KONSTANTINOS SKINDILIAS
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Empirical Studies ◽  
Jump Diffusion ◽  
Model Parameters ◽  
Underlying Distribution ◽  
Markov Chain Approximation ◽  
Proposed Model ◽  
Jump Diffusion Model ◽  
Chain Approximation

This paper presents an improved continuous-time Markov chain approximation (MCA) methodology for pricing derivatives and for calibrating model parameters. We propose a generalized nonequidistant grid model for a general stochastic differential equation, and extend the proposed model to accommodate a jump component. Because the prices of derivatives generated by the MCA models are sensitive to the setting of the chain's state space, we suggest a heuristic determination of the grid spacing such that the Kolmogorov–Smirnov distance between the underlying distribution and the MCA distribution is minimized. The continuous time setting allows us to introduce semi-analytical formulas for pricing European and American style options. The numerical examples demonstrate that the proposed model with a nonequidistant grid setting provides superior results over the equidistant grid setting. Finally, we present the MCA maximum likelihood estimator for a jump-diffusion process. The encouraging results from the simulation and empirical studies provide insight into calibration problems in finance where the density function of a jump-diffusion model is unknown.

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