MARKOV-CHAIN MODULATED IMPLIED LIQUIDITY: MODELING AND ESTIMATION

Date

2023-5-16

Author

Yerli, Çiğdem

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This thesis presents a methodology for modeling the implied liquidity which is introduced through the Conic Finance theory, and considered a proxy for the market liquidity level. We propose a partial information setting in which the dynamics of implied liquidity, representing the noisy information on the unobserved true market liquidity, follow a continuous-time Markov-chain modulated exponential OrnsteinUhlenbeck process. Model inference requires the filtering of the unobserved states of the true market liquidity, as well as the estimation of the unknown model parameters. We address the inference problem by the EM algorithm. The expectation step of the algorithm requires the derivation of finite dimensional filters for the quantities present in the likelihood function. To this end, we first review the existing EM algorithm for the OU process and provide detailed proofs. The application of the algorithm in practice needs discretizing the resulting filters. In order to avoid numerical issues and make the algorithm to function, we introduce filters that have a continuous dependence on the observations. The corresponding filters are known as robust filters. Instead of directly discretizing continuous time filters, we discretize the robust filters that help us to work under the discrete time setting and also enable us to obtain the variance estimate of the model within the EM algorithm. We evaluate the performance of the algorithm and compare it to existing alternatives in the literature using an extensive simulation study. The performance evaluation is based on the sensitivity to changes in step size, drift, and volatility parameters. This step is crucial for refining the methods and establishing a connection between theory and practice. Once the algorithm is tested with simulated data, we apply the proposed model to real world data. The data set is comprised of implied market liquidity series retrieved from the S&P 500 option data covering the period from January 2002 to August 2022. Our application results show that three liquidity regimes can describe the market liquidity level: high, intermediate and low. The estimation results confirm the effect of the overall economic environment on the market liquidity.

Subject Keywords

Expectation maximization (EM) algorithm, hidden Markov models, Ornstein-Uhlenbeck processes, robust filters, implied liquidity

URI

https://hdl.handle.net/11511/103699

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Graduate School of Applied Mathematics, Thesis