Parameter Estimation for Pricing a Guaranteed Minimum Maturity Benefit in a Hidden Markov Model Setting
Date
2021-07-23
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
The work attempts to understand the strengths and weaknesses of choosing between two calibrating techniques in a hidden Markov setting for pricing an equity-linked Guaranteed Minimum Maturity Benefit (GMMB) contract. We study an integrated framework for the valuation of GMMB. We assume that the dynamics of interest rate, mortality rate, and equity index are all driven by a hidden Markov model. All parameters are modulated using a discrete-time hidden Markov chain that switches between economic regimes reflecting different economic conditions. Numerical implementations use financial market data in real-time. First method uses a form of a static updating of parameters using the Expectation Maximization algorithm introduced by Hamilton (1989). The second method involves a dynamic updating of parameters. The method was introduced by Elliot (1994) and utilizes the change of measure technique to derive multivariate linear filters, which in turn is used to obtain online optimal parameter estimates. First, we carry out comprehensive simulation studies under both calibrating methods to investigate for the statistical computing stability and the accuracy of parameter estimates which are used in the pricing framework. A Monte Carlo simulation is used for pricing the GMMB under both frameworks. The study also provides a real-world example for pricing GMMBs using historical interest rates, force of mortality rates and equity indices values under the proposed methods. Finally, the study presents a detailed conclusion on strengths , weaknesses and aptness of using either methods. The work contributes to existing literature in two ways. Firstly, this research appears to be the first work to implement Expectation Minimization algorithm of Hamilton (1989) to discuss calibration of parameters for the purpose of pricing a GMMB in a unified framework. Secondly, the study contributes to existing literature through presenting a detailed comparative analysis of strengths and weaknesses of choosing between two prominent hidden Markov modelling Frameworks for pricing equity-linked GMMB contracts.
Description
Keywords
Guaranteed Minimum Maturity Benefit, Hidden Markov, Filtering, EM algorithm, Change of Probability
Citation
Thalagoda, G. K. (2021). Parameter Estimation for Pricing a Guaranteed Minimum Maturity Benefit in a Hidden Markov Model Setting (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.