Application of State Space Hidden Markov Models to the approximation of (embedded) option prices

Application of State Space Hidden Markov Models to the approximation of (embedded) option prices

Alberts, J.S.C.

Oosterlee, C.W. (mentor)

Electrical Engineering, Mathematics and Computer Science

Applied Mathematics

2016-11-25

This thesis discusses dimension reduction of the risk drivers that determine embedded option values by using the class of State Space Hidden Markov Models. As embedded options are typically valued by nested Monte Carlo simulations, this dimension reduction leads to a major reduction in computing time. This is especially important for insurance companies that are dealing with many embedded option valuations in order to determine the market value of their liabilities. To achieve the dimension reduction of the risk driver process, this thesis proposes a specifi c Hidden Markov Model approach. An overview on current methods for state and parameter inference within this class of models is presented. For the state-of-the-art CPF-SAEM method insights are obtained by investigating an example of the dimension reduction model. Furthermore, the satisfactory behavior of this HMM approach is investigated in more detail for multiple (market) cases. Lastly, the dimension reduction model is applied to calibration of the Heston model parameters to market data. It is shown that this approach avoids over fitting issues and results in a more stable model than direct calibration of the parameters.

dimension reduction
option valuation
state space hidden Markov models

http://resolver.tudelft.nl/uuid:4e193978-6886-461a-8225-4d338c354b98

Student theses

master thesis

(c) 2016 Alberts, J.S.C.