A generalized Esscher transform for option valuation with regime switching risk

2021 ◽  
pp. 1-15
Author(s):  
R. J. Elliott ◽  
T. K. Siu
Keyword(s):  
Regime Switching ◽  
Option Valuation ◽  
Esscher Transform

OPTION PRICING FOR GARCH MODELS WITH MARKOV SWITCHING

2006 ◽  
Vol 09 (06) ◽  
pp. 825-841 ◽  
Author(s):  
ROBERT J. ELLIOTT ◽  
TAK KUEN SIU ◽  
LEUNGLUNG CHAN
Keyword(s):  
Markov Switching ◽  
Martingale Measure ◽  
Maximization Problem ◽  
Option Valuation ◽  
Chain Process ◽  
Esscher Transform ◽  
Actuarial Science ◽  
Power Utility ◽  
Alternative Approach ◽  
Utility Maximization Problem

In this paper we develop a method for pricing derivatives under a Markov switching version of the Heston-Nandi GARCH (1, 1) model by using a well known tool from actuarial science, namely the Esscher transform. We suppose that the dynamics of the GARCH process switch over time according to one of the regimes described by the states of an observable Markov chain process. By augmenting the conditional Esscher transform with the observable Markov switching process, a Markov switching conditional Esscher transform (MSCET) is developed to identify a martingale measure for option valuation in the incomplete market described by our model. We provide an alternative approach for the derivation of an analytical option valuation formula under the Markov switching Heston-Nandi GARCH (1, 1) model. The use of the MSCET can be justified by considering a utility maximization problem with respect to a power utility function associated with the Markov switching risk-averse parameters.

Option pricing and Esscher transform under regime switching

2005 ◽  
Vol 1 (4) ◽  
pp. 423-432 ◽  
Author(s):  
Robert J. Elliott ◽  
Leunglung Chan ◽  
Tak Kuen Siu
Keyword(s):  
Option Pricing ◽  
Regime Switching ◽  
Esscher Transform

scholarly journals Pricing equity linked annuities under regime-switching generalized gamma process

2015 ◽  
Vol 12 (3) ◽  
pp. 250-260
Author(s):  
Armin Pourkhanali ◽  
Farzad Alavi Fard
Keyword(s):  
Continuous Time ◽  
Regime Switching ◽  
Continuous Time Markov Chain ◽  
Option Prices ◽  
Esscher Transform ◽  
Gamma Model ◽  
Generalized Gamma ◽  
Market Interest Rate ◽  
Embedded Options ◽  
Simulation Results

We propose a model for valuing equity linked annuity (ELA) products under a generalized gamma model with a Markov-switching compensator. We suppose that the market interest rate and all the parameters of the underlying reference portfolio switch over time according to the state of an economy, which is modelled by a continuous-time Markov chain. The model considered here can provide market practitioners with flexibility in modelling the dynamics of the reference portfolio. We price the ELA by pricing its embedded options, for which we employ the regime-switching version of Esscher transform to determine the pricing kernel. A system of coupled partial-differential-integral equations satisfied by the embedded option prices is derived. Simulation results of the model have been presented and discussed

Option Valuation Under a Double Regime-Switching Model

2013 ◽  
Vol 34 (5) ◽  
pp. 451-478 ◽  
Author(s):  
Yang Shen ◽  
Kun Fan ◽  
Tak Kuen Siu
Keyword(s):  
Regime Switching ◽  
Option Valuation ◽  
Regime Switching Model ◽  
Switching Model
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