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On the modelling of nested risk-neutral stochastic processes with applications in insurance

On the modelling of nested risk-neutral stochastic processes with applications in insurance We propose a modelling framework for risk-neutral stochastic processes nested in a real-world stochastic process. The framework is important for insurers that deal with the valuation of embedded options and in particular at future points in time. We make use of the class of State Space Hidden Markov models for modelling the joint behaviour of the parameters of a risk-neutral model and the dynamics of option market instruments. This modelling concept enables us to perform non-linear estimation, forecasting and robust calibration. The proposed method is applied to the Heston model for which we find highly satisfactory results. We use the estimated Heston model to compute the required capital of an insurance company under Solvency II and we find large differences compared to a basic calibration method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematical Finance Taylor & Francis

On the modelling of nested risk-neutral stochastic processes with applications in insurance

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On the modelling of nested risk-neutral stochastic processes with applications in insurance

Abstract

We propose a modelling framework for risk-neutral stochastic processes nested in a real-world stochastic process. The framework is important for insurers that deal with the valuation of embedded options and in particular at future points in time. We make use of the class of State Space Hidden Markov models for modelling the joint behaviour of the parameters of a risk-neutral model and the dynamics of option market instruments. This modelling concept enables us to perform non-linear...
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Publisher
Taylor & Francis
Copyright
© 2017 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1466-4313
eISSN
1350-486X
DOI
10.1080/1350486X.2017.1378583
Publisher site
See Article on Publisher Site

Abstract

We propose a modelling framework for risk-neutral stochastic processes nested in a real-world stochastic process. The framework is important for insurers that deal with the valuation of embedded options and in particular at future points in time. We make use of the class of State Space Hidden Markov models for modelling the joint behaviour of the parameters of a risk-neutral model and the dynamics of option market instruments. This modelling concept enables us to perform non-linear estimation, forecasting and robust calibration. The proposed method is applied to the Heston model for which we find highly satisfactory results. We use the estimated Heston model to compute the required capital of an insurance company under Solvency II and we find large differences compared to a basic calibration method.

Journal

Applied Mathematical Finance – Taylor & Francis

Published: Jul 4, 2017

Keywords: State Space Hidden Markov; nested simulations; risk-neutral valuation; robust calibration; Heston; solvency II

References

  • On the Calculation of the Solvency Capital Requirement Based on Nested Simulations
  • Solvency II and Nested Simulations–A Least-Squares Monte Carlo Approach
  • On the Risk-Neutral Valuation of Life Insurance Contracts with Numerical Methods in View
  • Inference in Hidden Markov Models
  • A New Simple Approach for For Constructing Implied Volatility Surfaces
  • Dynamics of Implied Volatility Surfaces
  • Fins: A Framework for Accelerating Nested Simulations on Heterogeneous Platforms
  • Convergence of a Stochastic Approximation Version of the EM Algorithm
  • Maximum Likelihood from Incomplete Data via the EM Algorithm
  • A Tutorial on Particle Filtering and Smoothing: Fifteen Years Later
  • A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions
  • Efficient Computation of Exposure Profiles on Real-World and Risk-Neutral Scenarios for Bermudan Swaptions
  • Arbitrage-Free SVI Volatility Surfaces
  • On the Heston Model with Stochastic Interest Rates
  • A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
  • Implied Volatility Surface: Construction Methodologies and Characteristics
  • The Stochastic Grid Bundling Method: Efficient Pricing of Bermudan Options and Their Greeks
  • Coupling a Stochastic Approximation Version of EM with an MCMC Procedure
  • An Efficient Stochastic Approximation EM Algorithm Using Conditional Particle Filters
  • Particle Gibbs with Ancestor Sampling
  • System Identification of Nonlinear State-Space Models
  • Joining Risks and Rewards
  • Fixing Underexposed Snapshots–Proper Computation of Credit Exposures under the Real World and Risk Neutral Measures