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November 2013Abstract In this paper we propose a multivariate asset model based on Lévy processes for pricing of products written on more than one underlying asset. Our construction is based on a two factor representation of the dynamics of the asset log-returns. We investigate the properties of the model and introduce a multivariate generalization of some processes which are quite common in financial applications, such as subordinated Brownian motions, jump diffusion processes and time changed Lévy processes. Finally, we explore the issue of model calibration for the proposed setting and illustrate its robustness on a number of numerical examples.
In this note we introduce a theoretical model for the pricing and valuation of guaranteed annuity conversion options associated with certain deferred annuity pension-type contracts in the UK. The valuation approach is based on the similarity between the payoff structure of the contract and a call option written on a coupon-bearing bond. The model makes use of a one-factor Heath-Jarrow-Morton framework for the term structure of interest rates. Numerical results are investigated and the sensitivity of the price of the option to changes in the key parameters is also analyzed.
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AbstractIn this communication, we develop suitable valuation techniques for a with-profit/unitized with profit life insurance policy providing interest rate guarantees, when a jump-diffusion process for the evolution of the underlying reference portfolio is used. Particular attention is given to the mispricing generated by the misspecification of a jump-diffusion process for the underlying asset as a pure diffusion process, and to which extent this mispricing affects the profitability and the solvency of the life insurance company issuing these contracts.
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AbstractThe purpose of the paper is to apply contingent claim theory to the valuation of the type of participating life insurance policies commonly sold in the UK. The paper extends the techniques developed by Haberman et al. (2003) to allow for the default option. The default option is a feature of the design of these policies, which recognizes that the insurance company's liability is limited by the market value of the reference portfolio of assets underlying the policies that have been sold. The valuation approach is based on the classical contingent claim pricing "machinery", underpinned by Monte Carlo techniques for the computation of fair values. The paper addresses in particular the issue of a fair contract design for a complex type of participating policy and analyzes in detail the feasible set of policy design parameters that would lead to a fair contract and the trade-offs between these parameters.
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