Dynamic Hedging Under Jump Diffusion with Transaction Costs

Kennedy, J. S.; Vetzal, Kenneth R.

doi:10.1287/opre.1080.0598

Cited by 44 publications

(19 citation statements)

References 27 publications

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“…Table 5 shows that ignoring the possibility of jumps for long term guarantees may severely underestimate the hedging cost. Methods for hedging contracts under jump diffusions are discussed in (He et al, 2006;Kennedy et al, 2006).…”

Section: Incorporating Price Jumpsmentioning

confidence: 99%

The effect of modelling parameters on the value of GMWB guarantees

Chen

Vetzal

Forsyth

2008

Insurance: Mathematics and Economics

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In this article, an extensive study of the no-arbitrage fee for Guaranteed Minimum Withdrawal Benefit (GMWB) variable annuity riders is carried out. Taking into account such contractual features as the separation of mutual fund fees and the fees earmarked for hedging the guarantee, as well as the possibility of jumps in the value of the underlying asset, increases the value of the GMWB guarantee considerably. We also explore the effects of various modelling assumptions on the optimal withdrawal strategy of the contract holder, as well as the impact on the guarantee value of sub-optimal withdrawal behaviour. Our general conclusions are that only if several unrealistic modelling assumptions are made is it possible to obtain GMWB fees in the same range as is normally charged. In all other cases, it would appear that typical fees are not enough to cover the cost of hedging these guarantees.

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Section: Incorporating Price Jumpsmentioning

confidence: 99%

The effect of modelling parameters on the value of GMWB guarantees

Chen

Vetzal

Forsyth

2008

Insurance: Mathematics and Economics

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“…This contrasts with the jump-diffusion model with random jump size when perfect hedging is impossible as it would require an infinite number of hedging instruments. However even in this case it has been found that an acceptable reduction in risk can be achieved with a fairly small number of hedging assets (Kennedy et al, 2009). …”

Section: Specification Of the Optimal Harvesting Problem And Its Numementioning

confidence: 95%

Regime switching in stochastic models of commodity prices: An application to an optimal tree harvesting problem

Shan

Insley

2012

Journal of Economic Dynamics and Control

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This paper investigates whether a regime switching model of stochastic lumber prices is better for the analysis of optimal harvesting problems in forestry than a more traditional single regime model. Prices of lumber derivatives are used to calibrate a regime switching model, with each of two regimes characterized by a different mean reverting process. A single regime, mean reverting process is also calibrated. The value of a representative stand of trees and optimal harvesting prices are determined by specifying a Hamilton-JacobiBellman Variational Inequality, which is solved for both pricing models using a fully implicit finite difference approach. The regime switching model is found to more closely match the behaviour of futures prices than the single regime model. In addition, analysis of a tree harvesting problem indicates significant differences in terms of land value and optimal harvest thresholds between the regime switching and single regime models.JEL Classification: C63, C61, Q23, D81

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“…A typical modelling choice for the probability density of the jump size p(ξ) is to assume a log-normal distribution [20,1,17],…”

Section: Formulationmentioning

confidence: 99%

Iterative methods for the solution of a singular control formulation of a GMWB pricing problem

Huang

Labahn

2012

Numer. Math.

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Discretized singular control problems in finance result in highly nonlinear algebraic equations which must be solved at each timestep. We consider a singular stochastic control problem arising in pricing a Guaranteed Minimum Withdrawal Benefit (GMWB), where the underlying asset is assumed to follow a jump diffusion process. We use a scaled direct control formulation of the singular control problem and examine the conditions required to ensure that a fast fixed point policy iteration scheme converges. Our methods take advantage of the special structure of the GMWB problem in order to obtain a rapidly convergent iteration. The direct control method has a scaling parameter which must be set by the user. We give estimates for bounds on the scaling parameter so that convergence can be expected in the presence of round-off error. Example computations verify that these estimates are of the correct order. Finally, we compare the scaled direct control formulation to a formulation based on a block version of the penalty method [15]. We show that the scaled direct control method has some advantages over the penalty method.

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Dynamic Hedging Under Jump Diffusion with Transaction Costs

Cited by 44 publications

References 27 publications

The effect of modelling parameters on the value of GMWB guarantees

The effect of modelling parameters on the value of GMWB guarantees

Regime switching in stochastic models of commodity prices: An application to an optimal tree harvesting problem

Iterative methods for the solution of a singular control formulation of a GMWB pricing problem

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