Volatility Targeting Using Delayed Diffusions |
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Authors: | Lorenzo Torricelli |
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Affiliation: | 1. Department of Mathematics, Ludwig Maximilians Universit?t München, München, Germanytorricel@math.lmu.de |
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Abstract: | ABSTRACTA target volatility strategy (TVS) is a risky asset-riskless bond dynamic portfolio allocation which makes use of the risky asset historical volatility as an allocation rule with the aim of maintaining the instantaneous volatility of the investment constant at a target level. In a market with stochastic volatility, we consider a diffusion model for the value of a target volatility fund (TVF) which employs a system of stochastic delayed differential equations (SDDEs) involving the asset realized variance. First we prove that under some technical assumptions, contingent claim valuation on a TVF is approximately of Black-Scholes type, which is consistent with and supports the standing market practice. In second place, we develop a computational framework using recent results on Markovian approximations of SDDEs systems, which we then implement in the Heston variance model using an ad hoc Euler scheme. Our framework allows for efficient numerical valuation of derivatives on TVFs, whose typical purpose is the assessment of the guarantee costs of such funds for insurers. |
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Keywords: | Target volatility portfolio strategy stochastic delayed differential equations finite-dimensional Markovian representation guarantee costs Euler scheme |
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