Volatility Targeting Using Delayed Diffusions
35 Pages Posted: 21 Jan 2017 Last revised: 29 Jan 2018
Date Written: January 22, 2018
A 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. Firstly 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.
Keywords: target volatility, portfolio strategy, stochastic delayed differential equations, finite-dimensional Markovian representation, stochastic volatility, guarantee costs, Euler scheme.
JEL Classification: C01, G13
Suggested Citation: Suggested Citation