Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/258023 
Authors: 
Year of Publication: 
2020
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 8 [Issue:] 3 [Article No.:] 70 [Publisher:] MDPI [Place:] Basel [Year:] 2020 [Pages:] 1-34
Publisher: 
MDPI, Basel
Abstract: 
This paper studies the effect of variance swap in hedging volatility risk under the mean-variance criterion. We consider two mean-variance portfolio selection problems under Heston's stochastic volatility model. In the first problem, the financial market is complete and contains three primitive assets: a bank account, a stock and a variance swap, where the variance swap can be used to hedge against the volatility risk. In the second problem, only the bank account and the stock can be traded in the market, which is incomplete since the idiosyncratic volatility risk is unhedgeable. Under an exponential integrability assumption, we use a linear-quadratic control approach in conjunction with backward stochastic differential equations to solve the two problems. Efficient portfolio strategies and efficient frontiers are derived in closed-form and represented in terms of the unique solutions to backward stochastic differential equations. Numerical examples are provided to compare the solutions to the two problems. It is found that adding the variance swap in the portfolio can remarkably reduce the portfolio risk.
Subjects: 
backward stochastic differential equation
efficient frontier
heston&#x2019
s model
mean-variance portfolio selection
variance swap
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Document Type: 
Article
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