A Note on the Cost of Hedging Variable Annuities

• Activity Number: 506
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Risk Analysis
• Author(s): Liang Hong*+
• Companies: Bradley University
• Keywords: Cost of Hedging ; Variable Annuities ; Re-balancing ; Random Walk ; Fixed Transaction Cost ; Proportional Transaction Cost

Abstract

For variable annuities, the cost of hedging must be taken into consideration when firms use dynamic hedging strategies. For a long time, some finance and risk management experts argue without proof that re-balancing delta to the hedge limit is always more cost-efficient than re-balancing delta to the initial position. We study this problem rigorously when the hedge position follows a random walk. Using the ergodic method of semi-Markov processes, we find that re-balancing delta to the initial position is more cost-efficient than re-balancing it to the edge for a fixed transaction cost. However, when the transaction cost is proportional to the hedge limit, re-balancing to the initial position is less cost-efficient than re-balancing to the edge. The results in this paper may allow practicing actuaries and finance professionals to make judicious decisions.