Title: Hedging derivative securities with volatility futures

Authors: Nelson Yap; Kian-Guan Lim; Yibao Zhao

Addresses: Lee Kong Chian School of Business, Singapore Management University, Singapore 178899, Singapore ' Lee Kong Chian School of Business, Singapore Management University, Singapore 178899, Singapore ' Lee Kong Chian School of Business, Singapore Management University, Singapore 178899, Singapore

Abstract: We show a method to replicate S&P 500 exchange traded fund (ETF) European synthetic put by optimally rebalancing a portfolio of the underlying ETF shares, the VIX futures contracts, and treasury bonds over discrete periods. The motivation for this study is two-fold. Firstly, market-makers in S&P 500 index options may need to hedge a large short position synthetically when the puts are in short supply. Secondly, for an institutional investor holding a large diversified portfolio of US stocks, constructing a long position in synthetic puts is tantamount to providing portfolio insurance. The put replication is useful as the alternative of buying US puts can be prohibitively expensive in a distressed market. The numerical method of Gauss-Hermite quadrature is employed in the optimal solution. Both simulations and empirical validation using historical S&P 500 index ETF and VIX futures price data show effectiveness in the put pricing versus more traditional methods.

Keywords: optimal replication; dynamic portfolio; stochastic volatility; hedging; derivative securities; volatility futures; derivatives; Gauss-Hermite quadrature; simulation; put replication.

DOI: 10.1504/IJFMD.2016.081688

International Journal of Financial Markets and Derivatives, 2016 Vol.5 No.2/3/4, pp.111 - 127

Received: 21 Jul 2015
Accepted: 05 Apr 2016

Published online: 20 Jan 2017 *

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