Pricing and Hedging Options on Assets with Options on Related Assets

Abstract

The question addressed is the pricing of options on the CBOE Skew Index. The option pricing theory developed partially hedges risk by taking positions in the market for options on a related asset. The option is then priced at the cost of this hedge. The theory is applied to pricing Volatility Index (VIX) options hedged by the SPDR S&P 500 ETF Trust (SPY) options and pricing options on JPMorgan hedged by Financial Select Sector SPDR (XLF) options. The approach is then applied to illustrate the pricing of CBOE Skew Index options with a hedge in the market for SPY options. The Skew Index smile is then seen to imply the VIX and SKEW of the Skew Index itself. The pricing of VIX options with SPY as the related asset has the Gaussian copula underpricing options while the t-copula significantly overprices them. The multivariate bilateral gamma models are closer to market. The premia of cross-asset hedge prices over the market price are observed to fall with moneyness and maturity and rise with the level of the VIX.

TOPICS: Derivatives, options, exchange-traded funds and applications, quantitative methods, statistical methods, performance measurement

Key Findings

• ▪ Time series data on physical returns may be used to obtain market relevant option prices provided market-relevant hedging costs are incorporated.

• ▪ Options on the CBOE Skew Index are priced at the cost of an SPY option hedge portfolio.

• ▪ Residual risk pricing technologies may be applied more widely with market calibrated parameters if desired.