Pricing and Hedging Options on Assets with Options on Related Assets

Dilip B. Madan,King Wang
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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.
用相关资产期权定价和对冲资产期权
问题是芝加哥期权交易所(CBOE)扭曲指数的期权定价。期权定价理论通过在相关资产的期权市场上建立头寸来部分对冲风险。然后,期权按照对冲的成本定价。该理论应用于由SPDR标准普尔500指数ETF信托(SPY)期权对冲的波动率指数(VIX)定价期权,以及由金融精选板块SPDR (XLF)期权对冲的摩根大通定价期权。然后应用该方法来说明CBOE倾斜指数期权在SPY期权市场上的对冲定价。扭曲指数的微笑暗示了波动率指数和扭曲指数本身。以SPY为相关资产的VIX期权定价存在高斯关联关系,低估期权,而t关联关系显著高估期权。多元双边伽马模型更接近市场。跨资产对冲价格相对于市场价格的溢价随货币规模和期限而下降,随波动率指数水平而上升。主题:衍生品,期权,交易所交易基金和应用,定量方法,统计方法,绩效测量关键发现▪实物回报的时间序列数据可以用来获得市场相关的期权价格,前提是纳入了市场相关的对冲成本。▪芝加哥期权交易所(CBOE)倾斜指数期权的定价是以SPY期权对冲投资组合的成本为基础的。剩余风险定价技术可根据需要更广泛地应用于市场校准参数。
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