The process of producing an implied volatility surface in the absence of reliable and frequent trade data is difficult. Bakshi, Kapadia and Madan (2003) detail a methodology for relating an index option smile structure with that of one of its constituents. Here we exploit this work to derive the single-stock option smile as a function of the index smile and a regressed relationship between the two underlying assets. Our non-parametric approach allows the market to estimate where implied volatilities should trade for illiquid derivative contracts away from at-the-money. The derived smile does not admit spread arbitrage.

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