Collateral smile

We analyze the impact of funding costs and margin requirements on index options traded on the CBOE. Assuming differential borrowing and lending rates, we derive no-arbitrage bounds for European options. We show that funding costs and the CBOE's margin requirements lead to a price increase, which translates into skew and smile patterns for implied volatility curves even under constant volatilities. Empirical tests confirm that our model-implied slopes have significant statistical power in explaining the slopes observed in the market. Hence, at least in part, funding costs and collateral requirements offer an institutional explanation of the volatility smile phenomenon.