41 Pages Posted: 17 Mar 2012
Date Written: March 15, 2012
We analyze the impact of funding costs and margin requirements on prices of index options traded on the CBOE. Margin requirements are the collateral the option sellers are enforced to deposit with exchanges. Funding costs refer to the spread between borrowing rates and lending rates. Testing the Put-Call parity and bid-ask spreads of options, we find evidence of non-zero funding costs. Under a dynamic incomplete market where differential borrowing rates and lending rates are allowed, we propose a model that gives upper bounds and lower bounds for option prices in the absence of arbitrage. As we want to isolate the effect of these costs on implied volatilities, we choose the classical Black-Scholes model as starting point. We derive price bounds for European options in semi closed-form. Numerical estimations show that funding costs and margin requirements give a sensible increase to option prices which could translate into skew and smile patterns for implied volatility curves even under constant volatilities. Empirical tests show that the slopes our model generates have significant statistical power in explaining the slopes observed in the market. Hence, funding costs and collateral requirements offer an institutional explanation of the volatility smile phenomenon without leaving the constant volatility assumption.
Keywords: collateral requirements, funding costs, volatility smile, option pricing
JEL Classification: G01, G12, G13
Suggested Citation: Suggested Citation