A Simple Non-Parametric Approach to Bond Futures Option Pricing

Abstract

The most popular option contracts at the Chicago Board of Trade are options on Treasury note and bond futures contracts. An extensive empirical study of their valuation found that the Black model underprices in-the-money compared to out-of-the-money calls; that is, implied volatilites of the former calls exceeded those of the latter, especially for shorter term options. To investigate the cause of the misvaluation, the authors apply an option pricing model called canonical valuation, which uses the historical time series of the underlying futures price to estimate non-parametrically the probability distribution of the futures price on the expiration date. The canonical model does not underprice in-the-money calls relative to others and also has a lower mean absolute pricing error. It predicts that implied volatilities should be higher for shorter-term in-the-money calls than for other calls and should be higher in regimes of low-bond prices (i.e., high long-term interest rates), which is consistent with empirical evidence.