Leverage Constraints and the Optimal Hedging of Stock and Bond Options

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Abstract
This paper considers the problem of a financial institution that needs to hedge a stream of state-contingent cash flows while facing borrowing and short-sales restrictions. The study determines analytically the strategy that minimizes the initial cost of hedging the desired cash flow, which is also the upper bound on its market price, and shows that the impact of leverage constraints on the cost of hedging call and put options is significant and, therefore, the biases detected by tests of option pricing models may not represent arbitrage opportunities. The paper also shows that with credit limits, it is optimal to reduce the rate of trading; thus, these constraints need to be recognized when estimating the trading volume generated in replicating contingent payoffs such as portfolio insurance.

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