Box Spread and Put-Call Parity Tests for the S&P 500 Index LEAPS Market

Abstract

“Option pricing models are based on arbitrage, but setting up a delta-neutral position and rebalancing it continuously over an optionÕs lifetime is often a difficult and costly trading strategy. Pricing violations, therefore, may not indicate significant market inefficiency, particularly given uncertainty over the volatility parameter. By contrast, put-call parity is an option price relationship that, if violated, generates a straightforward arbitrage trade that does not require rebalancing or information about volatility. Only an inefficient market would allow substantial violations of put-call parity. A box spread uses two calls and two puts, but no position in the underlying asset, to produce a similar position to that used for put-call parity arbitrage. The box spread arbitrage also is easily set up with minimal execution risk. Bharadwaj and Wiggins consider whether the market for LEAPS written on the S&P 500 index is efficient enough to preclude violations of put-call parity and the box spread pricing relationship. They find that while LEAPS puts are overpriced relative to calls about 80% of the time, the discrepancy is seldom enough to produce a reliable arbitrage profit after transaction costs. Further exploration, including trying to assess the impact of dividend uncertainty and considering a trading strategy using futures in place of the underlying cash index portfolio, does not resolve the put mispricing issue.”