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Option Pricing Bounds in Discrete Time

Stylianos Perrakis; Peter Ryan
Journal of Finance 1984 39(2), 519-525
Upper and lower bounds are derived for call options traded at discrete intervals. These bounds are independent of assumptions on the stock price distribution other than a restriction satisfied by the stock being “non‐negative beta.” The development of the bounds relies on the single‐price law and arbitrage arguments. Both single‐period and multiperiod results are produced, and put option bounds follow by extension. The bounds exist as equilibrium values given a consensus on stock price distribution; they are also valid for empirical studies, being adjustable for dividends and commissions.

Are Options on Index Futures Profitable for Risk‐Averse Investors? Empirical Evidence

George M. Constantinides; MICHAL CZERWONKO; JENS CARSTEN JACKWERTH; Stylianos Perrakis
Journal of Finance 2011 66(4), 1407-1437 open access
American options on the S&P 500 index futures that violate the stochastic dominance bounds of Constantinides and Perrakis (2009) from 1983 to 2006 are identified as potentially profitable trades. Call bid prices more frequently violate their upper bound than put bid prices do, while violations of the lower bounds by ask prices are infrequent. In out‐of‐sample tests of stochastic dominance, the writing of options that violate the upper bound increases the expected utility of any risk‐averse investor holding the market and cash, net of transaction costs and bid‐ask spreads. The results are economically significant and robust.