Pricing and hedging long-term options

Do long-term and short-term options contain differential information? If so, can long-term options better differentiate among alternative models? To answer these questions, we first demonstrate analytically that differences among alternative models usually may not surface when applied to short-term options, but do so when applied to long-term contracts. Using S&P 500 options and LEAPS, we find that short- and long-term contracts indeed contain different information. While the data suggest little gains from modeling stochastic interest rates or random jumps (beyond stochastic volatility) for pricing LEAPS, incorporating stochastic interest rates can nonetheless enhance hedging performance in certain cases involving long-term contracts.