Analytical Upper Bounds for American Option Prices
推导了随机利率、随机波动率和跳跃下美式期权价格的解析上界，在双因子随机波动率模型中，计算上界所需时间远少于精确计算美式期权价格。
American options require numerical methods, namely lattice models, to provide accurate price estimates. The computations can become expensive when more than one state variable is involved. Analytical upper bounds can therefore provide a useful guideline for how high American values can reach. In this paper, we derive analytical (closed-form) upper bounds for American option prices under stochastic interest rates, stochastic volatility, and jumps where American option prices are difficult to compute with accuracy. In a stochastic volatility model (Heston (1993) and Scott (1997)) that has two random factors, we demonstrate that the upper bound only takes a very small fraction of the time that the American option needs to compute.