Invisible Parameters in Option Prices
Published: 07/01/1993 | DOI: 10.1111/j.1540-6261.1993.tb04025.x
STEVEN L. HESTON
This paper characterizes contingent claim formulas that are independent of parameters governing the probability distribution of asset returns. While these parameters may affect stock, bond, and option values, they are “invisible” because they do not appear in the option formulas. For example, the Black‐Scholes (1973) formula is independent of the mean of the stock return. This paper presents a new formula based on the log‐negative‐binomial distribution. In analogy with Cox, Ross, and Rubinstein's (1979) log‐binomial formula, the log‐negative‐binomial option price does not depend on the jump probability. This paper also presents a new formula based on the log‐gamma distribution. In this formula, the option price does not depend on the scale of the stock return, but does depend on the mean of the stock return. This paper extends the log‐gamma formula to continuous time by defining a gamma process. The gamma process is a jump process with independent increments that generalizes the Wiener process. Unlike the Poisson process, the gamma process can instantaneously jump to a continuum of values. Hence, it is fundamentally “unhedgeable.” If the gamma process jumps upward, then stock returns are positively skewed, and if the gamma process jumps downward, then stock returns are negatively skewed. The gamma process has one more parameter than a Wiener process; this parameter controls the jump intensity and skewness of the process. The skewness of the log‐gamma process generates strike biases in options. In contrast to the results of diffusion models, these biases increase for short maturity options. Thus, the log‐gamma model produces a parsimonious option‐pricing formula that is consistent with empirical biases in the Black‐Scholes formula.
Intraday Patterns in the Cross‐section of Stock Returns
Published: 07/15/2010 | DOI: 10.1111/j.1540-6261.2010.01573.x
STEVEN L. HESTON, ROBERT A. KORAJCZYK, RONNIE SADKA
Motivated by the literature on investment flows and optimal trading, we examine intraday predictability in the cross‐section of stock returns. We find a striking pattern of return continuation at half‐hour intervals that are exact multiples of a trading day, and this effect lasts for at least 40 trading days. Volume, order imbalance, volatility, and bid‐ask spreads exhibit similar patterns, but do not explain the return patterns. We also show that short‐term return reversal is driven by temporary liquidity imbalances lasting less than an hour and bid‐ask bounce. Timing trades can reduce execution costs by the equivalent of the effective spread.
Option Momentum
Published: 09/17/2023 | DOI: 10.1111/jofi.13279
STEVEN L. HESTON, CHRISTOPHER S. JONES, MEHDI KHORRAM, SHUAIQI LI, HAITAO MO
This paper investigates the performance of option investments across different stocks by computing monthly returns on at‐the‐money straddles on individual equities. We find that options with high historical returns continue to significantly outperform options with low historical returns over horizons ranging from 6 to 36 months. This phenomenon is robust to including out‐of‐the‐money options or delta‐hedging the returns. Unlike stock momentum, option return continuation is not followed by long‐run reversal. Significant returns remain after factor risk adjustment and after controlling for implied volatility and other characteristics. Across stocks, trading costs are unrelated to the magnitude of momentum profits.