The Journal of Finance

Trading Volume: Implications of an Intertemporal Capital Asset Pricing Model

Published: 01/11/2007   |   DOI: 10.1111/j.1540-6261.2006.01005.x

ANDREW W. LO, JIANG WANG

We derive an intertemporal asset pricing model and explore its implications for trading volume and asset returns. We show that investors trade in only two portfolios: the market portfolio, and a hedging portfolio that is used to hedge the risk of changing market conditions. We empirically identify the hedging portfolio using weekly volume and returns data for U.S. stocks, and then test two of its properties implied by the theory: Its return should be an additional risk factor in explaining the cross section of asset returns, and should also be the best predictor of future market returns.

Implementing Option Pricing Models When Asset Returns Are Predictable

Published: 03/01/1995   |   DOI: 10.1111/j.1540-6261.1995.tb05168.x

ANDREW W. LO, JIANG WANG

The predictability of an asset's returns will affect the prices of options on that asset, even though predictability is typically induced by the drift, which does not enter the option pricing formula. For discretely‐sampled data, predictability is linked to the parameters that do enter the option pricing formula. We construct an adjustment for predictability to the Black‐Scholes formula and show that this adjustment can be important even for small levels of predictability, especially for longer maturity options. We propose several continuous‐time linear diffusion processes that can capture broader forms of predictability, and provide numerical examples that illustrate their importance for pricing options.

Nonparametric Estimation of State‐Price Densities Implicit in Financial Asset Prices

Published: 12/17/2002   |   DOI: 10.1111/0022-1082.215228

Yacine Aït‐Sahalia, Andrew W. Lo

Implicit in the prices of traded financial assets are Arrow–Debreu prices or, with continuous states, the state‐price density (SPD). We construct a nonparametric estimator for the SPD implicit in option prices and we derive its asymptotic sampling theory. This estimator provides an arbitrage‐free method of pricing new, complex, or illiquid securities while capturing those features of the data that are most relevant from an asset‐pricing perspective, for example, negative skewness and excess kurtosis for asset returns, and volatility “smiles” for option prices. We perform Monte Carlo experiments and extract the SPD from actual S&P 500 option prices.

Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation

Published: 12/17/2002   |   DOI: 10.1111/0022-1082.00265

Andrew W. Lo, Harry Mamaysky, Jiang Wang

Technical analysis, also known as “charting,” has been a part of financial practice for many decades, but this discipline has not received the same level of academic scrutiny and acceptance as more traditional approaches such as fundamental analysis. One of the main obstacles is the highly subjective nature of technical analysis—the presence of geometric shapes in historical price charts is often in the eyes of the beholder. In this paper, we propose a systematic and automatic approach to technical pattern recognition using nonparametric kernel regression, and we apply this method to a large number of U.S. stocks from 1962 to 1996 to evaluate the effectiveness of technical analysis. By comparing the unconditional empirical distribution of daily stock returns to the conditional distribution—conditioned on specific technical indicators such as head‐and‐shoulders or double bottoms—we find that over the 31‐year sample period, several technical indicators do provide incremental information and may have some practical value.

A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks

Published: 07/01/1994   |   DOI: 10.1111/j.1540-6261.1994.tb00081.x

JAMES M. HUTCHINSON, ANDREW W. LO, TOMASO POGGIO

We propose a nonparametric method for estimating the pricing formula of a derivative asset using learning networks. Although not a substitute for the more traditional arbitrage‐based pricing formulas, network‐pricing formulas may be more accurate and computationally more efficient alternatives when the underlying asset's price dynamics are unknown, or when the pricing equation associated with the no‐arbitrage condition cannot be solved analytically. To assess the potential value of network pricing formulas, we simulate Black‐Scholes option prices and show that learning networks can recover the Black‐Scholes formula from a two‐year training set of daily options prices, and that the resulting network formula can be used successfully to both price and delta‐hedge options out‐of‐sample. For comparison, we estimate models using four popular methods: ordinary least squares, radial basis function networks, multilayer perceptron networks, and projection pursuit. To illustrate the practical relevance of our network pricing approach, we apply it to the pricing and delta‐hedging of S&P 500 futures options from 1987 to 1991.