Martingale Pricing, Return Prediction, and Neural Networks
Summary
The document distinguishes derivative pricing from investment management when discussing the martingale view of asset prices. In derivative pricing, martingale methods provide a framework for valuing contingent claims under specified assumptions. In investment management, the question is whether historical prices contain exploitable predictive structure, which is different from pricing a derivative under a model.
The answer points to momentum research as evidence that observed returns can depart from a simple martingale description, while noting that attempts to trade such effects have had mixed outcomes. It characterizes neural network stock prediction as an unsettled, marginal line of work rather than established evidence that prices are readily forecastable. A second response gestures toward agent-dependent valuations and utility processes, but offers little detail. The discussion gives conceptual distinctions and examples, not a neural-network method, empirical dataset, or definitive test of market efficiency.
Key ideas
- Martingale methods are widely used in derivative pricing under model assumptions.
- Investment prediction asks whether returns contain exploitable patterns, a different question from derivative valuation.
- Momentum research is cited as evidence of departures from a simple martingale pattern.
- Reported success in trading such deviations is mixed.
- The document offers no specific neural-network design or empirical performance analysis.
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Full text
# martingale anomaly in pricing risky assets # martingale anomaly in pricing risky assets If stock prices are meant to follow a martingale, then why are neural networks used in efficient pricing, given that they train themselves from historical data ## Answer by Alex C (score 2, accepted) https://quant.stackexchange.com/a/31837 It has been shown theoretically (Samuelson, 1973) that in an informationally efficient market prices of securities follow a martingale. Cox Ross Rubinstein showed in 1973 how this hypothesis combined with Black-Scholes-Merton dynamic hedging could be used to price derivatives namely options, and this was made into a general theory of derivative pricing by Harrison an Kreps in 1979 (the so called martingale pricing theory). Empirical work at about this time also confirmed that stock prices to a large extent conform to the martingale idea. Today Quant Finance is divided into two parts: Derivative Pricing and Quant Investment Management. In Derivative Pricing the martingale methods are routinely used to price a large number of derivatives. These methods are used extensively in practice and are quite successful. The martingale assumption serves as a foundation for this kind of work. In Quant Investment Management the situation is more complicated. Much work takes a martingale approach, however there has also been empirical work that demonstrates some deviations of stock prices from martingales; the most famous being the momentum effect of Jegadeesh and Titman (1993). Some attempts have been made to capture this effect in an investment strategy, with mixed results. Many people continue to believe that the martingale hypothesis has merit. Finally there is a small number of people, out of the mainstream of Finance, who have attempted to use Neural Networks to predict stock prices. This work is on the fringes, has not been very successful as far as I know, and appears misguided to those of us who still believe that stock prices are close to martingales. (Still science sometimes advances by having people try out seemingly strange new ideas, so I'll keep an open mind about neural networks). ## Answer by Tim (score 0) https://quant.stackexchange.com/a/31829 Real-world stock prices can follow a martingale. Just not directly. You can indirectly make assumptions about how price evolution itself, can construct utilities, payoffs and various perceptions of risk, for particular agents/players in the market. As a vague example, you can extract a particular "martingale" price (or neighborhood), from various BSDEs, PDEs, FBSDEs, where if an agent observes market price hit a "martingale" price, then her utilities become martingales themselves (pure 50-50 fair game).
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