Prospect Theory in Options Trading Behaviour

Abstract
Traditional financial theory assumes that investors are rational agents who maximize expected utility under stable preferences. However, decades of behavioral research suggest that real-world trading behavior systematically deviates from these assumptions. Prospect Theory, developed by Daniel Kahneman and Amos Tversky, provides a descriptive framework for understanding how individuals evaluate risky prospects under uncertainty. This article examines how Prospect Theory shapes options trading behavior, particularly retail investor demand for lottery-like payoffs, out-of-the-money calls and puts, volatility products, and asymmetric strategies. We synthesize theoretical foundations, experimental evidence, and empirical findings from equity options markets, explore structural models incorporating cumulative prospect theory, and discuss implications for pricing, volatility surfaces, and regulatory oversight. We conclude by highlighting directions for future research at the intersection of behavioral finance, derivative markets, and quantitative modeling.

1. Introduction
Options markets represent one of the purest laboratories for studying risk preferences. Unlike stocks, options allow investors to engineer nonlinear payoff structures with extreme skewness and leverage. Traditional models such as expected utility theory and the Black–Scholes framework assume rational pricing under no-arbitrage conditions. However, observed trading patterns — particularly among retail investors — frequently deviate from predictions based on mean–variance efficiency or expected utility maximization.

Prospect Theory (PT) offers a behavioral explanation for such deviations. Rather than maximizing expected utility over final wealth, investors evaluate gains and losses relative to a reference point, exhibit loss aversion, and distort probabilities in systematic ways. These features can naturally explain:

Persistent demand for out-of-the-money (OTM) call options
Overpayment for lottery-like payoffs
Asymmetric volatility smiles
Excess trading volume in short-dated options
Retail concentration in zero-day-to-expiration (0DTE) contracts
This article investigates how Prospect Theory alters both individual trading decisions and aggregate market outcomes in options markets.

2. Theoretical Foundations
2.1 Expected Utility Theory
Expected Utility Theory (EUT), formalized by John von Neumann and Oskar Morgenstern, assumes individuals maximize:

where ( p_i ) represents objective probabilities and ( u(w_i) ) is a concave utility function over final wealth.

Under EUT:

Investors are risk-averse over gains.
Preferences are stable and time-consistent.
Decisions depend only on terminal wealth.
However, empirical anomalies — such as the Allais paradox — challenge this framework.

2.2 Prospect Theory
Prospect Theory (1979) proposes three key elements:

Reference Dependence
Outcomes are evaluated relative to a reference point.

Loss Aversion
Losses loom larger than gains.

Empirically, the loss aversion coefficient λ ≈ 2–2.5.

Probability Weighting
Individuals overweight small probabilities and underweight moderate to high probabilities.

The value function:

with α, β < 1 (concavity for gains, convexity for losses).

Cumulative Prospect Theory (1992) refines probability weighting for continuous distributions.

3. Why Options Markets Are Ideal for Prospect Theory
Options are especially relevant for PT analysis because:

They provide explicit gain/loss asymmetry.
They allow exposure to extreme tail events.
They create payoff convexity and skewness.
They amplify small probability events.
An OTM call resembles a lottery ticket:

Small cost
Small probability of large gain
Limited downside
This payoff structure aligns directly with PT’s overweighting of small probabilities.

4. Probability Weighting and OTM Call Demand
Empirical studies show persistent overpricing of OTM calls and puts relative to risk-neutral benchmarks. Under risk-neutral pricing, OTM options should reflect objective probabilities adjusted for risk premia.

However, Prospect Theory implies:

Where ( w(p) ) overweights small probabilities.

For deep OTM calls:

Objective probability: 2%
Subjective probability: possibly perceived as 5–8%
This distortion leads to excess demand and higher implied volatility in the wings of the volatility surface.

5. The Volatility Smile as a Behavioral Artifact
The volatility smile — where implied volatility increases for deep OTM options — cannot be explained solely by Black–Scholes.

Behavioral interpretation:

Investors overpay for crash protection (OTM puts) due to loss aversion.
Investors overpay for upside lotteries (OTM calls) due to probability overweighting.
Dealers demand compensation for absorbing skewed retail demand.
Thus, the volatility surface may partially reflect aggregate Prospect Theory preferences.

6. Retail Trading Behavior
Recent market events — particularly during meme-stock episodes — provide rich behavioral evidence.

For example, in stocks such as GameStop and AMC Entertainment:

Retail traders concentrated in short-dated OTM calls.
Gamma squeezes amplified price movements.
Social media narratives reinforced lottery-like expectations.
These patterns align with PT:

High upside salience
Overweighting tail outcomes
Limited downside framing
7. Loss Aversion and Protective Puts
Protective puts provide downside insurance. Loss-averse investors:

Overvalue downside protection.
Accept negative expected returns for emotional comfort.
Maintain reference points anchored to purchase price.
This helps explain:

Persistent negative returns in long-volatility strategies.
Excessive hedging during market stress.
Demand spikes after drawdowns.
8. Dynamic Reference Points
Reference points shift over time:

Purchase price
High-water mark
Recent gains
Peer comparison
In options trading, traders may:

Double down on losing positions to break even.
Close winning options early to “lock gains.”
Hold losers too long due to break-even framing.
These behaviors align with the disposition effect, extensively documented in equity markets.

9. Structural Models Incorporating Prospect Theory
Recent quantitative finance research embeds PT into equilibrium asset pricing models.

Representative-agent PT models produce:

Endogenous skewness
Time-varying risk premia
State-dependent volatility surfaces
Under PT preferences:

Crash risk commands higher premia.
Skewness becomes priced.
Options pricing deviates from log-normal assumptions.
These models bridge behavioral microfoundations with macro-level pricing.

10. Empirical Evidence
Studies find:

OTM calls underperform relative to CAPM expectations.
Lottery-like stocks exhibit lower subsequent returns.
Retail traders earn negative abnormal returns in options.
Short-term OTM options display persistent overpricing.
These findings support PT predictions regarding skewness preference.

11. Implications for Market Efficiency
Prospect Theory implies partial inefficiency:

Prices reflect heterogeneous beliefs.
Arbitrage is limited by capital constraints.
Behavioral demand can persist.
However, sophisticated traders may exploit:

Volatility risk premia
Tail risk overpricing
Short-volatility strategies
The interaction between behavioral demand and arbitrage capital determines equilibrium outcomes.

12. Regulatory and Risk Implications
Behavioral distortions raise concerns:

Excessive leverage
Overtrading
Financial vulnerability
Platforms lowering transaction costs may amplify PT-driven biases, particularly in short-dated options.

Educational interventions could focus on:

Probability calibration
Expected value understanding
Skewness-return tradeoffs
13. Future Research Directions
PT in zero-day options (0DTE)
AI-driven retail behavior and gamification
Cross-country differences in options markets
Neuroeconomic studies of derivative trading
14. Conclusion
Prospect Theory provides a powerful explanatory framework for understanding options trading behavior. By incorporating reference dependence, loss aversion, and probability distortion, PT explains persistent demand for skewed payoffs, volatility smiles, and lottery-like contracts.

Options markets thus serve as a natural behavioral laboratory — revealing how cognitive biases shape financial outcomes. Integrating behavioral finance with derivative pricing remains a critical frontier for both academics and practitioners.

References
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