This paper challenges the realism of the risk-neutral framework underlying the Black–Scholes model.

The authors argue that buyers and sellers operate with different expectations about volatility, growth, and market behavior, making purely risk-neutral valuation an incomplete representation of actual trading decisions.

To address this, the paper proposes an expected profit–expected loss (EP–EL) pricing framework based on real-world trading considerations such as profitability and profit-to-loss ratios.

Unlike traditional no-arbitrage models, the EP–EL approach is designed around trader outcomes and can operate under both real-world and risk-neutral assumptions.

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