Derivative prices equal discounted expected payoffs under an equivalent martingale measure

Evidence

Harrison and Kreps showed that in a “frictionless” market with no opportunities for arbitrage there existed an “equivalent martingale measure,” a way of assigning probabilities to the path followed by the price of an asset such that the value of an option or other derivative contract on that asset was simply the expected value of its payoff discounted back to the present. — Donald MacKenzie, An Engine, Not a Camera, 621

Categorization

• DEFINE: Defines the equivalent martingale measure, the core technical mechanism by which no-arbitrage assumptions fix derivative prices.
• QUESTION: The uniqueness claim for complete markets is stated tersely — worth pinning down exactly what ‘span’ requires in practice.
• XREF: connects to: A derivative is a time-bounded bet, not a property claim — Mark Blyth, Austerity: The History of a Dangerous…, 87; Merton’s stochastic calculus reframed derivatives pricing in terms of martingale theory — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 143; Martingale models replaced random walks as the preferred formulation of weak-form efficiency. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 293 (+3 more)

Broader Connections

• Option prices equal the expected payoff discounted at the riskless rate #corroborates (0.95) — Donald MacKenzie, An Engine, Not a Camera, 1284
• the risk-neutral valuation insight lets options be priced by discounting at the riskless rate #qualifies (0.85) — Donald MacKenzie, An Engine, Not a Camera, 583