Merton’s stochastic calculus reframed derivatives pricing in terms of martingale theory

Evidence

Merton developed an approach to option pricing that led to the same equation that Black and Scholes had derived but which rested on different foundations. Merton’s derivation did not invoke the Capital Asset Pricing Model, although it too involved assumptions about markets that were markedly at odds with the actual conditions of the early 1970s. Other contributions to option theory quickly followed, and their level of mathematical sophistication rapidly grew. Merton had introduced the use of rigorous stochastic calculus, and by the end of the 1970s the problem of derivatives pricing was reformulated in terms of martingale theory, an advanced area of “pure mathematics.” The mathematical repertoire of Wall Street’s quantitative finance specialists (first called “rocket scientists,” then “quants”) was being assembled. — Donald MacKenzie, An Engine, Not a Camera, 143

Categorization

• XREF: Connects to the rise of quantitative finance and ‘quants’ — the broader financialization/quant revolution literature. The shift from CAPM-based to martingale-based pricing is a key sequence point in the history of financial theory. — connects to: CAPM’s economic rationale licensed mathematically unrigorous stochastic calculus by Black and Scholes — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 586; Derivative prices equal discounted expected payoffs under an equivalent martingale measure — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 621; Martingale models replaced random walks as the preferred formulation of weak-form efficiency. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 293
• DEFINE: Defines the shift from Black-Scholes to martingale theory as the mathematical foundation of derivatives pricing.

Broader Connections

• Derivative prices equal discounted expected payoffs under an equivalent martingale measure #expands (0.90) — Donald MacKenzie, An Engine, Not a Camera, 621
• CAPM’s economic rationale licensed mathematically unrigorous stochastic calculus by Black and Scholes #complicates (0.78) — Donald MacKenzie, An Engine, Not a Camera, 586