Robert Merton and Myron Scholes
Citation: For a new method to determine the value of derivatives.
The key idea
Black-Scholes-Merton: under no-arbitrage and continuous trading, a European option's value is determined by underlying price, strike, time, vol, and rate — independent of expected return.
The explanation
Merton's continuous-time stochastic calculus generalised the Black-Scholes formula to a wide class of derivatives and stochastic processes. Scholes (with Fischer Black, who died in 1995) derived the original 1973 formula via the delta-hedging argument. The framework launched the trillion-dollar derivatives industry.
Why Africa should care
Black-Scholes is the framework behind every option-pricing model used in Johannesburg, Lagos, Nairobi. African employee stock-option valuations under IFRS 2 require Black-Scholes computation. Currency-option pricing for African importers and exporters hedging USD exposure is similarly framework-dependent. Merton's structural credit-risk model is the basis of every distance-to-default computation used by African banks under Basel.
How to use it
When pricing or valuing any contingent claim, the Black-Scholes framework — risk-neutral expectation under an equivalent martingale measure — is the universal starting point. Stochastic Calculus Modules 7-9 of the LeadAfrik Quant Math curriculum derive every step.
Watch out for
Scholes and Merton co-founded LTCM, which collapsed in 1998 — a reminder that pricing models assume liquidity and correlation behaviour that fail in crises.
Canonical works
- Fischer Black and Myron Scholes (1973) "The Pricing of Options and Corporate Liabilities" Journal of Political Economy
- Robert C. Merton (1973) "Theory of Rational Option Pricing" Bell Journal of Economics and Management Science
- Roger Lowenstein (2000) "When Genius Failed: The Rise and Fall of Long-Term Capital Management" Random House
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