Theory of Rational Option Pricing
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What they found
Published alongside Black-Scholes, Merton's paper put option pricing on rigorous mathematical footing and extended it. He derived general no-arbitrage bounds that any option price must satisfy, showed that an American call on a non-dividend-paying stock should never be exercised early, extended the model to dividends and stochastic interest rates, and introduced the continuous-time hedging argument that is now the standard derivation. Merton shared the 1997 Nobel Prize with Scholes for this work.
What you can use
- Never exercise an American call early on a stock without dividends; sell it instead, because the time value is worth more.
- No-arbitrage bounds tell you when an option quote is simply wrong, independent of any model.
- Dividends and rates change option values in predictable ways; the basic model needs adjusting for them.
Caveats
Highly mathematical. Same restrictive assumptions as Black-Scholes.
Tags: options, pricing, theory, early-exercise
Summaries are our own reading of the paper, not the authors' words. Educational only, not advice. Discuss it in Book Club.