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The Black–Scholes–Merton Model

In: AN INTRODUCTION TO Derivative Securities, Financial Markets, and Risk Management

Author

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  • ROBERT A. JARROW
  • ARKADEV CHATTERJEA

Abstract

The following sections are included:IntroductionNobel Prize–Winning Works (1973)The AssumptionsEXTENSION 19.1: Bubbles and Option PricingThe Pricing and Hedging ArgumentThe Black–Scholes–Merton FormulaUnderstanding the Black–Scholes–Merton ModelStock Prices and MartingalesRisk-Neutral ValuationActual versus Pseudo-probabilitiesThe GreeksInterpreting the GreeksSome Road Bumps AheadEXTENSION 19.2: Market Manipulation and Option PricingThe InputsObservable InputsVolatility: The Elusive InputExtending the Black–Scholes–Merton ModelAdjusting for DividendsForeign Currency OptionsValuing American OptionsEXTENSION 19.3: Exotic OptionsSummaryAppendixModeling the Stock Price EvolutionContinuously Compounded (Logarithmic) ReturnIntroducing UncertaintyThe Central Limit TheoremFirst Derivation of the Black–Scholes–Merton Formula (as a Limit of the Binomial Model)Second Derivation of the Black–Scholes–Merton Formula (Using Risk-Neutral Valuation)The Probabilities and the Risk PremiumProof of (24)CasesQuestions and Problems

Suggested Citation

  • Robert A. Jarrow & Arkadev Chatterjea, 2024. "The Black–Scholes–Merton Model," World Scientific Book Chapters, in: AN INTRODUCTION TO Derivative Securities, Financial Markets, and Risk Management, chapter 19, pages 419-458, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789811291654_0019
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    Keywords

    Derivatives; Financial Markets; Risk Management; Arbitrage; Financial Engineering; Forwards; Futures; Call Options; Put Options; European Options; American Options; Swaps; Currency Swaps; Interest Rate Swaps; Commodity Swaps; Equity Swaps; Credit Default Swaps; Commodity Derivatives; Equity Derivatives; Index Derivatives; Interest Rate Derivatives; Commodities; Margins and Daily Settlements; Binomial Model; Black-Scholes Model; Black-Scholes-Merton Model; Delta Hedging; Gamma Hedging; Heath-Jarrow-Morton Model; Libor Model; Forward Rate Agreements; Interest Rate Futures; Interest Rate Options; Market Manipulation; Regulation; Derivatives Exchanges;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G1 - Financial Economics - - General Financial Markets
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G2 - Financial Economics - - Financial Institutions and Services
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G20 - Financial Economics - - Financial Institutions and Services - - - General

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