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| Black-Scholes-Mertonオプション価格モデル× | マートン・ジャンプ拡散モデル× | |
|---|---|---|
| 分野 | ファイナンス | ファイナンス |
| 系統 | Regression model | Regression model |
| 提唱年≠ | 1973 | 1976 |
| 提唱者≠ | Fischer Black, Myron Scholes & Robert Merton | Robert C. Merton |
| 種類≠ | Continuous-time option-pricing model | Continuous-time asset price model (diffusion plus Poisson jumps) |
| 原典≠ | Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637–654. DOI ↗ | Merton, R. C. (1976). Option Pricing When Underlying Stock Returns Are Discontinuous. Journal of Financial Economics, 3(1–2), 125–144. DOI ↗ |
| 別名≠ | Black-Scholes formula, Black-Scholes-Merton model, BSM model, Black-Scholes opsiyon fiyatlama modeli | Merton jump-diffusion, jump-diffusion process, Atlama Difüzyon Modeli (Merton Jump-Diffusion) |
| 関連 | 4 | 4 |
| 概要≠ | The Black-Scholes-Merton model, published by Fischer Black and Myron Scholes in 1973 with the theoretical framework extended by Robert Merton, gives a closed-form no-arbitrage price for European options. By assuming the underlying asset follows geometric Brownian motion with constant volatility, it derives a partial differential equation whose solution expresses the option price in terms of the stock price, strike, time to maturity, risk-free rate, and volatility — transforming option pricing from intuition into a rigorous, tractable formula. | The Merton Jump-Diffusion model, introduced by Robert C. Merton in 1976, extends Geometric Brownian Motion by adding sudden price jumps generated by a Poisson process. It captures the volatility smile and the fat-tailed return behaviour that standard Black-Scholes cannot explain, and is widely used in option pricing and risk management. |
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