So sánh phương pháp

	Định giá trung lập rủi ro	Thay đổi Numeraire
Lĩnh vực	Tài chính định lượng	Tài chính định lượng
Họ	Regression model	Regression model
Năm ra đời	1979	1995
Người khởi xướng	John Harrison and David Kreps	Hélyette Geman, Nicole El Karoui, Jean-Charles Rochet
Loại	Fundamental Principle	Measure Theory
Công trình gốc	Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20(3), 381-408.	Geman, H., El Karoui, N., & Rochet, J. C. (1995). Changes of numeraire, changes of probability measure and option pricing. Journal of Applied Probability, 32(2), 443-458.
Tên gọi khác	Risk-Neutral Measure, Q-Measure	Numeraire Switching, Measure Change
Liên quan	4	3
Tóm tắt	Risk-neutral valuation (1979) is the fundamental principle that derivative prices equal the expected payoff discounted at the risk-free rate, computed under a risk-neutral probability measure (Q-measure). This principle, formalized by Harrison and Kreps, eliminates the need to estimate risk premia and is the foundation of modern derivatives pricing.	Change of numeraire is a mathematical technique for simplifying option pricing by changing the choice of discount factor (numeraire). By selecting a numeraire aligned with the payoff structure, complex problems become simple. The technique is essential for LIBOR market models and multi-currency derivatives.