In mathematical finance, a risk-neutral measure (also called an equilibrium measure, or equivalent martingale measure) is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure.This is heavily used in the pricing of financial derivatives due to the fundamental theorem of asset pricing, which implies that in a complete market, a derivative's price is the discounted expected value of the future payoff under the unique risk-neutral measure. Such a measure exists if and only if the market is arbitrage-free.
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| - Martingalmaß (de)
- Medida de neutralidad al riesgo (es)
- Misura di probabilità neutrale al rischio (it)
- 위험중립측도 (ko)
- リスク中立確率 (ja)
- Miara martyngałowa (pl)
- Risk-neutral measure (en)
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| - Das Martingalmaß (auch risikoneutrales Maß) ist ein Begriff aus der Finanzmathematik. Die Bedeutung von Martingalmaßen liegt darin, dass bei einem vorgegebenen Marktmodell mit Wahrscheinlichkeitsmaß genau dann äquivalente Martingalmaße existieren, falls es keine Arbitragemöglichkeit im Marktmodell gibt. Dies ist genau die Aussage des ersten Fundamentalsatzes der Arbitragepreistheorie. (de)
- En matemática financiera la medida de neutralidad al riesgo, también llamada medida de equivalencia martingala, se utiliza para establecer precios de derivados por mor del , el cual implica que en un el precio de un derivado es igual al valor esperado descontado del pago futuro bajo la única medida de neutralidad. (es)
- 위험중립측도(risk-neutral measure)는 금융공학에서 폭넓게 쓰이는 마팅게일 측도의 하나로, 파생상품의 가격결정에 필요한 핵심적인 요소 중의 하나이다. 에 따르면 에서 거래되는 파생상품의 가격은 위험중립측도 하에서 계산한 기대가치의 현재가치이며, 따라서 이를 구하기 위해서는 반드시 위험중립측도가 존재하여야 한다. (ko)
- リスク中立確率（リスクちゅうりつかくりつ、英: risk-neutral probability）とは、金融経済学や数理ファイナンス、金融工学などにおいて、金融資産の理論的な価格を決定するために用いられる仮想上の確率である。確率測度であることを強調して、リスク中立確率測度（英: risk-neutral probability measure）やリスク中立測度（英: risk-neutral measure）と呼ばれたり、またその数学的特性から同値マルチンゲール測度（英: equivalent martingale measure）と呼ばれることもある。リスク中立確率の下では全ての資産価格が（局所）マルチンゲールとなる。多くの資産価格理論において中核的な役割を果たしており、確率的割引ファクターや無裁定価格理論などとも深く関連する重要な概念である。 (ja)
- In finanza, la misura di probabilità neutrale al rischio è una misura di probabilità sotto la quale il prezzo corretto (ossia, di non arbitraggio) di un'attività finanziaria è pari al suo valore atteso futuro scontato al tasso privo di rischio. È anche nota come misura a martingala equivalente (dall'inglese equivalent martingale measure). (it)
- Miara martyngałowa (lub miara obojętna na ryzyko) – jedno z podstawowych pojęć z zakresu matematyki finansowej. Używa się go do wyceny instrumentów bazowych oraz pochodnych na . (pl)
- In mathematical finance, a risk-neutral measure (also called an equilibrium measure, or equivalent martingale measure) is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure.This is heavily used in the pricing of financial derivatives due to the fundamental theorem of asset pricing, which implies that in a complete market, a derivative's price is the discounted expected value of the future payoff under the unique risk-neutral measure. Such a measure exists if and only if the market is arbitrage-free. (en)
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| - Das Martingalmaß (auch risikoneutrales Maß) ist ein Begriff aus der Finanzmathematik. Die Bedeutung von Martingalmaßen liegt darin, dass bei einem vorgegebenen Marktmodell mit Wahrscheinlichkeitsmaß genau dann äquivalente Martingalmaße existieren, falls es keine Arbitragemöglichkeit im Marktmodell gibt. Dies ist genau die Aussage des ersten Fundamentalsatzes der Arbitragepreistheorie. (de)
- En matemática financiera la medida de neutralidad al riesgo, también llamada medida de equivalencia martingala, se utiliza para establecer precios de derivados por mor del , el cual implica que en un el precio de un derivado es igual al valor esperado descontado del pago futuro bajo la única medida de neutralidad. (es)
- In mathematical finance, a risk-neutral measure (also called an equilibrium measure, or equivalent martingale measure) is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure.This is heavily used in the pricing of financial derivatives due to the fundamental theorem of asset pricing, which implies that in a complete market, a derivative's price is the discounted expected value of the future payoff under the unique risk-neutral measure. Such a measure exists if and only if the market is arbitrage-free. The easiest way to remember what the risk-neutral measure is, or to explain it to a probability generalist who might not know much about finance, is to realize that it is: 1.
* The probability measure of a transformed random variable. Typically this transformation is the utility function of the payoff. The risk-neutral measure would be the measure corresponding to an expectation of the payoff with a linear utility. 2.
* An implied probability measure, that is one implied from the current observable/posted/traded prices of the relevant instruments. Relevant means those instruments that are causally linked to the events in the probability space under consideration (i.e. underlying prices plus derivatives), and 3.
* It is the implied probability measure (solves a kind of inverse problem) that is defined using a linear (risk-neutral) utility in the payoff, assuming some known model for the payoff. This means that you try to find the risk-neutral measure by solving the equation where current prices are the expected present value of the future pay-offs under the risk-neutral measure. The concept of a unique risk-neutral measure is most useful when one imagines making prices across a number of derivatives that would make a unique risk-neutral measure since it implies a kind of consistency in ones hypothetical untraded prices and, theoretically points to arbitrage opportunities in markets where bid/ask prices are visible. It is also worth noting that in most introductory applications in finance, the pay-offs under consideration are deterministic given knowledge of prices at some terminal or future point in time. This is not strictly necessary to make use of these techniques. (en)
- 위험중립측도(risk-neutral measure)는 금융공학에서 폭넓게 쓰이는 마팅게일 측도의 하나로, 파생상품의 가격결정에 필요한 핵심적인 요소 중의 하나이다. 에 따르면 에서 거래되는 파생상품의 가격은 위험중립측도 하에서 계산한 기대가치의 현재가치이며, 따라서 이를 구하기 위해서는 반드시 위험중립측도가 존재하여야 한다. (ko)
- リスク中立確率（リスクちゅうりつかくりつ、英: risk-neutral probability）とは、金融経済学や数理ファイナンス、金融工学などにおいて、金融資産の理論的な価格を決定するために用いられる仮想上の確率である。確率測度であることを強調して、リスク中立確率測度（英: risk-neutral probability measure）やリスク中立測度（英: risk-neutral measure）と呼ばれたり、またその数学的特性から同値マルチンゲール測度（英: equivalent martingale measure）と呼ばれることもある。リスク中立確率の下では全ての資産価格が（局所）マルチンゲールとなる。多くの資産価格理論において中核的な役割を果たしており、確率的割引ファクターや無裁定価格理論などとも深く関連する重要な概念である。 (ja)
- In finanza, la misura di probabilità neutrale al rischio è una misura di probabilità sotto la quale il prezzo corretto (ossia, di non arbitraggio) di un'attività finanziaria è pari al suo valore atteso futuro scontato al tasso privo di rischio. È anche nota come misura a martingala equivalente (dall'inglese equivalent martingale measure). (it)
- Miara martyngałowa (lub miara obojętna na ryzyko) – jedno z podstawowych pojęć z zakresu matematyki finansowej. Używa się go do wyceny instrumentów bazowych oraz pochodnych na . (pl)
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