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In mathematical finance, the Greeks are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of these sensitivities are denoted by Greek letters (as are some other finance measures). Collectively these have also been called the risk sensitivities, risk measures or hedge parameters. (en) En matemática financiera, el término griega se refiere a cantidades que representan la sensibilidad del mercado de los instrumentos derivados. Su nombre proviene del hecho de que cada una de las medidas se representa con diferentes letras griegas. Cada griega mide diferentes aspectos del riesgo de la posición del instrumento con respecto a un sobre el que el instrumento en cuestión (o el portfolio) es dependiente. (es) Les lettres grecques ou grecques ou grecs sont les instruments de base de la gestion financière des options. Elles découlent des principaux modèles d'évaluation d'option, notamment de celui de Black Scholes. Ces indicateurs calculent l'impact sur le prix de l'option d'une variation des paramètres qui le forment : * le prix du sous-jacent (ou spot) , * le prix d'exercice fixé par l'option (ou strike) , * la volatilité implicite , * l'échéance de l'option , c'est-à-dire le temps au bout duquel l'option peut être exécutée * le taux d'intérêt (ou interest rate) . * * * , la fonction de densité de probabilité de la loi normale centrée réduite. * , la fonction de répartition de la loi normale centrée réduite. (fr) 그릭스(Greeeks) 옵션 가격결정 함수의 변수 중 하나를 가리키는 문자이다. 는 S, K, r, T, t, σ라는 모수와 변수들로 이루어진 함수이다. 포트폴리오의 가치나 옵션 가격을 이 모수들과 변수들로 미분한 것을 그릭스라고 한다. Greeks라 불리 우는 이유는 이 미분함수들이 △, Γ, Θ, ν, ρ의 그리스 문자로 이루어져 있기 때문이다. (1) Delta[Δ] Δ=∂V/∂S델타는 기초자산의 가격 변화에 대한 파생상품의 변화로 정의된다. (2) Gamma[Γ] Γ=∂∆/∂S=∂/∂S (∂V/∂S)=(∂^2 V)/(∂S^2 )옵션포트폴리오의 감마(gamma[Γ])는 기초자산의 가격변화에 대한 포트폴리오 델타의 변화이다. 이는 자산가격에 대한 포트폴리오의 2차 편도함수(second partial derivative)이다. (3) Theta[Θ] Θ= ∂V/∂t세타(Theta[Θ])는 시간 t가 경과함에 따라 파생상품증권의 가격 V가 어떻게 변화하는지 나타내는 척도로 다음과 같이 정의된다. (4) Vega[ν] ν= ∂V/∂σBSM Formula를 유도할 때, S_t(t시점에서 기초자산의 가격)의 변동성이 일정하다고 가정하였다. 그러나 실제로 변동성은 시간 t에 대해서 상수가 아니다. 변동성 σ가 변화할 때 파생상품 증권의가격 V가 어떻게 변화하는지 보는 척도가 바로 베가이다. 따라서 베가는 파생상품의 가격을 변동성σ로 미분한 값이다. (5) Rho[ρ] ρ= ∂V/∂r무위험자산의 이자율 r이 변화할 때 파생상품증권의 가격 V가 어떻게 변화하는지 나타내는 척도로서 Rho가 사용된다. (ko) Le greche rappresentano numericamente, in forma sintetica e semplice, le diverse dimensioni del rischio connesso al possesso di opzioni. Sono il risultato di specifiche funzioni. In base al diverso fattore di rischio analizzato, si hanno greche diverse di seguito elencate per fattore di rischio e nome tra parentesi. (it) De grieken zijn in de financiële wereld de parameters die de risico's van opties en andere derivaten weergeven. De grieken geven aan wat de risico's zijn van een optie, maar ook grote posities met veel verschillende losse calls en puts over verschillende looptijden worden aangestuurd op deze variabelen - door alle grieken van de losse opties bij elkaar op te tellen. De impact van deze variabelen wordt weergegeven met letters uit het Griekse alfabet, vandaar de term grieken. (nl) W matematyce finansowej współczynniki greckie oznaczają wrażliwość rynku opcji lub innych instrumentów pochodnych. Greckie współczynniki mierzą zmianę wartości opcji w stosunku do zmiany czynników wpływających na wartość opcji. (pl) У фінансовій математиці, греки — це величини, що відображають чутливість ціни похідних цінних паперів, таких як опціони до зміни основних параметрів контракту, від яких залежить вартість інструменту або портфеля фінансових інструментів. Ім'я використовується тому, що найпоширеніші з цих величин позначаються грецькими буквами (як і деякі інші фінансові показники). Всіх разом ці величини також називають чутливості ризику, міри ризику:742 або параметри хеджування. (uk) |
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In mathematical finance, the Greeks are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of these sensitivities are denoted by Greek letters (as are some other finance measures). Collectively these have also been called the risk sensitivities, risk measures or hedge parameters. (en) En matemática financiera, el término griega se refiere a cantidades que representan la sensibilidad del mercado de los instrumentos derivados. Su nombre proviene del hecho de que cada una de las medidas se representa con diferentes letras griegas. Cada griega mide diferentes aspectos del riesgo de la posición del instrumento con respecto a un sobre el que el instrumento en cuestión (o el portfolio) es dependiente. (es) Le greche rappresentano numericamente, in forma sintetica e semplice, le diverse dimensioni del rischio connesso al possesso di opzioni. Sono il risultato di specifiche funzioni. In base al diverso fattore di rischio analizzato, si hanno greche diverse di seguito elencate per fattore di rischio e nome tra parentesi. (it) De grieken zijn in de financiële wereld de parameters die de risico's van opties en andere derivaten weergeven. De grieken geven aan wat de risico's zijn van een optie, maar ook grote posities met veel verschillende losse calls en puts over verschillende looptijden worden aangestuurd op deze variabelen - door alle grieken van de losse opties bij elkaar op te tellen. De impact van deze variabelen wordt weergegeven met letters uit het Griekse alfabet, vandaar de term grieken. (nl) W matematyce finansowej współczynniki greckie oznaczają wrażliwość rynku opcji lub innych instrumentów pochodnych. Greckie współczynniki mierzą zmianę wartości opcji w stosunku do zmiany czynników wpływających na wartość opcji. (pl) У фінансовій математиці, греки — це величини, що відображають чутливість ціни похідних цінних паперів, таких як опціони до зміни основних параметрів контракту, від яких залежить вартість інструменту або портфеля фінансових інструментів. Ім'я використовується тому, що найпоширеніші з цих величин позначаються грецькими буквами (як і деякі інші фінансові показники). Всіх разом ці величини також називають чутливості ризику, міри ризику:742 або параметри хеджування. (uk) Les lettres grecques ou grecques ou grecs sont les instruments de base de la gestion financière des options. Elles découlent des principaux modèles d'évaluation d'option, notamment de celui de Black Scholes. Ces indicateurs calculent l'impact sur le prix de l'option d'une variation des paramètres qui le forment : (fr) 그릭스(Greeeks) 옵션 가격결정 함수의 변수 중 하나를 가리키는 문자이다. 는 S, K, r, T, t, σ라는 모수와 변수들로 이루어진 함수이다. 포트폴리오의 가치나 옵션 가격을 이 모수들과 변수들로 미분한 것을 그릭스라고 한다. Greeks라 불리 우는 이유는 이 미분함수들이 △, Γ, Θ, ν, ρ의 그리스 문자로 이루어져 있기 때문이다. (1) Delta[Δ] Δ=∂V/∂S델타는 기초자산의 가격 변화에 대한 파생상품의 변화로 정의된다. (2) Gamma[Γ] Γ=∂∆/∂S=∂/∂S (∂V/∂S)=(∂^2 V)/(∂S^2 )옵션포트폴리오의 감마(gamma[Γ])는 기초자산의 가격변화에 대한 포트폴리오 델타의 변화이다. 이는 자산가격에 대한 포트폴리오의 2차 편도함수(second partial derivative)이다. (3) Theta[Θ] Θ= ∂V/∂t세타(Theta[Θ])는 시간 t가 경과함에 따라 파생상품증권의 가격 V가 어떻게 변화하는지 나타내는 척도로 다음과 같이 정의된다. (5) Rho[ρ] ρ= ∂V/∂r무위험자산의 이자율 r이 변화할 때 파생상품증권의 가격 V가 어떻게 변화하는지 나타내는 척도로서 Rho가 사용된다. (ko) |
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