. . . . . "10179"^^ . "La convexit\u00E9 (en anglais : bond convexity) est un indicateur du risque de taux li\u00E9 \u00E0 un instrument \u00E0 taux fixe, comme une obligation, qui compl\u00E8te la sensibilit\u00E9 ou la duration"@fr . "Convexitat d'un bo"@ca . . . . . "849779"^^ . . . . "In matematica finanziaria, la convexity definisce il grado di curvatura della funzione prezzo V(i), e si calcola come il rapporto tra la derivata seconda (calcolata rispetto a variazioni del tasso di interesse) e la funzione stessa. \u00C8 un indice che permette di tenere conto degli aspetti relativi alla convessit\u00E0 della funzione prezzo. Infatti a differenza della duration, che fornisce un'approssimazione lineare della funzione in questione, la convexity serve ad effettuare l'approssimazione della funzione tramite una parabola (che consente di tenere conto del grado di curvatura, ovvero della convessit\u00E0 del titolo) e quindi pi\u00F9 precisa. Inoltre viene solitamente utilizzato come indicatore di rischio per un titolo per la sua capacit\u00E0 di riflettere in un valore sintetico la sensibilit\u00E0 del prezzo del titolo stesso a variazioni di tasso. \u00C8 approssimabile alla sommatoria della somma delle differenze dei tempi al quadrato moltiplicato per i singoli flussi e per il fattore di attualizzazione, tutto diviso la sommatoria dei valori attuali dei flussi.A differenza della convexity, la duration ha natura locale cio\u00E8 a variazioni del prezzo corrispondono variazioni infinitesimali del tasso di interesse, quindi non si possono trarre delle conclusioni attendibili sul prezzo del titolo. La convexity aumenta con la duration, e a parit\u00E0 di duration, aumenta con la varianza dei flussi dal baricentro delle masse.La convexity non ha un significato immediato di durata, ma semplicemente maggiore \u00E8 la convexity maggiore \u00E8 il rischio del prezzo al fattore convexity, maggiore \u00E8 l'errore insito nella duration. All'aumentare della convexity, aumenta la variazione positiva del valore del titolo al diminuire del tasso e si attenua la variazione negativa al crescere del tasso. Per tale motivo \u00E8 chiaro che la convexity sia una caratteristica molta vantaggiosa per quel che riguarda la scelta di titoli alternativi. A parit\u00E0 di duration, infatti, ci si potrebbe porre come obiettivo quello di massimizzare la convexity, per godere del vantaggio di smorzare i ribassi dei prezzi in seguito ad un rialzo del tasso e di accentuarne i rialzi in seguito ad un ribasso del tasso di riferimento."@it . . "\u0641\u064A \u0645\u062C\u0627\u0644 \u0627\u0644\u062A\u0645\u0648\u064A\u0644 \u060C \u064A\u0639\u062F \u062A\u062D\u062F\u0628 \u0627\u0644\u0633\u0646\u062F\u0627\u062A (Bond convexity) \u0645\u0642\u064A\u0627\u0633\u064B\u0627 \u0644\u0644\u0639\u0644\u0627\u0642\u0629 \u063A\u064A\u0631 \u0627\u0644\u062E\u0637\u064A\u0629 \u0644\u0623\u0633\u0639\u0627\u0631 \u0627\u0644\u0633\u0646\u062F\u0627\u062A \u0628\u0627\u0644\u062A\u063A\u064A\u0631\u0627\u062A \u0641\u064A \u0623\u0633\u0639\u0627\u0631 \u0627\u0644\u0641\u0627\u0626\u062F\u0629 \u060C \u0648\u0627\u0644\u0645\u0634\u062A\u0642 \u0627\u0644\u062B\u0627\u0646\u064A \u0644\u0633\u0639\u0631 \u0627\u0644\u0633\u0646\u062F \u0641\u064A\u0645\u0627 \u064A\u062A\u0639\u0644\u0642 \u0628\u0623\u0633\u0639\u0627\u0631 \u0627\u0644\u0641\u0627\u0626\u062F\u0629 (\u0627\u0644\u0645\u062F\u0629 \u0647\u064A \u0627\u0644\u0645\u0634\u062A\u0642 \u0627\u0644\u0623\u0648\u0644). \u0628\u0634\u0643\u0644 \u0639\u0627\u0645 \u060C \u0643\u0644\u0645\u0627 \u0632\u0627\u062F\u062A \u0627\u0644\u0645\u062F\u0629 \u060C \u0643\u0644\u0645\u0627 \u0643\u0627\u0646 \u0633\u0639\u0631 \u0627\u0644\u0633\u0646\u062F \u0623\u0643\u062B\u0631 \u062D\u0633\u0627\u0633\u064A\u0629 \u0644\u0644\u062A\u063A\u064A\u0631 \u0641\u064A \u0623\u0633\u0639\u0627\u0631 \u0627\u0644\u0641\u0627\u0626\u062F\u0629. \u064A\u0639\u062F \u062A\u062D\u062F\u0628 \u0627\u0644\u0633\u0646\u062F\u0627\u062A \u0623\u062D\u062F \u0623\u0643\u062B\u0631 \u0623\u0634\u0643\u0627\u0644 \u0627\u0644\u062A\u062D\u062F\u0628 \u0627\u0644\u0623\u0633\u0627\u0633\u064A\u0629 \u0648\u0627\u0644\u0645\u0633\u062A\u062E\u062F\u0645\u0629 \u0639\u0644\u0649 \u0646\u0637\u0627\u0642 \u0648\u0627\u0633\u0639 \u0641\u064A \u0627\u0644\u062A\u0645\u0648\u064A\u0644."@ar . . "\u0641\u064A \u0645\u062C\u0627\u0644 \u0627\u0644\u062A\u0645\u0648\u064A\u0644 \u060C \u064A\u0639\u062F \u062A\u062D\u062F\u0628 \u0627\u0644\u0633\u0646\u062F\u0627\u062A (Bond convexity) \u0645\u0642\u064A\u0627\u0633\u064B\u0627 \u0644\u0644\u0639\u0644\u0627\u0642\u0629 \u063A\u064A\u0631 \u0627\u0644\u062E\u0637\u064A\u0629 \u0644\u0623\u0633\u0639\u0627\u0631 \u0627\u0644\u0633\u0646\u062F\u0627\u062A \u0628\u0627\u0644\u062A\u063A\u064A\u0631\u0627\u062A \u0641\u064A \u0623\u0633\u0639\u0627\u0631 \u0627\u0644\u0641\u0627\u0626\u062F\u0629 \u060C \u0648\u0627\u0644\u0645\u0634\u062A\u0642 \u0627\u0644\u062B\u0627\u0646\u064A \u0644\u0633\u0639\u0631 \u0627\u0644\u0633\u0646\u062F \u0641\u064A\u0645\u0627 \u064A\u062A\u0639\u0644\u0642 \u0628\u0623\u0633\u0639\u0627\u0631 \u0627\u0644\u0641\u0627\u0626\u062F\u0629 (\u0627\u0644\u0645\u062F\u0629 \u0647\u064A \u0627\u0644\u0645\u0634\u062A\u0642 \u0627\u0644\u0623\u0648\u0644). \u0628\u0634\u0643\u0644 \u0639\u0627\u0645 \u060C \u0643\u0644\u0645\u0627 \u0632\u0627\u062F\u062A \u0627\u0644\u0645\u062F\u0629 \u060C \u0643\u0644\u0645\u0627 \u0643\u0627\u0646 \u0633\u0639\u0631 \u0627\u0644\u0633\u0646\u062F \u0623\u0643\u062B\u0631 \u062D\u0633\u0627\u0633\u064A\u0629 \u0644\u0644\u062A\u063A\u064A\u0631 \u0641\u064A \u0623\u0633\u0639\u0627\u0631 \u0627\u0644\u0641\u0627\u0626\u062F\u0629. \u064A\u0639\u062F \u062A\u062D\u062F\u0628 \u0627\u0644\u0633\u0646\u062F\u0627\u062A \u0623\u062D\u062F \u0623\u0643\u062B\u0631 \u0623\u0634\u0643\u0627\u0644 \u0627\u0644\u062A\u062D\u062F\u0628 \u0627\u0644\u0623\u0633\u0627\u0633\u064A\u0629 \u0648\u0627\u0644\u0645\u0633\u062A\u062E\u062F\u0645\u0629 \u0639\u0644\u0649 \u0646\u0637\u0627\u0642 \u0648\u0627\u0633\u0639 \u0641\u064A \u0627\u0644\u062A\u0645\u0648\u064A\u0644."@ar . "Wypuk\u0142o\u015B\u0107 obligacji"@pl . . . "Konvexit\u00E4t ist eine Kennzahl aus der Finanzmathematik zur Beschreibung des Verhaltens einer Anleihe bei Zins\u00E4nderungen. Es ist eine Erweiterung bzw. Verbesserung der Duration und \u2013 wie diese \u2013 nur eine Sch\u00E4tzung der \u00C4nderung des Barwertes. Der Verlauf des Barwertes von Anleihen im Falle von Zins\u00E4nderungen ist konvex. Da die Duration lediglich die erste Ableitung \u2013 also die Steigung \u2013 ber\u00FCcksichtigt, ist sie nur f\u00FCr kleine Zins\u00E4nderungen zu gebrauchen bzw. wird umso ungenauer, je gr\u00F6\u00DFer die Zins\u00E4nderung ausf\u00E4llt. Die Konvexit\u00E4t ber\u00FCcksichtigt auch die zweite Ableitung \u2013 die Kr\u00FCmmung \u2013 und ist daher eine genauere Ann\u00E4herung an die tats\u00E4chliche Wertver\u00E4nderung. Die Formel zur Berechnung der Konvexit\u00E4t lautet: wobei P0 den Wert der Anleihe zum Zeitpunkt 0 darstellt und i0 den entsprechenden Zinssatz. Ist P0(i0) beispielsweise mit N = Nominale, c = Kupon und i = Zinssatz, so ist die erste Ableitung in diesem Fall und die zweite Ableitung Die Ver\u00E4nderung des Barwertes einer Anleihe nach dem Prinzip der Konvexit\u00E4t erfolgt folgenderma\u00DFen: wobei D = Modifizierte DurationP = Preis (inkl. St\u00FCckzins, sog. \u201Edirty price\u201C) der AnleihedP = Ver\u00E4nderung dieses PreisesdY = Zins\u00E4nderung, z. B. 0,005 bei einer \u00C4nderung von 50 Basispunkten (100 Basispunkte = 1 %)C = Konvexit\u00E4t (Convexity)"@de . "\u0412\u044B\u043F\u0443\u043A\u043B\u043E\u0441\u0442\u044C \u0434\u0435\u043D\u0435\u0436\u043D\u043E\u0433\u043E \u043F\u043E\u0442\u043E\u043A\u0430"@ru . . "In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, the second derivative of the price of the bond with respect to interest rates (duration is the first derivative). In general, the higher the duration, the more sensitive the bond price is to the change in interest rates. Bond convexity is one of the most basic and widely used forms of convexity in finance. Convexity was based on the work of Hon-Fei Lai and popularized by Stanley Diller."@en . "Convexit\u00E9 (finance)"@fr . . "La convexitat d'un bo \u00E9s una mesura de la sensibilitat de la davant la variaci\u00F3 dels tipus d'inter\u00E8s. En general, com m\u00E9s alta sigui la convexitat d'un bo, m\u00E9s sensible ser\u00E0 el preu del bo davant reduccions del tipus d'inter\u00E8s, mentre que ho ser\u00E0 en menor proporci\u00F3 als increments. Per tant, davant dos bons iguals, un inversor preferir\u00E0 aquell bo de major convexitat."@ca . . "La convexit\u00E9 (en anglais : bond convexity) est un indicateur du risque de taux li\u00E9 \u00E0 un instrument \u00E0 taux fixe, comme une obligation, qui compl\u00E8te la sensibilit\u00E9 ou la duration"@fr . . . . "Konvexit\u00E4t (Finanzmathematik)"@de . . . . . . . . "\u062A\u062D\u062F\u0628"@ar . . . . . . . . . . . . "\u0412\u044B\u043F\u0443\u043A\u043B\u043E\u0441\u0442\u044C \u2014 \u0445\u0430\u0440\u0430\u043A\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043A\u0430 \u0434\u0435\u043D\u0435\u0436\u043D\u043E\u0433\u043E \u043F\u043E\u0442\u043E\u043A\u0430 \u0438\u043D\u0441\u0442\u0440\u0443\u043C\u0435\u043D\u0442\u0430 (\u043D\u0430\u043F\u0440\u0438\u043C\u0435\u0440, \u043E\u0431\u043B\u0438\u0433\u0430\u0446\u0438\u0438), \u044F\u0432\u043B\u044F\u044E\u0449\u0430\u044F\u0441\u044F \u043C\u0435\u0440\u043E\u0439 \u0447\u0443\u0432\u0441\u0442\u0432\u0438\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u0438 \u0435\u0433\u043E \u0434\u044E\u0440\u0430\u0446\u0438\u0438 \u043A \u043F\u0440\u043E\u0446\u0435\u043D\u0442\u043D\u044B\u043C \u0441\u0442\u0430\u0432\u043A\u0430\u043C. \u0412\u044B\u043F\u0443\u043A\u043B\u043E\u0441\u0442\u044C \u0441\u043B\u0443\u0436\u0438\u0442 \u043F\u043E\u043F\u0440\u0430\u0432\u043A\u043E\u0439 \u0432\u0442\u043E\u0440\u043E\u0433\u043E \u043F\u043E\u0440\u044F\u0434\u043A\u0430, \u043A\u043E\u0442\u043E\u0440\u0430\u044F \u043F\u043E\u0437\u0432\u043E\u043B\u044F\u0435\u0442 \u0443\u0442\u043E\u0447\u043D\u0438\u0442\u044C \u0432\u043B\u0438\u044F\u043D\u0438\u0435 \u043F\u0440\u043E\u0446\u0435\u043D\u0442\u043D\u044B\u0445 \u0441\u0442\u0430\u0432\u043E\u043A \u043D\u0430 \u0442\u0435\u043A\u0443\u0449\u0443\u044E \u0441\u0442\u043E\u0438\u043C\u043E\u0441\u0442\u044C \u0434\u0435\u043D\u0435\u0436\u043D\u043E\u0433\u043E \u043F\u043E\u0442\u043E\u043A\u0430 \u043E\u0431\u043B\u0438\u0433\u0430\u0446\u0438\u0438. \u041F\u043E\u043F\u0440\u0430\u0432\u043A\u0430 \u043E\u0431\u0443\u0441\u043B\u043E\u0432\u043B\u0435\u043D\u0430 \u0442\u0435\u043C, \u0447\u0442\u043E \u0437\u0430\u0432\u0438\u0441\u0438\u043C\u043E\u0441\u0442\u044C \u0442\u0435\u043A\u0443\u0449\u0435\u0439 \u0441\u0442\u043E\u0438\u043C\u043E\u0441\u0442\u0438 \u043E\u0442 \u043F\u0440\u043E\u0446\u0435\u043D\u0442\u043D\u043E\u0439 \u0441\u0442\u0430\u0432\u043A\u0438 \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043D\u0435\u043B\u0438\u043D\u0435\u0439\u043D\u043E\u0439, \u043F\u043E\u044D\u0442\u043E\u043C\u0443 \u043B\u0438\u043D\u0435\u0430\u0440\u0438\u0437\u0430\u0446\u0438\u044F \u044D\u0442\u043E\u0439 \u0437\u0430\u0432\u0438\u0441\u0438\u043C\u043E\u0441\u0442\u0438 \u0441 \u043F\u043E\u043C\u043E\u0449\u044C\u044E \u0434\u044E\u0440\u0430\u0446\u0438\u0438 \u043C\u043E\u0436\u0435\u0442 \u043D\u0435\u0434\u043E\u0441\u0442\u0430\u0442\u043E\u0447\u043D\u043E \u0442\u043E\u0447\u043D\u043E \u043E\u0442\u0440\u0430\u0437\u0438\u0442\u044C \u0432\u043B\u0438\u044F\u043D\u0438\u0435 \u043F\u0440\u043E\u0446\u0435\u043D\u0442\u043D\u044B\u0445 \u0441\u0442\u0430\u0432\u043E\u043A."@ru . . "Convexity"@it . . "\u503A\u5238\u51F8\u6027\uFF08\u82F1\u8A9E\uFF1Abond convexity\uFF09\u5728\u91D1\u878D\u5B66\u4E2D\u662F\u6307\u503A\u5238\u4EF7\u683C\u4E0E\u5229\u7387\u95F4\u975E\u7EBF\u6027\u5173\u7CFB\u7684\u4E00\u79CD\u91CF\u5EA6\uFF0C\u8868\u793A\u4E3A\u503A\u5238\u4EF7\u683C\u5BF9\u5229\u7387\u7684\u4E8C\u9636\u5BFC\u6570\uFF0C\u5373\u4EF7\u683C\uFF0D\u5229\u7387\u66F2\u7EBF\u7684\u5F2F\u66F2\u7A0B\u5EA6\u3002\u4E0E\u5176\u76F8\u5173\u7684\u4E00\u4E2A\u6982\u5FF5\u4E3A\u503A\u5238\u4E45\u671F\uFF0C\u8868\u793A\u4E3A\u4EF7\u683C\u5BF9\u5229\u7387\u7684\u4E00\u9636\u5BFC\u6570\uFF0C\u5373\u4EF7\u683C\uFF0D\u5229\u7387\u66F2\u7EBF\u7684\u659C\u7387\u3002 \u5BF9\u4E45\u671F\u76F8\u540C\u7684\u4E24\u4E2A\u503A\u5238\uFF0C\u5F53\u5229\u7387\u4E0B\u964D\u65F6\uFF0C\u51F8\u6027\u5927\u7684\u503A\u5238\u4EF7\u683C\u4E0A\u6DA8\u5E45\u5EA6\u66F4\u5927\u3002\u800C\u5F53\u5229\u7387\u4E0A\u5347\u65F6\uFF0C\u51F8\u6027\u5927\u7684\u503A\u5238\u4EF7\u683C\u4E0B\u964D\u7684\u5E45\u5EA6\u66F4\u5C0F\u3002\u6545\u76F8\u540C\u6761\u4EF6\u4E0B\uFF0C\u503A\u5238\u7684\u51F8\u6027\u8D8A\u5927\u8D8A\u597D\u3002 \u5047\u8BBE\u503A\u5238\u4EF7\u683C\u4E3AB\u3001\u5229\u7387\u4E3Ar\uFF0C\u503A\u5238\u51F8\u6027C\u7684\u5B9A\u4E49\u4E3A\uFF1A \u6B64\u5916\uFF0C\u51F8\u6027\u8FD8\u53EF\u4EE5\u8868\u793A\u4E3A\u4FEE\u6B63\u4E45\u671FD\u7684\u51FD\u6570\u3002\u7531\u4E8ED\u6EE1\u8DB3 \u4EE3\u5165\u51F8\u6027\u5B9A\u4E49\u540E\u5F97\u5230 \u5316\u7B80\u4E0A\u5F0F\uFF0C\u53EF\u4EE5\u5F97\u5230\u51F8\u6027\u4E0E\u4FEE\u6B63\u4E45\u671F\u4E4B\u95F4\u7684\u5173\u7CFB"@zh . "W finansach wypuk\u0142o\u015B\u0107 obligacji jest miar\u0105 nieliniowo\u015Bci zmiany ceny obligacji w zale\u017Cno\u015Bci od st\u00F3p procentowych."@pl . . . . . . "Bond convexity"@en . . . "\u503A\u5238\u51F8\u6027"@zh . "In matematica finanziaria, la convexity definisce il grado di curvatura della funzione prezzo V(i), e si calcola come il rapporto tra la derivata seconda (calcolata rispetto a variazioni del tasso di interesse) e la funzione stessa. \u00C8 un indice che permette di tenere conto degli aspetti relativi alla convessit\u00E0 della funzione prezzo. Infatti a differenza della duration, che fornisce un'approssimazione lineare della funzione in questione, la convexity serve ad effettuare l'approssimazione della funzione tramite una parabola (che consente di tenere conto del grado di curvatura, ovvero della convessit\u00E0 del titolo) e quindi pi\u00F9 precisa. Inoltre viene solitamente utilizzato come indicatore di rischio per un titolo per la sua capacit\u00E0 di riflettere in un valore sintetico la sensibilit\u00E0 del prezz"@it . . "1112477210"^^ . . . "\u503A\u5238\u51F8\u6027\uFF08\u82F1\u8A9E\uFF1Abond convexity\uFF09\u5728\u91D1\u878D\u5B66\u4E2D\u662F\u6307\u503A\u5238\u4EF7\u683C\u4E0E\u5229\u7387\u95F4\u975E\u7EBF\u6027\u5173\u7CFB\u7684\u4E00\u79CD\u91CF\u5EA6\uFF0C\u8868\u793A\u4E3A\u503A\u5238\u4EF7\u683C\u5BF9\u5229\u7387\u7684\u4E8C\u9636\u5BFC\u6570\uFF0C\u5373\u4EF7\u683C\uFF0D\u5229\u7387\u66F2\u7EBF\u7684\u5F2F\u66F2\u7A0B\u5EA6\u3002\u4E0E\u5176\u76F8\u5173\u7684\u4E00\u4E2A\u6982\u5FF5\u4E3A\u503A\u5238\u4E45\u671F\uFF0C\u8868\u793A\u4E3A\u4EF7\u683C\u5BF9\u5229\u7387\u7684\u4E00\u9636\u5BFC\u6570\uFF0C\u5373\u4EF7\u683C\uFF0D\u5229\u7387\u66F2\u7EBF\u7684\u659C\u7387\u3002 \u5BF9\u4E45\u671F\u76F8\u540C\u7684\u4E24\u4E2A\u503A\u5238\uFF0C\u5F53\u5229\u7387\u4E0B\u964D\u65F6\uFF0C\u51F8\u6027\u5927\u7684\u503A\u5238\u4EF7\u683C\u4E0A\u6DA8\u5E45\u5EA6\u66F4\u5927\u3002\u800C\u5F53\u5229\u7387\u4E0A\u5347\u65F6\uFF0C\u51F8\u6027\u5927\u7684\u503A\u5238\u4EF7\u683C\u4E0B\u964D\u7684\u5E45\u5EA6\u66F4\u5C0F\u3002\u6545\u76F8\u540C\u6761\u4EF6\u4E0B\uFF0C\u503A\u5238\u7684\u51F8\u6027\u8D8A\u5927\u8D8A\u597D\u3002 \u5047\u8BBE\u503A\u5238\u4EF7\u683C\u4E3AB\u3001\u5229\u7387\u4E3Ar\uFF0C\u503A\u5238\u51F8\u6027C\u7684\u5B9A\u4E49\u4E3A\uFF1A \u6B64\u5916\uFF0C\u51F8\u6027\u8FD8\u53EF\u4EE5\u8868\u793A\u4E3A\u4FEE\u6B63\u4E45\u671FD\u7684\u51FD\u6570\u3002\u7531\u4E8ED\u6EE1\u8DB3 \u4EE3\u5165\u51F8\u6027\u5B9A\u4E49\u540E\u5F97\u5230 \u5316\u7B80\u4E0A\u5F0F\uFF0C\u53EF\u4EE5\u5F97\u5230\u51F8\u6027\u4E0E\u4FEE\u6B63\u4E45\u671F\u4E4B\u95F4\u7684\u5173\u7CFB"@zh . . . . "La convexitat d'un bo \u00E9s una mesura de la sensibilitat de la davant la variaci\u00F3 dels tipus d'inter\u00E8s. En general, com m\u00E9s alta sigui la convexitat d'un bo, m\u00E9s sensible ser\u00E0 el preu del bo davant reduccions del tipus d'inter\u00E8s, mentre que ho ser\u00E0 en menor proporci\u00F3 als increments. Per tant, davant dos bons iguals, un inversor preferir\u00E0 aquell bo de major convexitat."@ca . . "Konvexit\u00E4t ist eine Kennzahl aus der Finanzmathematik zur Beschreibung des Verhaltens einer Anleihe bei Zins\u00E4nderungen. Es ist eine Erweiterung bzw. Verbesserung der Duration und \u2013 wie diese \u2013 nur eine Sch\u00E4tzung der \u00C4nderung des Barwertes. Der Verlauf des Barwertes von Anleihen im Falle von Zins\u00E4nderungen ist konvex. Da die Duration lediglich die erste Ableitung \u2013 also die Steigung \u2013 ber\u00FCcksichtigt, ist sie nur f\u00FCr kleine Zins\u00E4nderungen zu gebrauchen bzw. wird umso ungenauer, je gr\u00F6\u00DFer die Zins\u00E4nderung ausf\u00E4llt. Ist P0(i0) beispielsweise und die zweite Ableitung wobei"@de . . . . . . "In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, the second derivative of the price of the bond with respect to interest rates (duration is the first derivative). In general, the higher the duration, the more sensitive the bond price is to the change in interest rates. Bond convexity is one of the most basic and widely used forms of convexity in finance. Convexity was based on the work of Hon-Fei Lai and popularized by Stanley Diller."@en . 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"W finansach wypuk\u0142o\u015B\u0107 obligacji jest miar\u0105 nieliniowo\u015Bci zmiany ceny obligacji w zale\u017Cno\u015Bci od st\u00F3p procentowych."@pl .