Convexity is a characteristic number from mathematics of finance for the description of the behavior of a loan to be suspended with changes of interest into different directions differently strong exchange rate fluctuations. A usual loan with regular coupon and complete with maturity will more strongly rise with net yield decreases in the course than it with net yield rises in the course will fall. This phenomenon of the convexity becomes under a change of the Duration of the loan with changing net yields. Falling interest causes an increase of the Duration of the loan and thus its interest sensitivity, so that with far falling net yields the improvement in prices accelerates itself. With rising net yields it behaves in reverse.

The price adjustment of a loan becomes estimated as follows by means of the Duration:

dP/P = - D*dY

how

dP = change of the price (inclusive. Share interest, so-called "“dirty price"”) of the loan

P = price (inclusive. Share interest, so-called "“dirty price"”) of the loan

Y = net yield/interest

dY = change of net yield/interest

This formula supplies only for relatively small changes of interest useful results. With larger changes of interest the effect of the convexity is to be considered:

dP/P = - D*dY + 1/2*C*dY2

how

C = convexity

See also

Convexity

Articles in category "Convexity (mathematics of finance)"

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