Please provide steps. and the convexity model predicts thatP(r+ Ar) = P(r)D·P-Ar +1+rcx P (Ar)".СХ Р.Consider the cash flow stream and r in (c). If r increases from 10% to11%, what is the new present values predicted by the duration modeland the convexity model, respectively? Which one of them predicts moreaccurately? 3. (Duration and Convexity for General Cashflow Streams) Equation (4) and (11)in the Lecture Notes 2 give the duration and convexity for the coupon bonds.This question illustrates duration and convexity calculations for general cashflow streams. Consider the n-period cash flow stream (n > 1) depicted on Page23 of Lecture Notes 2, with xo = 0, xx > 0 for k = 1, 2, ..., n – 1, and x, > 0.Assume that all periods have equal length of 1 year (therefore, R= r). Denotethe present value of this cash flow stream as%3DX2XnP = P(r) =+(1+r)²+(1+r)"'(1)1+rRequired precision: 4 digits after decimal point.1+r dP Find out the expression for wk,P dr(a) The duration is defined as D =k = 1, ...,n which satisfy the following conditions: wi+w2+·..+Wn = 1,Wk 2 0, k = 1,..., n, andD = w1 •1+ w2 · 2 + · · · + Wn · N.EP. Find out the expression for wk,1 ď²PP dr² ·(b) The convexity is defined as CX =k = 1, ...,n which satisfy the following conditions: wi+w2+·..+Wn = 1,Wk 2 0, k = 1,..., n, and%3D%3D1• [W1 •1· 2+ w2 · 2 · 3+ ..+ Wn · n· (n+1)].CX(1+r)²(c) Now consider a 5-period cash flow stream x10, xz = 5, with r = 10%. Calculate its present value, duration and convex-0, x40, x22, x3 =ity.(d) If the interest rate changes from r to r+Ar, the present value of the cashflow stream changes from P(r) to P(r+Ar). The duration model predictsthatD·PP(r + Ar) = P(r)1+r

As per the question we are given two models :Duration modelConvexity modelAnd we have to compare…

and the convexity model predicts that D.P 1 + r P(r + Ar) = P(r) - Ar + 1 CX · P · (Ar)². · Consider the cash flow stream and r in (c). If r increases from 10% to 11%, what is the new present values predicted by the duration model and the convexity model, respectively? Which one of them predicts more accurately?