Abstract
As the ten OAT have the same anniversary dates, in other words the different cash-flows are paid at the same dates (25-Apr-08, 25-Apr-09, 25-Apr-10,), then we used a direct method of calculation of the spot rates, through two steps. Using a polynomial interpolation, we can recover the yield curve. We use a cubic interpolation of the term structure of zero-coupon rates. The interpolated discount rate R(0,t) is defined by R(0,t) = at3+bt²+ct+d with te[t1,t4] and we impose that R(0,t) is on the curve. Given a, b, c and d for each segment, we can compute all the intermediate rates (Cf appendix 1) and draw the term structure of discount rates. For the linear interpolation, we use the following formula : R(0,t) = [(t2-t) R(0,t1) + (t1-t) R(0,t2)] / (t2-t1). The strength of this method is to give a better approximation than the linear interpolation. The limitations of this method are the approximation of intermediate rates and the imposition of real prices as fair prices: the polynomial interpolation is indeed a direct method.
