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**1 - 2**of**2**### To appear in Mathematical Finance GENERALIZATION OF THE DYBVIG–INGERSOLL–ROSS THEOREM AND ASYMPTOTIC MINIMALITY

, 2010

"... Abstract. The long-term limit of zero-coupon rates with respect to the maturity does not always exist. In this case we use the limit superior and prove corresponding versions of the Dybvig–Ingersoll–Ross theorem, which says that long-term spot and forward rates can never fall in an arbitrage-free mo ..."

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Abstract. The long-term limit of zero-coupon rates with respect to the maturity does not always exist. In this case we use the limit superior and prove corresponding versions of the Dybvig–Ingersoll–Ross theorem, which says that long-term spot and forward rates can never fall in an arbitrage-free model. Extensions of popular interest rate models needing this generalization are presented. In addition, we discuss several definitions of arbitrage, prove asymptotic minimality of the limit superior of the spot rates, and illustrate our results by several continuous-time short-rate models. 1.

### Time in Yrs Annual Coupon Market Price

"... The ordinary bootstrap method for computing forward rates from zero rates generates posynomial equations as introduced in an area of optimization termed geometric programming invented by Duffin, Peterson, and Zener [6]. posynomial disc. fns e−zk(tk−t0) �k−1 = i=0 x (ti+1−ti) i,i+1, k = 1,... express ..."

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The ordinary bootstrap method for computing forward rates from zero rates generates posynomial equations as introduced in an area of optimization termed geometric programming invented by Duffin, Peterson, and Zener [6]. posynomial disc. fns e−zk(tk−t0) �k−1 = i=0 x (ti+1−ti) i,i+1, k = 1,... express the forward rates zk(tk − t0) = � k−1 i=0 fi,i+1(ti+1 − ti), where xi,i+1 = e −fi,i+1 in Tables 2–4. Note that the are n equations in m unknowns (n = m =5). Ordinary bootstrapping does not work when n � = m, eg., if there were no 0.5 time T–Bill. 1 (1)