Download
1 / 17
180 likes | 303 Vues
This report by Andrew J. G. Cairns, presented by Zhang Guopei under the guidance of Professor Dai Tianshi, introduces discrete-time binomial models for interest rates. It explores fundamental concepts such as the no-arbitrage condition for zero-coupon bonds, the pricing dynamics of bonds maturing at future dates, and the calculation of the risk-free rate. The model examines scenarios of buying and selling treasury bonds based on the bond pricing at different times and discusses the concept of arbitrage, illustrating these principles through straightforward cases.
E N D
Interest Rate Models:An IntroductionCH3. Discrete-Time Binomial ModelsAndrew J. G. Cairns報告者:張國培指導教授:戴天時
3.1 A Simple No-Arbitrage Model • P(t,T) : the price at time t of a zero-coupon bond which matures at time T • Risk-free rate of interest r(t+s)= -logP(t,t+1) for 0≤s<1 • Cash account B(0)=1 B(t+1)=
Case1: When P(t,T)< sell 獲得 $ Buy units of the T-bond 花費 $ P(t,T)=1 Buy 1units of the t-bond 花費 $ 套利: $ >0 Case2: When P(t,T)> Sell units of the T-bond 獲得$ P(t,T)=1 Sell 1units of the t-bond 獲得$ 0 0 t t T T Buy 花費 $ 套利: $ ->0
