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3.1 A Simple No-Arbitrage Model

Interest Rate Models: An Introduction CH3. Discrete-Time Binomial Models Andrew 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

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3.1 A Simple No-Arbitrage Model

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  1. 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

  2. 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)=

  3. 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

  4. 3.3 Recombining Binomial Model

  5. ( q*u(T)+(1-q)*d(T)=1 )

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