Page 37 - PowerPoint Presentation
P. 37

LOS 35.e: Describe the process of calibrating a binomial
    interest rate tree (BIRT) to match a specific term structure.     READING 35: THE ARBITRAGE-FREE VALUATION FRAMEWORK

                                                                                MODULE 35.2: BINOMIAL TREES, PART 2


    EXAMPLE: Based on the par rate curve, spot rates, and forward rates below, Xi asked a colleague to generate a BIRT consistent
    with this data and an assumed volatility of 20%, the results are tabulated below:


                                                                                                     B
                                                                                                             = i 2,LL e 4σ           = (0.07198) e +0.40
                                                                                                                         = 0.1074 or 10.74%




                                                                                                        C   i 2,LU  = i 2,LL e2σ
                                                                                                            But, we don’t have adjacent..!
                                                                                                            Lets bootstrap F2 from S2 & S3:
                                                                               A                               (1 + S 3 ) = (1 + S 2 ) (1 + F2)
                                                                                                                    3
                                                                                                                            2
                                                                                                                                2
                                                                                                               → (1.05069) = (1.0402) (1 + F2)
                                                                                                                        3
                                                                                                                → F2  = 7.198%
    Binomial Tree with σ = 20% (One-year Forward Rates)
                                                           A. = (0.057883)e –(2 × 0.20)
                                                              = 0.0388 or 3.88%
                                                                                                     D    = i 2,LL  = i 2,LU e σ = (0.07198) e –0.40
                                                                                                                     –2
                                                                                                                        = 0.0483 or 4.83%




                                                                                                     TI BA II PLUS calculator:
                                                                                                     e –0.40  =  0.4 [+|–] [2ND] [LN]


    1. Calculate the forward rate indicated by A.
    2. Estimate the forward rate indicated by C.
    3. Estimate forward rates B and D.
                                                         The data and results of this example continues…
   32   33   34   35   36   37   38   39   40   41   42