Session 1 by kramkov

DATA CURVES FOR FINANCIAL MODELS

CONSTRUCTION OF YIELD CURVE FROM DISCOUNT CURVE

initial time = 2
interest rate = 0.07

VALUES VERSUS TIME:

    time           value
   2.001            0.07
   2.476            0.07
   2.951            0.07
   3.426            0.07
   3.901            0.07
   4.376            0.07
   4.851            0.07
   5.326            0.07
   5.801            0.07
   6.276            0.07

NELSON-SIEGEL YIELD CURVE

c0 = 0.02
c1 = 0.04
c2 = 0.06
lambda = 0.05
initial time = 1.5

VALUES VERSUS TIME:

    time           value
     1.5            0.06
       2       0.0602418
     2.5       0.0604674
       3       0.0606774
     3.5       0.0608723
       4       0.0610527
     4.5       0.0612189
       5       0.0613714
     5.5       0.0615108
       6       0.0616374

STATIONARY IMPLIED VOLATILITY IN BLACK MODEL

lambda = 0.05
sigma = 0.2
initial time = 0.75

VALUES VERSUS TIME:

    time           value
    0.75            0.05
    0.85       0.0495041
    0.95       0.0490165
    1.05       0.0485368
    1.15       0.0480651
    1.25       0.0476011
    1.35       0.0471447
    1.45       0.0466958
    1.55       0.0462543
    1.65         0.04582

FORWARD PRICES FOR A STOCK WITH DIVIDENDS

initial time = 1
interest rate = 0.12
spot = 100

Stock dividends:

      time           value      
       1.5               5      
         2               5      
       2.5               5      
         3               5      
       3.5               5      
         4               5      
       4.5               5      
         5               5      
       5.5               5      
         6               5      

VALUES VERSUS TIME:

    time           value
       1             100
   1.233         102.835
   1.466         105.751
   1.699         103.629
   1.932         106.567
   2.165         104.489
   2.398         107.452
   2.631         105.419
   2.864         108.408
   3.097         106.424

