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					                                    Call Option Payoff
        Time 0                                                                     Time 1


                                                                       Final payoff of a call,
Cash Flow to long a call < 0                                           Max[ST - X;0] > 0

                                 From time 0 to T:                                                   Cash flows for
                                 Cash flow = 0 for european call                                     the call buyer
                                 Cash Flow > 0 for an american call.




                                                                       Payment of the final payoff
                                                                       of a call                =-
Writing a call , cash flow > 0                                         Max[ST - X; 0] < 0

                                                                                                     Cash Flows for
                                                                                                     the call writer
                                 From time 0 to T:
                                 Cash flow = 0 for european call
                                 Cash Flow > 0 for an american call.




                                     Put Option Payoff
       Tempo 0                                                                  Tempo 1
Long a put                                             Put final payoff
 cash flow < 0                                         Max[X - ST;0] > 0
                                                                                      Cash flows for
                                                                                      the put buyer


                 From time 0 to T:
                 Cash flow = 0 for european call
                 Cash Flow > 0 for an american call.



                                                       Payment for the final payoff
                                                       of a put
Writing a put                                          = - Max[X - ST; 0] < 0
cash flow > 0
                                                                                      Cash flows for
                                                                                      the put writer


                 From time 0 to T:
                 Cash flow = 0 for european call
                 Cash Flow > 0 for an american call.
                                              Data for figures 13.3



                                     Profit/loss for GP stock and option prices
Initial Price Stock GP                    40
Final Price Stock GP                      70

Profit for buying the stock                30 #NAME?
profit for short selling the stock        -30 #NAME?

Strike Price                               40
Call Price July                             4
Long call                                  26 #NAME?
Writing a call profit                     -26 #NAME?

Strike price for Put                      40
Prezzo Put, July                           2
Profit for long a put                     -2 #NAME?
Profit for selling a put                   2 #NAME?


                                      Final
                                      Price        Long        Short selling      Buy a
                                      Stock        stock          stock            call
                                           0           -40                  40        -4
                                           5           -35                  35        -4
                                          10           -30                  30        -4
                                          15           -25                  25        -4
                                          20           -20                  20        -4
                                          25           -15                  15        -4
                                          30           -10                  10        -4
                                          35             -5                   5       -4
                                          40              0                   0       -4
                                          45              5                  -5        1
                                          50            10                 -10         6
                                          55            15                 -15        11
                                          60            20                 -20        16
                                          65            25                 -25        21
                                          70            30                 -30        26
                                          75            35                 -35        31




                                                    Page 3
                        Data for figures 13.3




Sell         By         Sell
call         put        put
         4         38          -38
         4         33          -33
         4         28          -28
         4         23          -23
         4         18          -18
         4         13          -13
         4          8           -8
         4          3           -3
         4         -2            2
        -1         -2            2
        -6         -2            2
       -11         -2            2
       -16         -2            2
       -21         -2            2
       -26         -2            2
       -31         -2            2




                               Page 4
                                                        UN-10F



                                               Stock profits


            50


            40


            30


            20


            10
Profit($)




             0
                  0   10   20   30                 40                   50         60   70   80

            -10


            -20


            -30


            -40                  Long stock                  Short selling stock

            -50
                                     Final Price of the Stock, ST ($)




                                                        Page 5
                                                     UN-10G



                                        Payoff for the call

               40



               30



               20



               10
Profitto ($)




                0
                     0   10   20   30                 40                 50   60   70   80


               -10



               -20



               -30

                                        Buy a call           Sell call
               -40
                                            Stock final price, ST ($)
                                                   13.3 c



                                        Payoff for the put


               50


               40


               30


               20


               10
Profitto ($)




                0
                     0   10   20   30                40                50   60   70   80

               -10


               -20


               -30                       By put           Sell put

               -40


               -50
                                          Stock Final price , ST ($)




                                                   Page 7
                                    Dati grafico 13.4 a



                              Protection Put
Initial Price for the stock        40
Stock final price                  30

Strike price for the put           40
Put Price, July                     2

Stock profit, sept.               -10 #NAME?
Put profit, sept.                   8 #NAME?
Final put profit                   -2 #NAME?

                                        Final     Stock Profit    Put      Final
                                        Stock                    Profit     put
                                        Price                              profit

                                              0            -40        38            -2
                                              5            -35        33            -2
                                             10            -30        28            -2
                                             15            -25        23            -2
                                             20            -20        18            -2
                                             25            -15        13            -2
                                             30            -10         8            -2
                                             35             -5         3            -2
                                             40              0        -2            -2
                                             45              5        -2             3
                                             50             10        -2             8
                                             55             15        -2            13
                                             60             20        -2            18
                                             65             25        -2            23
                                             70             30        -2            28




                                         Page 8
                                     Protective put payoff
         50

         40

         30

         20

         10
Profit




          0
 ($)




               0     10        20      30           40            50    60        70        80
         -10

         -20

         -30
                   Profitto azione             Profitto put              Final put profit
         -40

         -50

                                            Final Stock price, ST ($)
                                    Dati grafico 13.4 b



                                         STRANGLE
Call Price, X=23                                    2
Call Price, X=50                                   23
Final stock price, ST                              24

Profit from writing a call X = 50                  22 #NAME?                           1
Profit from buying a call X = 40                   -1 #NAME?
                                                   21 #NAME?
Strike della put                                   25
prezzo della put                                    3
profit from buying a put                            1 Stock       Buy       Buy Put
                                                       Price   call, X=23   put x=25

                                                           0           -4              44
                                                           5           -4              34
                                                          10           -4              24
                                                          15           -4              14
                                                          20           -4               4
                                                          21           -4               2
                                                          22           -4               0
                                                          23           -4              -2
                                                          24           -2              -4
                                                          25            0              -6
                                                          26            2              -6
                                                          27            4              -6
                                                          28            6              -6
                                                          29            8              -6
                                                          30           10              -6
                                                          35           20              -6
                                                          40           30              -6
                                                          45           40              -6
                                                          50           50              -6
                                                          55           60              -6
                                                          60           70              -6




                                         Page 10
                                                Dati grafico 13.4 b




  Profit
Bull-spread
              <-- Label for Hidden Data Table
         40
         30
         20
         10
          0
         -2
         -4
         -6
         -6
         -6
         -4
         -2
          0
          2
          4
         14
         24
         34
         44
         54
         64




                                                     Page 11
                                        UN-10J




                            Strategia A


                70
                65
                60
                55
                50
                45
                40
Profitto ($)

                35
                30
                25
                20                                      Buy call, X=23
                15
                10                                      Buy Put put x=25
                 5
                 0
                -5 0                                    Profit Bull-spread
                       20               40                60
               -10
                            Final stock price, ST ($)
                                        A                                B       C
1   Theorem 1 -- Lower bounds for the call prices (are going to be set higher)
2
3   Stock price, S0                                                        83
4   Option maturity, T                                                    0.5
5   Strike price, X                                                        80
6   Risk free rate, r                                                    10%
7
8   Minimum option price "naif", Max(S0-X;0)                                 3 #NAME?
9 Teorema 1 - Lower bounds for the option price, Max(S0 - Exp(-rT)X;0)   6.902 #NAME?
Theorem 3 -- Lower bounds for the put

Stock price, S0                                          55
Option maturity, T                                      0.5
Strike price for the option, X                           80
Risk free rate, r                                      10%

Min. put option price "Naif", Max(X- S0;0)               25 #NAME?
Lower bound for the put price, Max(Exp(-rT)X- S0;0)   21.098 #NAME?
                          A                      B           C           D           E           F
 1   Put-Call Parity
 2
 3   Stock price, S0                                 55
 4   Option maturity, T                             0.5
 5   Strike price, X                                 60
 6   Risk free rate, r                            10%
 7   call price, C                                    3
 8   Put price                                  5.0738 #NAME?
 9
10   This spreadsheet uses the put call parity to estimate the put price given the call price,
11   the risk free rate, r, the maturity, T, and the strike price, X.
            STRANGLE
Call Price, X=23                     2
Call Price, X=50                    23
Final stock price, ST               24

Profit from writing a call X = 50   22   #NAME?                                          1
Profit from buying a call X = 40    -1   #NAME?
                                    21   #NAME?
Strike della put                    25
prezzo della put                     3
profit from buying a put             1   Stock         sell 2 call         sell 2 put
                                         Price         call, X=23          put x=25

                                                   0                   4                -44
                                                   5                   4                -34
                                                  10                   4                -24
                                                  15                   4                -14
                                                  20                   4                 -4
                                                  21                   4                 -2
                                                  22                   4                  0
                                                  23                   4                  2
                                                  24                   2                  4
                                                  25                   0                  6
                                                  26                  -2                  6
                                                  27                  -4                  6
                                                  28                  -6                  6
                                                  29                  -8                  6
                                                  30                 -10                  6
                                                  35                 -20                  6
                                                  40                 -30                  6
                                                  45                 -40                  6
                                                  50                 -50                  6
                                                  55                 -60                  6
                                                  60                 -70                  6
  Profit
Bull-spread                                  Strategia b
              -40
              -30
              -20
                    20
              -10
                0   10
                2
                4    0
                6         0   10   20   30        40       50   60   70
                6   -10
                6
                4   -20
                2
                0   -30
               -2
                    -40
               -4
              -14   -50
              -24
              -34
              -44
              -54
              -64

				
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