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Risk Management and Derivatives Final Q1. You work for a UK building society (ie. mortgage bank) which is considering to launch a 10 year fixed mortgage based on the potential demand for such a...

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Risk Management and Derivatives Final
Q1. You work for a UK building society (ie. mortgage bank) which is considering to launch a 10 year fixed mortgage based on the potential demand for such a product and similar products which are available from some of your competitors. but in the future it is expected that rates are going to rise (possible due to inflationary pressure). The Board of Directors knows that you have just completed a module in Derivatives and Risk Management and they want you to present to them the case of offering such a product with the potential risks to your institution highlighted and how you could deal with them. How would you launch a 10 year fixed rate mortgage product? [35 marks]
Q2. Use the BOPM to price a call and put option. Use Excel to build a 10 nodes tree. The time to expiry should be 1 year and interest rates are 1% per annum. You need to choose your own stock price, strike price and volatility. (Important : You need to choose different parameters than given in the Excel spreadsheet provided for the module). Price a European Call, European Put, American Call and American Put option. Compare your results against the Black-Scholes model and make suggestions how you could improve on the calculations undertaken in the BOPM. [30 marks]
Q3.You are a UK based asset management company and you hold the following international portfolio. On the 20th of December 2018 you set up the following international portfolio. You investment is just less than £10,000. Use data provided in ‘cw Data 2020.xlsx’.
    Country  
    Company
    Number of Shares
    US  
    Bank of America  
    85
    Germany  
    BMW
    30
    Germany  
    Lufthansa
    130
    US
    Amazon
    3
    UK
    Tesco
    273
(a.) Calculate the 10 day VaR of your portfolio at the 95% confidence level based on the variance-covariance method on the 10th June 2019, 24th June 2019, and 8th July 2019.
(b.) Repeat the calculations above, but use the exponential moving average for your volatility forecast in the calculation of the VaR using the variance-covariance method.
(c.) Repeat the calculations of the VaR of your portfolio using historic simulation.
(d.) Calculate the actual change in the value of your portfolio over the following 10 days. Compare your calculations with your VaR calculations performed in (a.) to (c.) and critically asses them. Comment critical on the practical implications. Explain what we understand by backtesting, how you would do it and what is the significance of it.
(Make any reasonable assumptions you need for the calculations.) [35 marks]
Hint : You have to draw standard normally distributed random variables. In Excel that can be done with the following command : NORMSINV(RAND())

Normal Distribution
    Cumulative Normal Distribution : N(0,1)
    z    0    0.01    0.02    0.03    0.04    0.05    0.06    0.07    0.08    0.09
    0    0.5    0.504    0.508    0.512    0.516    0.5199    0.5239    0.5279    0.5319    0.5359
    0.1    0.5398    0.5438    0.5478    0.5517    0.5557    0.5596    0.5636    0.5675    0.5714    0.5753
    0.2    0.5793    0.5832    0.5871    0.591    0.5948    0.5987    0.6026    0.6064    0.6103    0.6141
    0.3    0.6179    0.6217    0.6255    0.6293    0.6331    0.6368    0.6406    0.6443    0.648    0.6517
    0.4    0.6554    0.6591    0.6628    0.6664    0.67    0.6736    0.6772    0.6808    0.6844    0.6879
    0.5    0.6915    0.695    0.6985    0.7019    0.7054    0.7088    0.7123    0.7157    0.719    0.7224
    0.6    0.7257    0.7291    0.7324    0.7357    0.7389    0.7422    0.7454    0.7486    0.7517    0.7549
    0.7    0.758    0.7611    0.7642    0.7673    0.7704    0.7734    0.7764    0.7794    0.7823    0.7852
    0.8    0.7881    0.791    0.7939    0.7967    0.7995    0.8023    0.8051    0.8078    0.8106    0.8133
    0.9    0.8159    0.8186    0.8212    0.8238    0.8264    0.8289    0.8315    0.834    0.8365    0.8389
    1    0.8413    0.8438    0.8461    0.8485    0.8508    0.8531    0.8554    0.8577    0.8599    0.8621
    1.1    0.8643    0.8665    0.8686    0.8708    0.8729    0.8749    0.877    0.879    0.881    0.883
    1.2    0.8849    0.8869    0.8888    0.8907    0.8925    0.8944    0.8962    0.898    0.8997    0.9015
    1.3    0.9032    0.9049    0.9066    0.9082    0.9099    0.9115    0.9131    0.9147    0.9162    0.9177
    1.4    0.9192    0.9207    0.9222    0.9236    0.9251    0.9265    0.9279    0.9292    0.9306    0.9319
    1.5    0.9332    0.9345    0.9357    0.937    0.9382    0.9394    0.9406    0.9418    0.9429    0.9441
    1.6    0.9452    0.9463    0.9474    0.9484    0.9495    0.9505    0.9515    0.9525    0.9535    0.9545
    1.7    0.9554    0.9564    0.9573    0.9582    0.9591    0.9599    0.9608    0.9616    0.9625    0.9633
    1.8    0.9641    0.9649    0.9656    0.9664    0.9671    0.9678    0.9686    0.9693    0.9699    0.9706
    1.9    0.9713    0.9719    0.9726    0.9732    0.9738    0.9744    0.975    0.9756    0.9761    0.9767
    2    0.9772    0.9778    0.9783    0.9788    0.9793    0.9798    0.9803    0.9808    0.9812    0.9817
    2.1    0.9821    0.9826    0.983    0.9834    0.9838    0.9842    0.9846    0.985    0.9854    0.9857
    2.2    0.9861    0.9864    0.9868    0.9871    0.9875    0.9878    0.9881    0.9884    0.9887    0.989
    2.3    0.9893    0.9896    0.9898    0.9901    0.9904    0.9906    0.9909    0.9911    0.9913    0.9916
    2.4    0.9918    0.992    0.9922    0.9925    0.9927    0.9929    0.9931    0.9932    0.9934    0.9936
    2.5    0.9938    0.994    0.9941    0.9943    0.9945    0.9946    0.9948    0.9949    0.9951    0.9952
    2.6    0.9953    0.9955    0.9956    0.9957    0.9959    0.996    0.9961    0.9962    0.9963    0.9964
    2.7    0.9965    0.9966    0.9967    0.9968    0.9969    0.997    0.9971    0.9972    0.9973    0.9974
    2.8    0.9974    0.9975    0.9976    0.9977    0.9977    0.9978    0.9979    0.9979    0.998    0.9981
    2.9    0.9981    0.9982    0.9982    0.9983    0.9984    0.9984    0.9985    0.9985    0.9986    0.9986
    3    0.9987    0.9987    0.9987    0.9988    0.9988    0.9989    0.9989    0.9989    0.999    0.999
    3.1    0.999    0.9991    0.9991    0.9991    0.9992    0.9992    0.9992    0.9992    0.9993    0.9993
    3.2    0.9993    0.9993    0.9994    0.9994    0.9994    0.9994    0.9994    0.9995    0.9995    0.9995
    3.3    0.9995    0.9995    0.9995    0.9996    0.9996    0.9996    0.9996    0.9996    0.9996    0.9997
    3.4    0.9997    0.9997    0.9997    0.9997    0.9997    0.9997    0.9997    0.9997    0.9997    0.9998
BS Option Pricing Model
    Calculating the BS option price
    Put-call parity concept is used here to calculate the Put premium.
    only change the values in the yellow shaded area. Do not change anything else.
    S        120
    K        125
    r        0.02
    T         XXXXXXXXXX    165    days
    d        0
    Sigma        0.2
        B-S Call Premium         XXXXXXXXXX
        B-S Put Premium         XXXXXXXXXX
    Auxillary inputs to calculate B-S premia
        d1    d2    N -"dash"
                (d1)
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
Imp. Vol. Trial and E
o
    Calculating the Implied Volatility (using Trial and E
or)
    Data Inputs
    S        164
    K        165
    r        0.0521
    T        0.0959
    d        0
    Quoted C Premium        5.75
    Trial and E
or calculations
    Choose different values for "sigma" and calculate the "theoretical"
    call premium using B-S until the latter equals the actual quoted call premium
    Trial    d1    d2    N -"dash"    Call
    values for            (d1)    Premium
    Sigma                using B-S
    0.281     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
    0.282     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
    0.283     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
    0.284     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
    0.285     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
    0.286     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
    0.287     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
    0.288     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
    0.289     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX
    Sigma=0.288 gives quoted call premium
Imp. Vol. Sove
    Calculating the Implied Volatilities (Using "Solver")
    Data Inputs
    only change the values in the yellow shaded area. Do not change anything else.
    S        164
    K        165
    r        0.0521
    T        0.0959
    d        0
    Actual Call Premum        5.75
    B-S Call Premium         XXXXXXXXXX
    Cell to be minimised by SOLVER( Actual premium - B-S Premium)^2 =                             XXXXXXXXXX
    Start value (and final value) for Sigma for use in SOLVER =                            0.2
    Auxillary inputs to calculate B-S premia
        d1    d2    N -"dash"
                (d1)
         XXXXXXXXXX     XXXXXXXXXX     XXXXXXXXXX

Daily ExR Returns
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    33413
    33414
    33415
    33416
    33417
    33420
    33421
    33422
    33423
    33424
    33427
    33428
    33429
    33430
    33431
    33434
    33435
    33436
    33437
    33438
    33441
    33442
    33443
    33444
    33445
    33448
    33449
    33450
    33451
    33452
    33455
    33456
    33457
    33458
    33459
    33462
    33463
    33464
    33465
    33466
    33469
    33470
    33471
    33472
    33473
    33476
    33477
    33478
    33479
    33480
    33483
    33484
    33485
    33486
    33487
    33490
    33491
    33492
    33493
    33494
    33497
    33498
    33499
    33500
    33501
    33504
    33505
    33506
    33507
    33508
    33511
    33512
    33513
    33514
    33515
    33518
    33519
    33520
    33521
    33522
    33525
    33526
    33527
    33528
    33529
Answered Same Day Jul 31, 2021

Solution

Neenisha answered on Aug 06 2021
120 Votes
Question 1
Fixed rate mortgages is a loan for home which has fixed interest rate for the entire term. This means that the interest rate which is decided today will remain through the tenure of the mortgage. They usually have term of 10 – 3- years.
These mortgages are prefe
ed because they are predictable and the person who has bo
owed the loan knows that what amount is to be paid in every instalment and thus there is no volatility. This is because there is no fluctuation in the interest rates and they remain same.
Advantages of 10 year fixed rate mortgages
The major advantage is that they are fixed for long term and there is no fluctuation. This means that the bo
ower can budget the loan and its payment very easily.
Disadvantage of 10 year fixed rate mortgages
The major disadvantage is that since the interest rate is fixed, therefore, there is a possibility that the rate decreases in future and thus this means that you took a loan at high interest rate.
In United Kingdom these loans or mortgages are widely used especially by building societies, lenders prefer different type of mortgages from variable interest rate to fixed interest rate.
Question 2
Binomial Pricing Model
    Stock Price
    810
    Strike Price
    800
    Interest Rate
    1%
    Volatility
    30%
    Dividends
    0%
    Time to Maturity in Years
    1
    Binomial Steps
    10
    Delta T
    0.1
     
     
    Up Facto
    1.10
    Down Facto
    0.91
    Growth Factor (a)
    1.00
    p
    0.48
    q
    0.52
European Call Option
    
    
    
    
    
    
    
    
    
    
    2091.7
    
    
    
    
    
    
    
    
    
    
    1291.6
    
    
    
    
    
    
    
    
    
    1902.4
    
    
    
    
    
    
    
    
    
    
    1103.2
    1730.2
    
    
    
    
    
    
    
    
    1730.2
    
    930.2
    
    
    
    
    
    
    
    
    931.8
    1573.6
    
    
    
    
    
    
    
    
    1573.6
    
    774.4
    1431.2
    
    
    
    
    
    
    
    776.0
    1431.2
    
    631.2
    
    
    
    
    
    
    1431.2
    
    632.8
    1301.6
    
    
    
    
    
    
    
    634.4
    1301.6
    
    502.4
    1183.8
    
    
    
    
    
    1301.6
    
    504.0
    1183.8
    
    383.8
    
    
    
    
    
    505.6
    1183.8
    
    385.4
    1076.7
    
    
    
    
    
    1183.8
    
    387.0
    1076.7
    
    277.5
    979.2
    
    
    
    
    391.1
    1076.7
    
    279.1
    979.2
    
    179.2
    
    
    
    1076.7
    
    285.5
    979.2
    
    180.8
    890.6
    
    
    
    
    293.2
    979.2
    
    191.8
    890.6
    
    91.4
    810.0
    
    
    979.2
    
    202.7
    890.6
    
    111.1
    810.0
    
    10.0
    
    
    213.1
    890.6
    
    126.3
    810.0
    
    46.5
    736.7
    
    
    890.6
    
    139.1
    810.0
    
    65.6
    736.7
    
    4.8
    670.0
    
    150.5
    810.0
    
    80.3
    736.7
    
    23.6
    670.0
    
    0.0
    810.0
    
    92.6
    736.7
    
    37.7
    670.0
    
    2.3
    609.4
    
    103.5
    736.7
    
    49.6
    670.0
    
    11.9
    609.4
    
    0.0
    554.2
    
    60.1
    670.0
    
    21.3
    609.4
    
    1.1
    554.2
    
    0.0
    
    
    30.0
    609.4
    
    6.0
    554.2
    
    0.0
    504.1
    
    
    
    
    11.8
    554.2
    
    0.5
    504.1
    
    0.0
    458.4
    
    
    
    
    3.0
    504.1
    
    0.0
    458.4
    
    0.0
    
    
    
    
    
    0.3
    458.4
    
    0.0
    416.9
    
    
    
    
    
    
    
    0.0
    416.9
    
    0.0
    379.2
    
    
    
    
    
    
    
    0
    379.2
    
    0.0
    
    
    
    
    
    
    
    
    0.0
    344.9
    
    
    
    
    
    
    
    
    
    
    0.0
    313.7
    
    
    
    
    
    
    
    
    
    
    0.0
    
    
    
    
    
    
    
    
    
    
    
European Put Option
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    2091.7
    
    
    
    
    
    
    
    
    
    
    0.0
    
    
    
    
    
    
    
    
    
    1902.4
    
    
    
    
    
    
    
    
    
    
    0.0
    1730.2
    
    
    
    
    
    
    
    
    1730.2
    
    0.0
    
    
    
    
    
    
    
    
    0.0
    1573.6
    
    
    
    
    
    
    
    
    1573.6
    
    0.0
    1431.2
    
    
    
    
    
    
    
    0.0
    1431.2
    
    0.0
    
    
    
    
    
    
    1431.2
    
    0.0
    1301.6
    
    
    
    
    
    
    
    0.0
    1301.6
    
    0.0
    1183.8
    
    
    
    
    
    1301.6
    
    0.0
    1183.8
    
    0.0
    
    
    
    
    
    0.0
    1183.8
    
    0.0
    1076.7
    
    
    
    
    
    1183.8
    
    0.0
    1076.7
    
    0.0
    979.2
    
    
    
    
    2.5
    1076.7
    
    0.0
    979.2
    
    0.0
    
    
    
    1076.7
    
    4.8
    979.2
    
    0.0
    890.6
    
    
    
    
    10.9
    979.2
    
    9.4
    890.6
    
    0.0
    810.0
    
    
    979.2
    
    18.7
    890.6
    
    18.1
    810.0
    
    0.0
    
    
    27.5
    890.6
    
    31.7
    810.0
    
    34.9
    736.7
    
    
    890.6
    
    42.9
    810.0
    
    52.4
    736.7
    
    67.3
    670.0
    
    52.7
    810.0
    
    65.5
    736.7
     
    84.5
    670.0
    
    130.0
    810
    
    76.3
    736.7
    
    97.1
    670.0
    
    130.7
    609.4
    
    85.6
    736.7
    
    107.4
    670.0
    
    138.7
    609.4
    
    189.8
    554.2
    
    116.2
    670.0
    
    146.5
    609.4
    
    189.3
    554.2
    
    245.8
    
    
    153.6
    609.4
    
    192.6
    554.2
    
    244.2
    504.1
    
    
    
    
    196.8
    554.2
    
    243.1
    504.1
    
    295.1
    458.4
    
    
    
    
    244.0
    504.1
    
    293.5
    458.4
    
    341.6
    
    
    
    
    
    292.2
    458.4
    
    340.0
    416.9
    
    
    
    
    
    
    
    338.4
    416.9
    
    382.3
    379.2
    
    
    
    
    
    
    
    380.7
    379.2
    
    420.8
    
    
    
    
    
    
    
    
    419.2
    344.9
    
    
    
    
    
    
    
    
    
    
    454.3
    313.7
    
    
    
    
    
    
    
    
    
    
    486.3
American Call Options
    
    
    
    
    
    
    
    
    
    
    2091.7
    
    
    
    
    
    
    
    
    
    
    0.0
    
    
    
    
    
    
    
    
    
    1902.4
    
    
    
    
    
    
    
    
    
    
    0.0
    1730.2
    
    
    
    
    
    
    
    
    1730.2
    
    0.0
    
    
    
    
    
    
    
    
    0.0
    1573.6
    
    
    
    
    
    
    
    
    1573.6
    
    0.0
    1431.2
    
    
    
    
    
    
    
    0.0
    1431.2
    
    0.0
    
    
    
    
    
    
    1431.2
    
    0.0
    1301.6
    
    
    
    
    
    
    
    0.0
    1301.6
    
    0.0
    1183.8
    
    
    
    
    
    1301.6
    
    0.0
    1183.8
    
    0.0
    
    
    
    
    
    0.0
    1183.8
    
    0.0
    1076.7
    
    
    
    
    
    1183.8
    
    0.0
    1076.7
    
    0.0
    979.2
    
    
    
    
    2.5
    1076.7
    
    0.0
    979.2
    
    0.0
    
    
    
    1076.7
    
    4.8
    979.2
    
    0.0
    890.6
    
    
    
    
    10.9
    979.2
    
    9.4
    890.6
    
    0.0
    810.0
    
    
    979.2
    
    18.8
    890.6
    
    18.1
    810.0
    
    0.0
    
    
    27.6
    890.6
    
    31.7
    810.0
    
    34.9
    736.7
    
    
    890.6
    
    43.1
    810.0
    
    52.5
    736.7
    
    67.3
    670.0
    
    53.0
    810.0
    
    65.8
    736.7
    
    84.7
    670.0
    
    130.0
    810.0
    
    76.7
    736.7
    
    97.5
    670.0
    
    131.1
    609.4
    
    86.2
    736.7
    
    108.1
    670.0
    
    139.5
    609.4
    
    190.6
    554.2
    
    117.2
    670.0
    
    147.6
    609.4
    
    190.6
    554.2
    
    245.8
    
    
    155.0
    609.4
    
    194.4
    554.2
    
    245.8
    504.1
    
    
    
    
    198.8
    554.2
    
    245.8
    504.1
    
    295.9
    458.4
    
    
    
    
    246.8
    504.1
    
    295.9
    458.4
    
    341.6
    
    
    
    
    
    295.9
    458.4
    
    341.6
    416.9
    
    
    
    
    
    
    
    341.6
    416.9
    
    383.1
    379.2
    
    
    
    
    
    
    
    383.1
    379.2
    
    420.8
    
    
    
    
    
    
    
    
    420.8
    344.9
    
    
    
    
    
    
    
    
    
    
    455.1
    313.7
    
    
    
    
    
    
    
    
    
    
    486.3
    
    
    
    
    
    
    
    
    
    
    
American Put Option
    
    
    
    
    
    
    
    
    
    
    2091.7
    
    
    
    
    
    
    
    
    
    
    0.0
    
    
    
    
    
    
    
    
    
    1902.4
    
    
    
    
    
    
    
    
    
    
    0.0
    1730.2
    
    
    
    
    
    
    
    
    1730.2
    
    0.0
    
    
    
    
    
    
    
    
    0.0
    1573.6
    
    
    
    
    
    
    
    
    1573.6
    
    0.0
    1431.2
    
    
    
    
    
    
    
    0.0
    1431.2
    
    0.0
    
    
    
    
    
    
    1431.2
    
    0.0
    1301.6
    
    
    
    
    
    
    
    0.0
    1301.6
    
    0.0
    1183.8
    
    
    
    
    
    1301.6
    
    0.0
    1183.8
    
    0.0
    
    
    
    
    
    0.0
    1183.8
    
    0.0
    1076.7
    
    
    
    
    
    1183.8
    
    0.0
    1076.7
    
    0.0
    979.2
    
    
    
    
    2.5
    1076.7
    
    0.0
    979.2
    
    0.0
    
    
    
    1076.7
    
    4.8
    979.2
    
    0.0
    890.6
    
    
    
    
    10.9
    979.2
    
    9.4
    890.6
    
    0.0
    810.0
    
    
    979.2
    
    18.8
    890.6
    
    18.1
    810.0
    
    0.0
    
    
    27.6
    890.6
    
    31.7
    810.0
    
    34.9
    736.7
    
    
    890.6
    
    43.1
    810.0
    
    52.5
    736.7
    
    67.3
    670.0
    
    53.0
    810.0
    
    65.8
    736.7
    
    84.7
    670.0
    
    130.0
    810.0
    
    76.7
    736.7
    
    97.5
    670.0
    
    131.1
    609.4
    
    86.2
    736.7
    
    108.1
    670.0
    
    139.5
    609.4
    
    190.6
    554.2
    
    117.2
    670.0
    
    147.6
    609.4
    
    190.6
    554.2
    
    245.8
    
    
    155.0
    609.4
    
    194.4
    554.2
    
    245.8
    504.1
    
    
    
    
    198.8
    554.2
    
    245.8
    504.1
    
    295.9
    458.4
    
    
    
    
    246.8
    504.1
    
    295.9
    458.4
    
    341.6
    
    
    
    
    
    295.9
    458.4
    
    341.6
    416.9
    
    
    
    
    
    
    
    341.6
    416.9
    
    383.1
    379.2
    
    
    
    
    
    
    
    383.1
    379.2
    
    420.8
    
    
    
    
    
    
    
    
    420.8
    344.9
    
    
    
    
    
    
    
    
    
    
    455.1
    313.7
    
    
    
    
    
    
    
    
    
    
    486.3
    
    
    
    
    
    
    
    
    
    
    
    Stock Price
    810
    Strike Price
    800
    Interest Rate
    1%
    Volatility
    30%
    Dividends
    0%
    Time to Maturity in Years
    1
     
     
    
    
    
    
    d1
    0.2247
    d2
    -0.0753
    N (d1)
    0.5889
    N (d2)
    0.4700
    N (-d1)
    0.4111
    N (-d2)
    0.5300
    
    
    
    
    
    
    Call Option
    104.754629
    Put Option
    86.7944964
    Type of Option
    Method Used
    Option Price
    European Call Option
    Binomial Pricing Model
     $ 103.52
    European Put Option
    Binomial Pricing Model
     $ 85.56
    American Call Option
    Binomial Pricing Model
     $ 103.52
    American Put Option
    Binomial Pricing Model
     $ 86.17
     
    
     
    Call Option
    Black Scholes
     $ 104.75
    Put Option
    Black Scholes
     $ 86.79
According to binomial pricing model the price of European Call Option and American Call option the price is $ 103.52. However using Black Scholes, we get the price of call option as $ 104.75. In case of put option the price of European Put option is $ 85.56 and American Option is $ 86.17 in Binomial Pricing Model. In case of Black Scholes Model, the put option price is $ 86.79. Therefore, the price of call and put option is more when computed through Black Scholes. In case of Binomial Pricing Model we can improve our calculations by increasing the number of steps. There can be 25 steps to get precise answer. Since the difference between 25 steps and 1000 steps is very less. Thus we need to have 25 steps to get the precise results.
Question 3
Value at Risk (VaR)
    Stock Returns
    
    
    
    
    
    
     
    Bank of...
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