Risk Management and Derivatives FinalQ1. You work for a UK building society (ie. mortgage bank)...

Question

Risk Management and Derivatives FinalQ1. 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    0.9998BS 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     XXXXXXXXXXImp. Vol. Trial and Eo    Calculating the Implied Volatility (using Trial and Eor)    Data Inputs    S        164    K        165    r        0.0521    T        0.0959    d        0    Quoted C Premium        5.75    Trial and Eor 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 premiumImp. 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    32450    32451    32454    32455    32456    32457    32458    32461    32462    32463    32464    32465    32468    32469    32470    32471    32472    32475    32476    32477    32478    32479    32482    32483    32484    32485    32486    32489    32490    32491    32492    32493    32496    32497    32498    32499    32500    32503    32504    32505    32506    32507    32510    32511    32512    32513    32514    32517    32518    32519    32520    32521    32524    32525    32526    32527    32528    32531    32532    32533    32534    32535    32538    32539    32540    32541    32542    32545    32546    32547    32548    32549    32552    32553    32554    32555    32556    32559    32560    32561    32562    32563    32566    32567    32568    32569    32570    32573    32574    32575    32576    32577    32580    32581    32582    32583    32584    32587    32588    32589    32590    32591    32594    32595    32596    32597    32598    32601    32602    32603    32604    32605    32608    32609    32610    32611    32612    32615    32616    32617    32618    32619    32622    32623    32624    32625    32626    32629    32630    32631    32632    32633    32636    32637    32638    32639    32640    32643    32644    32645    32646    32647    32650    32651    32652    32653    32654    32657    32658    32659    32660    32661    32664    32665    32666    32667    32668    32671    32672    32673    32674    32675    32678    32679    32680    32681    32682    32685    32686    32687    32688    32689    32692    32693    32694    32695    32696    32699    32700    32701    32702    32703    32706    32707    32708    32709    32710    32713    32714    32715    32716    32717    32720    32721    32722    32723    32724    32727    32728    32729    32730    32731    32734    32735    32736    32737    32738    32741    32742    32743    32744    32745    32748    32749    32750    32751    32752    32755    32756    32757    32758    32759    32762    32763    32764    32765    32766    32769    32770    32771    32772    32773    32776    32777    32778    32779    32780    32783    32784    32785    32786    32787    32790    32791    32792    32793    32794    32797    32798    32799    32800    32801    32804    32805    32806    32807    32808    32811    32812    32813    32814    32815    32818    32819    32820    32821    32822    32825    32826    32827    32828    32829    32832    32833    32834    32835    32836    32839    32840    32841    32842    32843    32846    32847    32848    32849    32850    32853    32854    32855    32856    32857    32860    32861    32862    32863    32864    32867    32868    32869    32870    32871    32874    32875    32876    32877    32878    32881    32882    32883    32884    32885    32888    32889    32890    32891    32892    32895    32896    32897    32898    32899    32902    32903    32904    32905    32906    32909    32910    32911    32912    32913    32916    32917    32918    32919    32920    32923    32924    32925    32926    32927    32930    32931    32932    32933    32934    32937    32938    32939    32940    32941    32944    32945    32946    32947    32948    32951    32952    32953    32954    32955    32958    32959    32960    32961    32962    32965    32966    32967    32968    32969    32972    32973    32974    32975    32976    32979    32980    32981    32982    32983    32986    32987    32988    32989    32990    32993    32994    32995    32996    32997    33000    33001    33002    33003    33004    33007    33008    33009    33010    33011    33014    33015    33016    33017    33018    33021    33022    33023    33024    33025    33028    33029    33030    33031    33032    33035    33036    33037    33038    33039    33042    33043    33044    33045    33046    33049    33050    33051    33052    33053    33056    33057    33058    33059    33060    33063    33064    33065    33066    33067    33070    33071    33072    33073    33074    33077    33078    33079    33080    33081    33084    33085    33086    33087    33088    33091    33092    33093    33094    33095    33098    33099    33100    33101    33102    33105    33106    33107    33108    33109    33112    33113    33114    33115    33116    33119    33120    33121    33122    33123    33126    33127    33128    33129    33130    33133    33134    33135    33136    33137    33140    33141    33142    33143    33144    33147    33148    33149    33150    33151    33154    33155    33156    33157    33158    33161    33162    33163    33164    33165    33168    33169    33170    33171    33172    33175    33176    33177    33178    33179    33182    33183    33184    33185    33186    33189    33190    33191    33192    33193    33196    33197    33198    33199    33200    33203    33204    33205    33206    33207    33210    33211    33212    33213    33214    33217    33218    33219    33220    33221    33224    33225    33226    33227    33228    33231    33232    33233    33234    33235    33238    33239    33240    33241    33242    33245    33246    33247    33248    33249    33252    33253    33254    33255    33256    33259    33260    33261    33262    33263    33266    33267    33268    33269    33270    33273    33274    33275    33276    33277    33280    33281    33282    33283    33284    33287    33288    33289    33290    33291    33294    33295    33296    33297    33298    33301    33302    33303    33304    33305    33308    33309    33310    33311    33312    33315    33316    33317    33318    33319    33322    33323    33324    33325    33326    33329    33330    33331    33332    33333    33336    33337    33338    33339    33340    33343    33344    33345    33346    33347    33350    33351    33352    33353    33354    33357    33358    33359    33360    33361    33364    33365    33366    33367    33368    33371    33372    33373    33374    33375    33378    33379    33380    33381    33382    33385    33386    33387    33388    33389    33392    33393    33394    33395    33396    33399    33400    33401    33402    33403    33406    33407    33408    33409    33410    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

Neenisha · Accepted Answer

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 preferred because they are predictable and the person who has borrowed 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 borrower 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 Factor
	1.10
	Down Factor
	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 America
	BMW
	Lufthansa
	Amazon
	Tesco
	Dates
	Returns
	Returns
	Returns
	Returns
	Returns
	20/12/18
	-0.69%
	-1.97%
	-0.62%
	-2.72%
	-0.55%
	21/12/18
	-2.92%
	-0.37%
	2.25%
	-5.67%
	0.96%
	24/12/18
	-3.41%
	-0.32%
	-0.32%
	-3.10%
	-1.95%
	25/12/18
	0.30%
	0.22%
	0.22%
	0.30%
	0.00%
	26/12/18
	6.24%
	-0.03%
	-0.03%
	9.37%
	0.00%
	27/12/18
	0.98%
	-2.32%
	0.73%
	-0.72%
	-0.24%
	28/12/18
	-0.36%
	0.87%
	0.16%
	0.67%
	1.34%
	31/12/18
	0.57%
	-0.24%
	-0.24%
	1.16%
	-1.05%
	01/01/19
	0.09%
	-0.02%
	-0.02%
	0.09%
	0.00%
	02/01/19
	2.37%
	-1.26%
	0.61%
	3.52%
	0.76%
	03/01/19
	-1.79%
	-0.72%
	-2.62%
	-2.73%
	3.99%
	04/01/19
	3.35%
	3.03%
	1.94%
	4.16%
	-0.98%
	07/01/19
	-0.51%
	0.85%
	0.63%
	2.94%
	2.55%
	08/01/19
	0.30%
	0.33%
	2.30%
	2.14%
	2.73%
	09/01/19
	0.39%
	1.34%
	-0.82%
	-0.42%
	1.76%
	10/01/19
	0.19%
	-0.67%
	-2.32%
	0.11%
	2.15%
	11/01/19
	0.44%
	-1.93%
	0.21%
	-1.67%
	0.74%
	14/01/19
	1.10%
	-0.52%
	1.17%
	-1.63%
	0.00%
	15/01/19
	0.73%
	-0.41%
	-2.46%
	3.54%
	0.05%
	16/01/19
	6.73%
	-0.47%
	3.24%
	0.37%
	1.05%
	17/01/19
	1.08%
	-1.22%
	-0.11%
	-0.24%
	-0.59%
	18/01/19
	1.93%
	3.55%
	1.93%
	1.04%
	2.43%
	21/01/19
	-0.13%
	-0.58%
	1.84%
	-0.13%
	-1.71%
	22/01/19
	-1.22%
	-0.96%
	-0.64%
	-4.35%
	-0.14%
	23/01/19
	-1.44%
	-1.37%
	2.57%
	-0.38%
	1.44%
	24/01/19
	0.58%
	0.59%
	-0.63%
	0.93%
	-0.36%
	25/01/19
	0.68%
	1.54%
	0.56%
	-0.08%
	0.94%
	28/01/19
	0.49%
	-0.03%
	0.70%
	-1.66%
	-1.75%
	29/01/19
	-0.12%
	0.58%
	0.85%
	-2.03%
	-0.05%
	30/01/19
	-1.47%
	-0.66%
	1.21%
	4.31%
	1.04%
	31/01/19
	-2.03%
	-0.06%
	-1.45%
	2.90%
	-0.04%
	01/02/19
	-0.11%
	1.20%
	-0.04%
	-5.32%
	-0.49%
	04/02/19
	2.11%
	-1.02%
	0.51%
	0.80%
	-0.23%
	05/02/19
	0.30%
	0.91%
	1.71%
	2.20%
	1.88%
	06/02/19
	-0.02%
	-0.21%
	0.76%
	-0.97%
	1.76%
	07/02/19
	-1.89%
	-3.71%
	-2.95%
	-1.76%
	-0.83%
	08/02/19
	0.24%
	-2.57%
	-1.35%
	-1.57%
	-1.59%
	11/02/19
	1.07%
	0.14%
	1.87%
	0.82%
	0.36%
	12/02/19
	0.74%
	0.91%
	0.06%
	2.67%
	-0.67%
	13/02/19
	0.40%
	0.46%
	0.18%
	0.48%
	-1.94%
	14/02/19
	-0.74%
	-0.85%
	-1.46%
	-0.72%
	-0.59%
	15/02/19
	1.81%
	1.35%
	2.13%
	-1.60%
	2.85%
	18/02/19
	-0.26%
	-0.37%
	-0.92%
	-0.26%
	-0.40%
	19/02/19
	-1.01%
	-0.19%
	0.21%
	0.13%
	1.47%
	20/02/19
	1.06%
	2.12%
	2.76%
	-0.23%
	0.35%
	21/02/19
	-0.36%
	0.90%
	-0.25%
	-0.11%
	-0.57%
	22/02/19
	-0.81%
	-0.11%
	1.43%
	0.65%
	-1.47%
	25/02/19
	0.32%
	0.67%
	0.19%
	-0.24%
	0.27%
	26/02/19
	-1.10%
	-0.48%
	-0.51%
	-0.96%
	2.21%
	27/02/19
	0.39%
	-0.28%
	-2.46%
	-0.14%
	0.31%
	28/02/19
	-1.19%
	0.45%
	-1.97%
	0.27%
	-1.36%
	01/03/19
	1.21%
	0.98%
	2.41%
	2.35%
	1.45%
	04/03/19
	-0.76%
	-0.13%
	-2.22%
	1.65%
	-0.04%
	05/03/19
	0.19%
	0.24%
	0.65%
	-0.21%
	1.17%
	06/03/19
	-0.76%
	-0.67%
	-1.78%
	-1.33%
	0.17%
	07/03/19
	-0.38%
	-2.30%
	-0.12%
	-1.98%
	0.86%
	08/03/19
	0.91%
	-0.40%
	0.12%
	0.24%
	-2.51%
	11/03/19
	-0.04%
	0.47%
	0.86%
	1.98%
	-0.44%
	12/03/19
	0.60%
	0.86%
	1.54%
	0.75%
	0.35%
	13/03/19
	-0.82%
	-0.92%
	-0.85%
	-0.97%
	0.48%
	14/03/19
	1.31%
	0.72%
	-5.71%
	0.46%
	-0.48%
	15/03/19
	-0.92%
	0.23%
	-1.64%
	1.17%
	0.48%
	18/03/19
	2.04%
	0.49%
	-1.28%
	2.00%
	2.58%
	19/03/19
	-0.68%
	2.09%
	0.26%
	1.02%
	0.64%
	20/03/19
	-2.94%
	-3.99%
	-0.95%
	2.52%
	-1.02%
	21/03/19
	-0.95%
	-0.83%
	-1.00%
	1.89%
	-0.56%
	22/03/19
	-5.00%
	-3.58%
	-4.

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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