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Past exam questions. 723g28 Financial economics 2012. Example : from past exam.

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## Past exam questions

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**Pastexamquestions**723g28 Financialeconomics 2012**Example: from pastexam**• The current price of the stock of AstraZeneca is 300 kr. During each twelve-month period it will either rise by 25 % or fall by 20 %. The interest rate is 3 % a year. Assume no dividends during the life of the option. • Calculate the value of a two-year American put option on AstraZeneca with an exercise price of 250 kr.**Option valuation**• S=300 u=25% d=-20% rf =3%, no dividend, • Valueof a 2 yearAmericanput option at strike priceof 250? Put at strike =250 468,75 375 0 0 300 300 13,066 240 0 192 27,529 58 10 P=23%/45%=51,1111% 1-p=48,8889% The valueof the call is 13,07$, 27,53> intrinsicvalue 10, don’texercise!**Svar:**p = 51,1 % (1-p) = 48,9% P1 levande = 27,53 P1 död = 10 P1 levande > S1 död P0 = 13,07 kr**S=300, Strike price=250. rf=0,03, u=25%, d=-20%**• The valueof the share in 3 periods 585,93 468,75 375 375 300 300 240 240 192 153,6**Whatabout a 3 yearamerican option value? The same method:**• S=300 u=25% d=-20% rf =3%, no dividend, • Valueof a 3 yearAmericanput option at strike priceof 250? 0 0 2,253 13,66 0 4,7465 26,43 10 50,72 K-S=10 96,4 K-S=58 t t+1 t+3 t+2 Obs: Americanputcan not have less thanintrinsicvalue, option should be exercised at t+2!**Valueof an American call with 3 period**S-K=218,75 S-K= 125 335,94 226,0315 S-K=50 141,604 125 103,6197 62,028 31,703 0 0 0 The last period value S-K, K=250 Use (p*Cu+(1-p)*Cd)/(1+r)=C(t-1) Note, the american call can’t not be lowerthan the intrinsicvalue, otherwise it is an exercisepoint.**Exempel 2: en amerikansk säljoption utan utdelning**Du är innehavare av en 1-årig amerikansk säljoption utan utdelning under löptiden. Aktiens marknadsvärde är idag 100 kr och den kan under varje 6-månadersperiod antingen falla med 10 % eller stiga med 11,1 %. Säljoptionens lösenpris är 102 kr och den riskfria 6-månadersräntan är 5 %. Vad är din amerikanska säljoption utan utdelning värd idag?**Put option at strike price =102**• P=(5%+10%)/(11,1%+10%)=71,09% • 1-p=28,91% • Start from last period: K-S • (2*71,09%+21*28,91%)/1,05=7,136 • Etc. 123,43 0 111,1 0,5506 100 2,3376 2 100 90 7,1360 81 K-S=12 21 Americanput option can not be lowerthan the intrinsicvalue. Option should be exercised!**Examquestions:Value the following options:**A European call option written on SKF A selling for 145 kr. The exercise price is 140 kr. The stock’s yearly volatility is 30 %. The option matures in 6 months. The risk-free yearly interest rate is 3 %. A European put option written on the same stock at the same time, with the same EX and expiration date. What is the time value of the call option?**Call option price=?**S=145, K=140, rf=3%, σ=30% T=1/2 Get columnvalue=P0/PV(K) Rowvalue= σ* table value= C0/P0 • Rowvalue= 30%*=0,212 • Columnvalue=145/(140/(1,03)1/2 )=1,05125=1,05 • C0/table value=P0 (table value=(10,9+9,88)/2)=10,39% • C0=P0/table value= 145*10,39%= 15,07**Put option value is:**• P=c+PV(K)-S=15,07+140/(1+0,03)1/2 -145=8,0 • Timevalueof the call=call premium-(intrinsicvalue) =15,07-(145-140)=10,07**Black & Scholes metod**• En ”genväg” för att beräkna en köpoptions värde med hjälp av Black & Scholes metod: • Beräkna radvärde = σ * √ t • Beräkna kolumnvärde = P0 / PV(X) • Se i tabell 6 för att utläsa optionens värde i procent av underliggande tillgång (tabellvärde) • Köpoptionens värde (C0) = tabellvärde * P0 • Du får ut säjoptionens värde genom Put-Call parity**Options on Financial Assets**Executive Stock Options Warrants Convertible Bonds Callable Bonds**Replicating the call**• The price of the SCA A stock is 100 kr. During the next year the price may either rise by 33 % or fall by 25 %. The yearly interest rate is 3 %. You have an European one-year call option on SCA A with an exercise price of 120 kr. • Use the replicating-portfolio method to value this call option!**Strike=120, rf=3%**• ∆=(13-0)/(58)=22,41%, • B= -∆*Sd/(1+0,03)=-22,44%*75/1,03=-16,34 ∆*Su+B(1+r)=13 ∆=(13-0)/(133-75)=22,41% ∆*Sd+B(1+r)=0 B=-16,34 C=100*22,41%-16,34=6,07 133 C=13 100 75 0**NPV ofleaseagreement**NLT needs a new forklift. It can either buy it for 2 500 000 kr or lease it. The lease terms require NLT to make 3 annual payments of 1 000 000 kr. The lessor can depreciate the forklift for tax purposes over 3 years. NLT can borrow at 6 %. NLT and the lessor pays tax at 30 %. What is the NPV of the lease for NLT? Is it possible to create a financial lease that has a positive value for both the lessor and NLT? Explain!**The depreciation tax shield is a forgone benefit of leasing,**cash outflow. Discounting the after tax leasepayment and the lostdepreciation tax shield+ the benefit ofrenting the machine**Alternatively,Spread the costof 2,5 million over the**threeyears. • 2,5=a*(1/r*(1-1/(1+r)^3) • a=2,5/2,765=0,9042 (Max value for the company) • 0,25 yearlyforgone benefit ofdepreciation, • 0,7294 yearly cost+0,25>0,9042 n • it is a negative NPV leasecontract.

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