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  1. Pastexamquestions 723g28 Financialeconomics 2012

  2. 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.

  3. 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!

  4. Svar: p = 51,1 % (1-p) = 48,9% P1 levande = 27,53 P1 död = 10 P1 levande > S1 död P0 = 13,07 kr

  5. 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

  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!

  7. 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.

  8. 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?

  9. 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!

  10. 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?

  11. 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

  12. 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

  13. 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

  14. Options on Financial Assets Executive Stock Options Warrants Convertible Bonds Callable Bonds

  15. 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!

  16. 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

  17. 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!

  18. 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

  19. 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.