Chapter 7: Options and their ValuationProblem 13-month call:                                           Pay-offExercise pri...
Share price at expiration, St                       108              -4                                                   ...
Call premium                                       3        3     3    3Pay-off from call                                 ...
PV of call, C:                                                                8.57Problem 17Current market price, S0      ...
C = SN (d 1 ) − Ee              N (d 2 )Value of put                       P = C − S + Ee − rf t                13.81Delta...
Infosys call option:  Exercise price       3300  Premium               32.5Spot share price       3370Lot size            ...
Premium paid                        Gain                        Net pay-off120   130   140   150     160         170
Ch  07 financial management notes
Ch  07 financial management notes
Ch  07 financial management notes
Ch  07 financial management notes
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Ch 07 financial management notes

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Ch 07 financial management notes

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Transcript of "Ch 07 financial management notes"

  1. 1. Chapter 7: Options and their ValuationProblem 13-month call: Pay-offExercise price, E 51Current share price, S0 50Share price at expiration, St 47 0 54 3Problem 26-month call option (short): Pay-offExercise price, E 100Current share price, S0 100Share price, St 110 -10 90 0Problem 36-month call option: Pay-offExercise price, E 98Call premium 3Current share price, S0 100Share price at expiration, St 108 7 95 0Problem 4Call option: Pay-offExercise price, E 42Premium 5Current share price, S0 44Share price at maturity, St 45 -2 43 -4Problem 53-month put option: Pay-offExercise price, E 101Current share price, S0 100Share price at expiration, S 97 4 104 0Problem 66-month put option (short): Pay-offExercise price, E 100Current share price, S0 100Share price at maturity, St 110 -10 90 0Problem 76-month put option: PayoffExercise price, E 96Premium 4Current share price, S0 100
  2. 2. Share price at expiration, St 108 -4 95 -3You will not exercise your put option when price is Rs 108. So you lose Rs premium.When price is Rs 95, you exercise your put option, and you gain Re 1. Netting this againstthe premium of Rs 4, your net loss is Rs 3.Problem 8 Price at expiration Payoff3-month European put: 30 16Exercise price, E 50 40 6Premium 4 50 -4Current share price, So 52 60 -4Problem 96-month put option (short): Share price PayoffExercise price, E 70 60 -5Premium 5 65 0 70 5 75 5Problem 10Put option: Pay-offExercise price, E 42Premium 5Current market price, So 44Share price at expiration, St 45 -5 43 -5Sridharan will not exercise his put option since exercise price is less than expected shareprice. He would lose premium.Problem 11Call option: Pay-offExercise price, E 50Current share price, S0 45Share price at maturity, St 65 15 40 0No of shares 50 Value Payoff Total valueValue of shares 3250 750 4000Problem 12Share price at maturity, St 90 97 100 110Call option: Exercise price, E 100 100 100 100Pay-off from call 0 0 0 10Put option: Exercise price, E 97 97 97 97Pay-off from put 7 0 0 0Total pay-off 7 0 0 10Problem 13Share price at maturity, St 90 97 100 110Call option: Exercise price, E 100 100 100 100
  3. 3. Call premium 3 3 3 3Pay-off from call -3 -3 -3 7Put option: Exercise price, E 97 97 97 97Put premium 5 5 5 5Pay-off from put 2 -5 -5 -5Total pay-off -1 -8 -8 2Problem 143-month call & put:Share price at maturity, St 52 45Call option: Exercise price, E 50 50Call premium 4 4Pay-off from call -2 -4Put option: Exercise price, E 50 50Put premium 2 2Pay-off from put -2 3Total pay-off -4 -1Problem 15Share (long) + call (short):Current share price, S0 100Risk-free rate, rf 0.12Exercise price, E 97Share price at expiration, St 108 90Binomial approach:Call option pay-off 11 0(108 -11)=(90 -0) (delta)=(11-0)/(108-90) 0.611Portfolio value at maturity:(108 × 0.611)-11 or (90 × 0.61) 55PV of portfolio: 52.88PVF, 4% for 3 months 1/(1.04) 0.9615Value of call, C:(S0 × 0.611- C) = 52.88, C = 100*.611- 8.2352.88Risk-neutral method:Probability of price increase: p×8 0.778+ (1 - p) × -10 = 4, p= 14/18Value of call at maturity Ct: 11*0.778 8.56PV of call, C: 8.23Problem 16Share (long) + call (short):Current share price, S0 100Risk-free rate (annual), rf 0.1Exercise price, E 100Share price at expiration, St 115 90Call option pay-off 15 0PVF, 5% for 6 months 1/(1.05) 0.9524Risk-neutral method:Probability of price increase: p × 15 0.600+ (1 - p) × -10 = 5, p = 15/25Value of call at maturity Ct: 15 x 0.6 9
  4. 4. PV of call, C: 8.57Problem 17Current market price, S0 60Change in price at maturity 0.150 -0.10Price at expiration 69 54Risk-free rate (annual) 0.090Risk-free rate for 2 months 0.015Exercise price, E 65Value of call:Probability of price increase: p × 15 0.46+ (1 - p) × -10 =1.5, p=11.5/25Value of call at maturity: 1.84PV of call, C 1.81Present value of put: P = C - S + PV ofE 5.85Problem 18Risk-free rate 0.1Time to expiration (years) 0.5Exercise price, E 55Current share price, S0 60Volatility (SD) 0.4PV of Exercise price, PV (E) 52.32d1 = [ ln (S / E ) + r f + σ 2 / 2 t ] 0.6258 σ td 21 = [ ln (S / E ) + r f − σ 2 / 2 t ] 0.3430 σ tN(d1) 0.7343N(d2) 0.6342Value of call − rf tC = SN (d 1 ) − Ee N (d 2 ) 10.88Value of putP = C − S + Ee−rf t 3.20Delta 0.7343Problem 19Risk-free rate 0.12Time to expiration (years) 0.33333Exercise price, E 93Current share price, S 86Volatility (SD) 0.6PV of Exercise price, PV (E) 89.35 d1 = [ ln (S / E ) + r f + σ 2 / 2 t ] σ t 0.06278 d = [ ln (S / E ) + r f − σ 2 ] / 2 t 21 σ t -0.28363N(d1) 0.5250N(d2) 0.3883Value of call − rf tC = SN (d 1 ) − Ee N (d 2 ) 10.45
  5. 5. C = SN (d 1 ) − Ee N (d 2 )Value of put P = C − S + Ee − rf t 13.81Delta 0.5250Problem 20Risk-free rate 0.12Time to expiration (years) 8Face value of debt, E 95Current value of firm, S 230Volatility (SD) 0.25PV of Exercise price, PV (E) 36.37d1 = [ ] ln (S / E ) + r f + σ 2 / 2 t 2.9616 σ td 21 = [ ln (S / E ) + r f − σ 2 / 2 t ] 2.2545 σ tN(d1) 0.9985N(d2) 0.9879Value of equity − rf tC = SN (d 1 ) − Ee N (d 2 ) 193.71Market value of debt 36.29Problem 21Infosys call option 1: Exercise price 3400 Premium 186.15Infosys call option 2: Exercise price 3500 Premium 38.1Current share price 3469Lot size 100Expected share price range 3200 3300 3400 3500 3600 3700Call option 2 bought: gain 0 0 0 0 100 200 Premium paid -38.1 -38.1 -38.1 -38.1 -38.1 -38.1 Pay-off -38.1 -38.1 -38.1 -38.1 61.9 161.9Call option 1 sold: gain/loss 0 0 0 -100 -200 -300 Premium received 186.15 186.15 186.15 186.15 186.15 186.15 Pay-off 186.15 186.15 186.15 86.15 -13.85 -113.85Net pay-off 148.05 148.05 148.05 48.05 48.05 48.05Problem 22Current share price 123.7 30.00Daily volatility 2.74%Expected maximum share price 142.5 22.50Put option exercise price, E 150Premium 7.50 15.00Possible share price at expiration, S 120 130 140 150 160 170Premium paid -7.50 -7.50 -7.50 -7.50 -7.50 -7.50 7.50Gain 30 20 10 0 0 0Net pay-off 22.50 12.50 2.50 -7.50 -7.50 -7.50 0.00 120 130 140 -7.50Problem 23Infosys put option: Exercise price 3400 Premium 37.5
  6. 6. Infosys call option: Exercise price 3300 Premium 32.5Spot share price 3370Lot size 100Share price range 3200 3300 3400 3500 3600 3700Call option payoff:Premium -32.5 -32.5 -32.5 -32.5 -32.5 -32.5Gain 0 0 100 200 300 400Payoff -32.5 -32.5 67.5 167.5 267.5 367.5Put option payoff:Premium -37.5 -37.5 -37.5 -37.5 -37.5 -37.5Gain 200 100 0 0 0 0Payoff 162.5 62.5 -37.5 -37.5 -37.5 -37.5Net payoff 130 30 30 130 230 330
  7. 7. Premium paid Gain Net pay-off120 130 140 150 160 170

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