Ch 07 financial management notes

1. Chapter 7: Options and their Valuation
Problem 1
3-month call: Pay-off
Exercise price, E 51
Current share price, S0 50
Share price at expiration, St 47 0
54 3
Problem 2
6-month call option (short): Pay-off
Exercise price, E 100
Current share price, S0 100
Share price, St 110 -10
90 0
Problem 3
6-month call option: Pay-off
Exercise price, E 98
Call premium 3
Current share price, S0 100
Share price at expiration, St 108 7
95 0
Problem 4
Call option: Pay-off
Exercise price, E 42
Premium 5
Current share price, S0 44
Share price at maturity, St 45 -2
43 -4
Problem 5
3-month put option: Pay-off
Exercise price, E 101
Current share price, S0 100
Share price at expiration, S 97 4
104 0
Problem 6
6-month put option (short): Pay-off
Exercise price, E 100
Current share price, S0 100
Share price at maturity, St 110 -10
90 0
Problem 7
6-month put option: Payoff
Exercise price, E 96
Premium 4
Current share price, S0 100

2. Share price at expiration, St 108 -4
95 -3
You 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 against
the premium of Rs 4, your net loss is Rs 3.
Problem 8
Price at
expiration Payoff
3-month European put: 30 16
Exercise price, E 50 40 6
Premium 4 50 -4
Current share price, So 52 60 -4
Problem 9
6-month put option (short): Share price Payoff
Exercise price, E 70 60 -5
Premium 5 65 0
70 5
75 5
Problem 10
Put option: Pay-off
Exercise price, E 42
Premium 5
Current market price, So 44
Share price at expiration, St 45 -5
43 -5
Sridharan will not exercise his put option since exercise price is less than expected share
price. He would lose premium.
Problem 11
Call option: Pay-off
Exercise price, E 50
Current share price, S0 45
Share price at maturity, St 65 15
40 0
No of shares 50
Value Payoff Total
value
Value of shares 3250 750 4000
Problem 12
Share price at maturity, St 90 97 100 110
Call option: Exercise price, E 100 100 100 100
Pay-off from call 0 0 0 10
Put option: Exercise price, E 97 97 97 97
Pay-off from put 7 0 0 0
Total pay-off 7 0 0 10
Problem 13
Share price at maturity, St 90 97 100 110
Call option: Exercise price, E 100 100 100 100

3. Call premium 3 3 3 3
Pay-off from call -3 -3 -3 7
Put option: Exercise price, E 97 97 97 97
Put premium 5 5 5 5
Pay-off from put 2 -5 -5 -5
Total pay-off -1 -8 -8 2
Problem 14
3-month call & put:
Share price at maturity, St 52 45
Call option: Exercise price, E 50 50
Call premium 4 4
Pay-off from call -2 -4
Put option: Exercise price, E 50 50
Put premium 2 2
Pay-off from put -2 3
Total pay-off -4 -1
Problem 15
Share (long) + call (short):
Current share price, S0 100
Risk-free rate, rf 0.12
Exercise price, E 97
Share price at expiration, St 108 90
Binomial approach:
Call option pay-off 11 0
(108 -11)=(90 -0)
(delta)=(11-0)/(108-90) 0.611
Portfolio value at maturity:
(108 × 0.611)-11 or (90 × 0.61) 55
PV of portfolio: 52.88
PVF, 4% for 3 months 1/(1.04) 0.9615
Value of call, C:
(S0 × 0.611- C) = 52.88, C = 100*.611- 8.23
52.88
Risk-neutral method:
Probability of price increase: p×8 0.778
+ (1 - p) × -10 = 4, p
= 14/18
Value of call at maturity Ct: 11*0.778 8.56
PV of call, C: 8.23
Problem 16
Share (long) + call (short):
Current share price, S0 100
Risk-free rate (annual), rf 0.1
Exercise price, E 100
Share price at expiration, St 115 90
Call option pay-off 15 0
PVF, 5% for 6 months 1/(1.05) 0.9524
Risk-neutral method:
Probability of price increase: p × 15 0.600
+ (1 - p) × -10 = 5, p = 15/25
Value of call at maturity Ct: 15 x 0.6 9

4. PV of call, C: 8.57
Problem 17
Current market price, S0 60
Change in price at maturity 0.150 -0.10
Price at expiration 69 54
Risk-free rate (annual) 0.090
Risk-free rate for 2 months 0.015
Exercise price, E 65
Value of call:
Probability of price increase: p × 15 0.46
+ (1 - p) × -10 =1.5, p=
11.5/25
Value of call at maturity: 1.84
PV of call, C 1.81
Present value of put: P = C - S + PV of
E 5.85
Problem 18
Risk-free rate 0.1
Time to expiration (years) 0.5
Exercise price, E 55
Current share price, S0 60
Volatility (SD) 0.4
PV of Exercise price, PV (E) 52.32
d1 =
[
ln (S / E ) + r f + σ 2 / 2 t ]
0.6258
σ t
d 21 =
[
ln (S / E ) + r f − σ 2 / 2 t ]
0.3430
σ t
N(d1) 0.7343
N(d2) 0.6342
Value of call
− rf t
C = SN (d 1 ) − Ee N (d 2 ) 10.88
Value of put
P = C − S + Ee−rf t 3.20
Delta 0.7343
Problem 19
Risk-free rate 0.12
Time to expiration (years) 0.33333
Exercise price, E 93
Current share price, S 86
Volatility (SD) 0.6
PV 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
-0.28363
N(d1) 0.5250
N(d2) 0.3883
Value of call
− rf t
C = SN (d 1 ) − Ee N (d 2 ) 10.45

5. C = SN (d 1 ) − Ee N (d 2 )
Value of put
P = C − S + Ee − rf t 13.81
Delta 0.5250
Problem 20
Risk-free rate 0.12
Time to expiration (years) 8
Face value of debt, E 95
Current value of firm, S 230
Volatility (SD) 0.25
PV of Exercise price, PV (E) 36.37
d1 =
[ ]
ln (S / E ) + r f + σ 2 / 2 t
2.9616
σ t
d 21 =
[
ln (S / E ) + r f − σ 2 / 2 t ]
2.2545
σ t
N(d1) 0.9985
N(d2) 0.9879
Value of equity
− rf t
C = SN (d 1 ) − Ee N (d 2 ) 193.71
Market value of debt 36.29
Problem 21
Infosys call option 1:
Exercise price 3400
Premium 186.15
Infosys call option 2:
Exercise price 3500
Premium 38.1
Current share price 3469
Lot size 100
Expected share price range 3200 3300 3400 3500 3600 3700
Call 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 61.9 161.9
Call 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 -113.85
Net pay-off 148.05 148.05 148.05 48.05 48.05 48.05
Problem 22
Current share price 123.7 30.00
Daily volatility 2.74%
Expected maximum share price 142.5 22.50
Put option exercise price, E 150
Premium 7.50 15.00
Possible share price at expiration, S 120 130 140 150 160 170
Premium paid -7.50 -7.50 -7.50 -7.50 -7.50 -7.50 7.50
Gain 30 20 10 0 0 0
Net pay-off 22.50 12.50 2.50 -7.50 -7.50 -7.50 0.00
120 130 140
-7.50
Problem 23
Infosys put option:
Exercise price 3400
Premium 37.5

6. Infosys call option:
Exercise price 3300
Premium 32.5
Spot share price 3370
Lot size 100
Share price range 3200 3300 3400 3500 3600 3700
Call option payoff:
Premium -32.5 -32.5 -32.5 -32.5 -32.5 -32.5
Gain 0 0 100 200 300 400
Payoff -32.5 -32.5 67.5 167.5 267.5 367.5
Put option payoff:
Premium -37.5 -37.5 -37.5 -37.5 -37.5 -37.5
Gain 200 100 0 0 0 0
Payoff 162.5 62.5 -37.5 -37.5 -37.5 -37.5
Net payoff 130 30 30 130 230 330

11. Premium paid
Gain
Net pay-off
120 130 140 150 160 170