# Calculate Value of a Put Option PAP 16 5

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```					PAP 16.5

INPUTS
Current market price           \$47.375
Exercise price                  \$45.00
Interest rate                   8.00%
Time to expiration (years)      0.2466
Call price                       \$8.94

STEP 1
Calculate the present value of the exercise price:

PV of exercise price

STEP 2
Calculate the put price from the put-call parity relationship:

Put price
PAP 16.6

INPUTS
Current market price            \$50.00
Exercise price                  \$45.00
Interest rate                   7.00%
Time to expiration (years)      0.2466
Standard deviation             40.00%

STEP 1
Calculate the value of d1:

d1

STEP 2
Calculate the value of d2:

d2

STEP 3
Calculate the values of N(d1) and N(d2) by using the NORMSDIST function:

N(d1)
N(d2)

STEP 4
Calculate the value of the call option using the Black-Scholes model:

Call price

STEP 5
Calculate the value of the put from the put-call parity relationship:

Put price
PAP 16.8

INPUTS
Current market price          \$10.00
Exercise price                 \$9.50
Interest rate                 8.00%
Time to expiration (years)    0.4932
Standard deviation           60.00%

STEP 1
Calculate the value of d1:

d1

STEP 2
Calculate the value of N(d1) using the NORMSDIST function which gives the hedge ratio:

N(d1)

STEP 3
Multiply the hedge ratio by 1000 in order to determine the number of shares to be purchased:

Number of shares
PAP 16.9

INPUTS (ORIGINAL)                                   INPUTS (a)
Current market price            \$10.00              Current market price          \$10.00
Exercise Price                   \$9.50              Exercise Price                \$10.00
Interest rate                   8.00%               Interest rate                 8.00%
Time to expiration (years)      0.4932              Time to expiration (years)    0.4932
Standard Deviation             60.00%               Standard Deviation           60.00%

STEP 1
Calculate the value of d1 for each set of inputs:

d1                                                  d1

STEP 2
Calculate the value of d2 for each set of inputs:

d2                                                  d2

STEP 3
Calculate the values of N(d1) and N(d2) for each set of inputs by using the 'NORMSDIST' function:

N(d1)                                               N(d1)
N(d2)                                               N(d2)

STEP 4
Calculate the value of the call for each set of inputs using the Black-Scholes model:

Call Value                                          Call value

STEP 5
Subtract the original call value from the new call value:

Change in call value
INPUTS (b)                             INPUTS (c)
Current market price          \$10.00   Current market price          \$10.00
Exercise Price                 \$9.50   Exercise Price                 \$9.50
Interest rate                 8.00%    Interest rate                 8.00%
Time to expiration (years)    0.2192   Time to expiration (years)    0.0219
Standard Deviation           60.00%    Standard Deviation           60.00%

d1                                     d1

d2                                     d2

N(d1)                                  N(d1)
N(d2)                                  N(d2)

Call value                             Call value

Change in call value                   Change in call value
PAP 16.3 (New)

INPUTS
Current market price                           \$22.37
Exercise price                                 \$21.50
Interest rate                                  7.85%
Time to expiration (years)                     0.3288
Put price                                       \$1.92
Call price                                      \$3.38

STEP 1
Calculate the fair value of the call option through the the put-call parity relationship:

Call fair value

STEP 2
Subtract the traded call price from the call fair value to determine the size of the mispricing and the arbitrage opportunity availab

Arbitrage opportunity (per share)

STEP 3
Determine the net initial cash flow from opening the abritrage trading strategy:

Sell call (cash inflow)

Net initial cash flow

STEP 4
Calculate the amount to be repaid on the loan:

Loan repayment

STEP 5
Subtract the loan repayment from the exercise price at which the asset will be sold at the expiry of the call option in order to det

Arbitrage profit (per share)

Hence, the arbitrage profit earnt will be equivalent to the mispricing which existed when the strategy was initially implemented.
he arbitrage opportunity available:

of the call option in order to determine the profit from the strategy:

egy was initially implemented.
Exercise 16.3

INPUTS (ORIGINAL)                                       INPUTS (NEW)
Current market price                   \$4.73            Current market price            \$5.25
Exercise price                         \$4.90            Exercise price                  \$4.90
Interest rate                         4.50%             Interest rate                  4.50%
Time to expiration (years)            0.2685            Time to expiration (years)     0.2685
Standard deviation                   29.00%             Standard deviation            29.00%

STEP 1
Calculate the value of d1 for each share price:

d1 (CMP = \$4.73)                                        d1 (CMP = \$5.25)

STEP 2
Calculate the value of N(d1) for each share price using the NORMSDIST function which gives the hedge ratio:

N(d1) (CMP = \$4.73)                                     N(d1) (CMP = \$5.25)

STEP 3
Multiply the hedge ratio for each share price by 1000 in order to determine the number of shares to be sold:

No. of shares                                           No. of shares
No. of shares (rounded)                                 No. of shares (rounded)

STEP 4
Subtract the total number of shares to be sold when the CMP is \$5.25 from the total number of shares when the CMP is \$4.73
many more shares must be sold in order to remain fully hedged:

the hedge ratio:

res to be sold:

of shares when the CMP is \$4.73 to determine how
Exercise 16.6

In this instance, the most appropriate strategy would be to create a long straddle by going long in \$7.80 March calls and puts.

INPUTS
Call price (cost)                                  -\$0.27
Call exercise price                                 \$7.80
Put price (cost)                                   -\$0.25
Put exercise price                                  \$7.80

STEP 1
Construct a profit and loss table for this strategy:

Share Price    Long Straddle Long Call Long Put
\$5.80
\$6.20
\$6.60
\$7.00
\$7.40
\$7.80
\$8.20
\$8.60
\$9.00
\$9.40
\$9.80

Note: alternative share price ranges are also acceptable.

STEP 2
Use the Excel Chart Pack to create a profit and loss diagram of the long straddle strategy:

\$1.20
\$1.00
Profit/Loss

\$0.80
\$0.60
\$0.40
\$0.20                                                                                           Share Price

\$0.00
\$9.00
\$5.80

\$6.20

\$6.60

\$7.00

\$7.40

\$7.80

\$8.20

\$8.60

\$9.40

\$9.80
ing long in \$7.80 March calls and puts.

Share Price

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