Fin management materials / 11 P4AFM-Session12_j08

The longer the time to expiry the higher will be the time value of the option.

Solution 4

d1 = 1n(Pa/Pe )+(r +0.5s2 )t s t

d1 = 1n(14/14)+ (0.1 + (0.5x0.22 ))1 0.2 1

= 0.6

d2 = d1 – s t =0.6-0.2

=0.4

Now use the normal distribution tables – read the note given at the bottom of the tables.

N(d1) = probability that a normally distributed variable will be less than 0.6standard deviations above the mean

N(d1) = 0.5+0.2257 = 0.7257

N(d2) = 0.6554

Option price = PaN(d1) – PeN(d2)e-rt

=14×0.7257 – 14×0.6554e-0.1

=$1.8574

$1.8574 is the theoretical premium of this option. Note that the intrinsic value of the option is zero and therefore all of the premium must represent time value.

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SESSION 12 – OPTIONS

Solution 5

We have previously calculated the price of a call option as $1.8574

p= c – Pa + Pee-rt

p= 1.8574 – 14 + 14e-0.1

=1.8574 – 14 + 12.6672

=$0.5246

Solution 6

Strike price (X) = spot rate (as options are at the money) = 0.69

Time to expiry (T) = 0.25 years

Sterling risk free rate (r) = 0.046231

Annual standard deviation = 0.0635 × 12 = 0.22

Forward rate must be calculated using Interest Rate Parity theory:

Sterling 3 months interest = 0.046231 × 0.25 = 0.011557

N(d1) = 0.0359 + ((0.0398-0.0359) x 0.7) = 0.0386 0.0386 + 0.5 = 0.5386

N(d2) = 0.004 + ((0.008-0.004) x 0.3) = 0.0052 0.5 - 0.0052 = 0.4948

c = e-rt (F0N(d1) – XN(d2)) = e-0.011557 ((0.6932 x 0.5386) – (0.69 x 0.4948)) = 3.158 pence

Each contract is on 100,000 Euro and so the total price of each contract = 3.158pence x 100,000 = £3158

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SESSION 12 – OPTIONS

Solution 7

Value of call = PaN(d1) – PeN(d2)e-rt

=(100× 0.9564) – (40×0.6103 e-0.5)

=80.83

p = c – Pa + Pee-rt = 80.83 – 100 + 24.26 = $5.09m True value of project = 10 + 5.09 = $15.09m

This is still conservative as the option is American style in nature but has been valued as European style.

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