Solved problems on finance and investment

Question 1
a. Economic price option
f =e−rT [ p f u + ( 1−p ) f d ]
p= erT−d
u−d
f u=10 ×1.5=15−7=8
f d=10 × 0.5=5−7=0
p e0.05 × 0.17−0.5
1.5−0.5
p=0.5
f =e−0.05 × 0.17 [ 0.5 × 8+ ( 1−0.5 ) 0 ]
f =€ 3.966
Therefore the value of the option is €3.966

b. Arbitrate strategy
The best arbitrary at the scenario where call option is selling at $4 is to sell all the shares at that moment
because they will not making a loss but a profit because the option calculated up there was 3.996.
c. Since the optimal value f =$ 3.966 will be the early price and the price has increased to $4, there
will be loss if it is American because it allows to buy anytime which could have prompt someone
to sell at $3.966 only for price to increase to $4
(McMillan, 2002)
Question 2
a. Two-period binomial model
1 st f =e−rT [ p f u + ( 1− p ) f d ]
p= erT−d
u−d
f u=10 ×1.5=15 ×1.5=22.5−7=15.5
f d=10 × 0.5=5 × 1.5=7.5−7=0.5