Solved problems on finance and investment

This document contains solved problems on finance and investment including economic price option, arbitrate strategy, two-period binomial model, put delta, FTSE future trading and more. It also includes references for further reading.

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

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 ) 0.5 ]
f =4.214
2 nd f =e−0.05× 0.17 [ 0.5× 4.214+ ( 1−0.5 ) 0 ]
f =2.089
Therefore the option price is €2.089
b. If it could have been the American, it could be optimal. American put option do not wait for a
specific time to exercise, but can be exercised ant time.
Therefore;
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
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 ) 0.5 ]
f =4.214
The American option price will be $4.214
Question 3
Put delta=e−qt ¿
d1=
ln ( S0
X )+ t(r−q + σ2
2 )
σ √ t
N ( d1 ) =e
−d1
2 × 1
2 π ∧d2=d1−σ √ t

Gamma= e−qt
S0 σ √ t × 1
√ 2 π × −d2
2
e2
Vega=S0 √ T −t N (d1) e−q (T −t)
b. Delta position can be made neutral by lowering the component direction for the profit to be
made whether the underlying factors goes up or down.
c. In case the index increased to 515, the investor may look for an option where they can get
another delta position of -515 so that the delta can be neutralized. To do this she can look for
a company trading at delta -5 multiply the same amount of shares, she will neutralize the
delta.
Question 4
Total investment;
¿ 1000 ×27+1000 ×5=$ 32000
a. If the spot price on December is $20
total earnings will be=20 ×1000=$ 20000
Hence making a loss of $ 32000−$ 20000=$ 12000

b. If the spot price is $27
total earnings will be=27 ×1000=$ 27000
Hence making a loss of $ 32000−$ 27000=$ 5000
c. If the spot price is $32
total earnings will be=32 ×1000=$ 32000
Hence she will neither make a loss or a profit $ 32000−$ 32000=$ 0
d. If the spot price is $37
total earnings will be=37 ×1000=$ 37000
Hence making a profit of $ 37000−$ 32000=$ 5000
Question 5
1. Since the strike price $50 and the premium is $3, we can say that the intrinsic value is $3 there
you can buy a share between $50 to $53 and exercise it right away and reap a lot for example
from 100 shares will give the investor $300

2. The second strike price is $40 and the premium of $4 he can buy the shares and exercise them
immediately and still get good money for example from 100 shares he will reap $400
Option Strike price Premium Shares Profit
1 $50 $3 100 $300
2 $40 $4 100 $400
The underlying view might be because waiting for long before selling shares might be risky and can cause
a lot of loses. Therefore, even if this method is not giving good profit but it most assured and has few
risks. (Matthias Burghardt*, 2015)
Question 6
a. FTSE future trading graph shows the rising and falling. There is a classic trend where the price
tends to fall when the FTSE future trading graph is at the peak. Our making profit or loss will
therefore depend on the number of lower points on the graph.
b. The two values shows that there was sharp decrease in the value. The graph will show that there
was a sharp fall within a single day. Most probably due to the fact the share was trading a day
before making many people to buy, but the following day, it flooded the market making the
investors to sell them at a throw away price.
c. Total initial value=5250 × 5=26250
Final value=4000 ×5=20000

From the graph the value at 20000 shows the price is increasing therefore show good prospect of
investing after all since at that section the price is increase. (Telegraph., 2015) (Andrews, 2010)
References
Andrews, A., 2010. "Guardian and Apax snap up a fifth of Emap". Volume The Times..
Matthias Burghardt*, M. C. a. R. R., 2015. Retail Investor Sentiment and the Stock Market. p. 15.
McMillan, L. G., 2002. Options as a Strategic Investment. New York: New York Institute of Finance.
Telegraph., T., 2015. "Aviva and Friends Life rise in first day as a merged company. p. 13.