# Finance Problems Essay

963 Words Nov 12th, 2015 4 Pages
TA-Session 1

Triangular Arbitrage in real life:

| BID | ASK | USD/GBP | 1,5322 | 1,5431 | USD/EUR | 1,2647 | 1,2649 | | | | GBP/USD | 0,6480 | 0,6527 | EUR/USD | 0,7906 | 0,7907 |

a)
Converting EUR into GBP:
EUR1000 x USD1,2647/EUR = USD1264,7
USD1264,7 x GBP0,6480/USD = GBP819,5256

Reverse, convert back into EUR:
GBP 819,5256 x USD1,5322/GBP * 0,7906 EUR/USD = 992,78

Percentage loss = 0.722%

b)
S(GBP/EUR)BID =S(USD/EUR)BID x S(GBP/USD)BID = 1,2647 x 0,6480 = 0,8195
S(EUR/GBP)BID = 1/S(GBP/EUR)ASK = 1/0,8256 = 1,2112

Futures
a)
The firm do not hedge:
T0 T1 T2 GBP100 000 x USD0,66/GBP = -USD66 000

b)
Hedging using forward contract:
T0 T1 T2 GBP100 000 x USD0,65/GBP = -USD65 000

c)
Hedging using futures contract:
T0 T1 T2 GBP100 000 x (0,67 – 0,65) GBP100 000 x USD0,66/GBP = +USD2000 = -USD66 000
Payoff from futures GBP100 000*(0.66 – 0.67) = -USD1000
Account payable = GBP100 000 x USD0,66/GBP = -USD66 000
Time T2 total cash flow= -USD67000

Valuation of Put Option
Max(0,K-Su) = Pu
Max(0,K-Sd) = Pd

Su = 1,1 Pu = 0
Sd = 0,9 Pd =0,1

b=Pu-Pd(Su-Sd)(1+iEUR)=0-0,1(1,1-0,9)(1+0,03)=-0,4985
B=uPd-dPu(u-d)(1+iUS)=1,1x0,1-0,9x0(1,1-0,9)(1+0,02)=0.5489

Option Pricing
Effective interest rates:
1+ih = (1+ i * (T-t))^1/2 ih = 0.025, i*h = 0.005

a) h=1803602=0,25 u=eσh=e0,15 x 0,25=1,0779 d=e-σh=e-0,15 x 0,25=0,9277

S1u = S x u = 120 x 1,0779 = 129,348
S1d = S x d = 120 x 0,9277 = 111,324
S2uu = S1u x u = 129,348 x 1,0779 = 139,4242
S2ud = S1u x d = 129,348 x 0,9277 = 120
S2dd = S1d x

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