Submitted by: Submitted by h4yin
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Category: Business and Industry
Date Submitted: 04/14/2011 08:48 AM
It is stipulated in the contract that there is a margin call if $1,000 is lost. As a result, when the price of the futures rises from 450 cents to 470 cents per bushel(20cents multiply 5000=&1000). $1,500 can be withdrawn if the futures price falls by 30 cents from 450 to 420 cents per bushel. Divides two kinds of situations:
First, when price rises, the margin call is set. When
M0-Q×(F1-F0) ≤M or::
F1-F0 ≥(M0-M)/Q
F1-F0 ≥ (3000-2000)/5000=$0.2=20cents
Second, the company could withdraw W when
M0-Q×(F1-F0)-W ≥M.
F1-F0≤-W/Q
F1-F0≤-1500/5000=$0.3=-30cents
∴1500 can be withdrawn when the futures price falls by 30 cents to 420 cents per bushel.
4.25.
a).zero rate for maturity of 6 months:
Because it is semiannual compounding, the six-month rate could be :
(2×2)/98=4.08 per annum.
∴it is 2ln (1+0.0408/2)=4.04% with continuous compounding.
Zero rate (12 months) :
ln (1+5/95) =5.13%
Zero rate (18 months):
3.1e-0.5×0.0404 +3.1e-0.0513 +103.1e-1.5R =101
-1.5R =ln0.9216 so, R=5.44%
Zero rate (24 months):
4e-0.5×0.0404 +4e-0.0513 +4e-1.5×0.0544 +104e-2R =104
-2R=ln0.89 R=5.8%
Zero rates for maturities of 6 months, 12 months, 18 months, and 24 months are 4.04%, 5.13%, 5.44% and 5.8%
b). F= (0.0513-0.0404×0.5)/ (1-0.5) =6.22%
F= (1.5×0.0544-0.0513)/ (1.5-1) =6.06%
F= (0.058×2-1.5×0.0544)/ (2-1.5) =6.88%
Forward rates for the periods 6 to 12 months : 6.22%
12 to 18 months: 6.06%
18 to 24 months :6.88%.
c).m=2 6-mouth par yield:
A=d=e-0.5×0.0404 =0.98 c= (100-100×0.98) ×2/0.98=4.081
12-month par yield:
A=e-0.05×0.0404 +e-0.0513 =1.93 d=e-0.0513 =0.95
c= (100-100×0.95) ×2/1.93=5.18
18-month par yield:
A=e-0.05×0.0404 +e-0.0513 +e-1.5×0.0544 =2.85 d=e-1.5×0.0544 =0.9216
c= (100-100×0.9216) ×2/2.85=5.5
24-month par yield:
A=e-0.05×0.0404 +e-0.0513 +e-1.5×0.0544 +e-2×0.058 =3.742 d=e-2×0.058 =0.89
c= (100-100×0.89) ×2/3.742=5.8792
The 6-month, 12-month,...