12th batch solution
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This document discusses the results of an auction of government bonds. It allocates the bonds between four bidders based on their bid rates, with Bidder H&I&J receiving the highest rate of 5.07%. It then calculates the market price and settlement price for each bidder. Several bond pricing formulas are also presented. The document goes on to calculate interest rates between nodes in a term structure model and the prices of euro dollar and treasury futures contracts using provided formulas.
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12th batch solution
- 1. 12th Batch solution 1(b) Total auction = 100 billion, Non competitive bid = 0 Bidder Bid Quantity(B) A 5% 30 B&C 5.04% 35 D&E&F 5.05% 20 H&I&J 5.07% 65 Allocation 30 35 20 15 MPA 101.35 100.93 100.83 100.62 Price Paid SPA 100.62 100.62 100.62 100.62 Coupon rate = 5.07%+.06% =5.13% Formula for price determination SPA calculation P= )+ A = 5.13 r =.0507 n = 15 P =100.62 Other things will remain same for all the MPA price except for the change of r. A B&C D&E&F H&I&J 5% 5.04% 5.05% 5.07% Question 2(a) = .5ln ( ) OR, = 5ln ( OR, = 0.16 Question 2(b) )
- 2. = OR, 0.1075 = =0.0781 OR, 7.81% Again, = OR, 0.781= OR, 0.0567 or, 5.67% Question 2(c) Node A B C D E F Interest rate 7.5% 9% 6.5% 10.75% 7.81% 5.67% D( ) Coupon(12-r) 3 5.5 1.25 2.19 6.33 = 100+1.25 = 101.25 B (PU) E( A (P0) C (PD) PU = {(101.25X.5) + (102.19)} X ) = 100+2.19 = 102.19 = 100+6.33 = 106.33 F( ) + 3(Coupon) PU = 96.32 PD = {(102.19X.5) + (106.33)} X + 5.5 PD = 103.4 PO = {96.32 X.5) + (103.4 X 0.5)} X OR, PO = 92.68 Question 3(a) Theoretical price of Euro dollar future contract = 100-9 = 91 Question 3(b)
- 3. Calculation of the conversion factor Conversion factor is calculated using 6% as yield on the given coupon rate. A Hypothetical price is drawn from the given formula and then the hypothetical price is divided by 100 to get the conversion factor. P= )+ A=6 i = .03 n= 30 P = 158.80 Conversion factor = =1.588 Theoretical future price calculation: TFP = X[P-{AIt-AI0} + (P+ AI0) Given, P = 117.39 = .06 =0 = = 3.96 Theoretical future price = X [117.39-{3.96-0} + 0.06X = 72.84 Invoice price per contract = CF X (Future Price+ Accrued coupon) X = 1.58 X (72.84+ 3.96) X = 121344 X (117.39+ 0)