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ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.2 : (a) In the pricing of a coupon bond, the formula is : P = c / (1 + r) + (c + B) / [ (1 + r) (1 + r) ] for 2 years to maturity, where c = annual coupon payment (in dollars, not a percent), B = par value, P = purchase price. Five years ago someone bought a 20 year coupon bond and would like to get rid of it now : A coupon rate of 7 %, it matures in exactly 2 years, par value is $1000, current interest rate is 5 %. (i) Find the value of c. (ii) Find the value of r or interest rate. (iii) Find the value of P. (iv) Guess the formula for P when the maturity period is 3 years, if such formula for 1 year duration is P = (c + B) / (1 + r). (b) In lemma of Ito on a Forward, recall that a forward contract is priced at : ln F = ln S + rT. Find the value of F in 5 decimal points when S = $100, r = interest rate = 0.05 / year, T = duration = 1 year.
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Answer Posted / kangchuentat
ACCOUNTING AND FINANCIAL ENGINEERING - ANSWER 34.2 : (a) (i) c = $1000 x 0.07 = $70. (ii) r = 5 % = 0.05. (iii) P = c / (1 + r) + (c + B) / [ (1 + r) (1 + r) ] = 70 / (1 + 0.05) + (70 + 1000) / [ (1 + 0.05) (1 + 0.05) ] = $1037.19. (iv) For 3 year maturity period prediction by induction, P = c / (1 + r) + c / [ (1 + r) (1 + r) ] + (c + B) / [ (1 + r) (1 + r) (1 + r) ]. (b) Let ln F = ln S + rT = ln 100 + 0.05. Then F = $105.127109 or F = $105.12711 (in 5 decimal points). The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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