Question

Suppose that the current market interest rate is at 5% per annum in semi-annually compounding rate. A convertible bond issued by Study Inc has coupon rate of 5% per annum., a face value of £100, and time-to-maturity of 10 years. The coupon payment will pay to bondholders every 6 months. Bondholders may convert each unit of the bond into 100 shares of Study Inc shares at any time during the life of the bond. If the current stock price of Study Inc is trading at £10 per share, estimate the convexity of this convertible bond.

Answer 1

Market Rate	5%	Semi annually
Market Rate	5.0625%	Annlulized((1+5%/2)^2)-1
Bond Coupon	5%	Annual
Face value of bond	100
Maturity	10	Year
Coupon paymannt	2.5	Semi annually
Share Price	10
Bond 1 =	100	Share
Bond price	100

Part 1 = 1/P*(1+Y)^2

= 1/1000*(1+5.0625%)^2

= 0.001103812890625

Part 2 = Sum of (CFt/(1+Y)^t * (t^2 + t)  (See below Table)

Convexity = Part1 * Part2

= 0.01103812890625 * 30,762.74 (See below Table)

= 339.563057561907 Annual

= 339.563057561907 /4

= 84.8907643904767 Semi annual

Time(t)	Cash Flow	Discount Factior(1+y/2)^t	Present value (CF/(1+Y)^t	Time factor(t^2+t)	Present value (CF/(1+Y)^t*Time factor(t^2+t)
1	2.5	1.025313	2.44	2	4.88
2	2.5	1.051266	2.38	6	14.27
3	2.5	1.077876	2.32	12	27.83
4	2.5	1.105160	2.26	20	45.24
5	2.5	1.133134	2.21	30	66.19
6	2.5	1.161816	2.15	42	90.38
7	2.5	1.191225	2.10	56	117.53
8	2.5	1.221378	2.05	72	147.37
9	2.5	1.252294	2.00	90	179.67
10	2.5	1.283993	1.95	110	214.18
11	2.5	1.316494	1.90	132	250.67
12	2.5	1.349817	1.85	156	288.93
13	2.5	1.383985	1.81	182	328.76
14	2.5	1.419017	1.76	210	369.97
15	2.5	1.454936	1.72	240	412.39
16	2.5	1.491764	1.68	272	455.84
17	2.5	1.529524	1.63	306	500.16
18	2.5	1.568240	1.59	342	545.20
19	2.5	1.607936	1.55	380	590.82
20	102.5	1.648637	62.17	420	26,112.48
					30,762.74