Hello, does any one know how to find if there is an arbitrage opportunity in the following sets of bonds, after determining this how can you find which bonds to buy/sell to take advantage of this? B1: 1year $95pv 0coupon ~5%ytm B2: 2year $90pv 0coupon ~5%ytm B3: 2year $100pv 10%coupon ~10%ytm B1 B2 B3 100 0 10 0 100 110Next: B1: 1year $95pv 0coupon ~5%ytm 100 5 6B2: 2year $100pv 5%coupon ~5%ytm 0 105 106B3: 2year $101pv 6%coupon ~5.5%ytmB1 B2 B3100 5 6 0 105 106Next: B1: 1year $95pv 0coupon B2: 2year $101pv 6%coupon B3: 3year $98pv 4%coupon B4: 4year $104pv 5%coupon B1 B2 B3 B3 100 6 4 50 106 4 50 0 104 50 0 0 105Also do you guys know if it is possible to have excel find it for you, using VBA macro/developer? How much code do you think it would take for Excel/VBA to find the arbitrage opportunity and give you the proportion of bonds to purchase to take advantage of it? I understand its a matrix algebra problem?

anyone?

Here is the principle to solve this (I am telling you how to solve the first example and hopefully once you have understood the principle you can do the rest yourself :-)The zero coupon bonds (ZCBs) that mature in 1 year and 2 years give you the values of the discount factors from now to 1 year in the future (call it d1) and the discount factor between now and two years in the future (call it d2): therefore, to preclude arbitrage, it must be the case that a product that pays you A1 in 1 year and A2 in 2 years should have present value d1*A1 + d2*A2. (For instance the 10% bond with maturity 2 years pays you 10 in 1 year and 110 in 2 years so A1 = 10 and A2 = 110 and thus the price of this bond should be 10d1 + 110d2) If this product is more expensive than d1A1 + d2A2, then sell it and buy appropriate quantities of the zero coupon bonds to make your cash flow = 0 in 1 year and 2 years. You will end up making money right now and having no cash flows in the future -> arbitrage....... and if it s cheaper than d1A1 + d2B2 then buy it and sell ZCB -> arbitrage again.Hope this helps

first one:long 0.1 B1, long 1.1 B2, short 1 B3at day zero, cost is0.1 * 95 + 1.1 * 90 - 100 = 8.5cashflow at 1yr:0.1 * 100 - 10 = 0cashflow at 2yr:1.1 * 100 - 110 = 0So riskfree profit = 8.5 at day zero.The idea of the rest is the same. Two of the bonds can give the zero bond price. The third can be arbitraged if there is any price inconsistency