金融衍生工具讲义(香港中文大学 何佳).ppt

·??? Replication and arbitrage Two of the most basic concepts of modern finance are replication and arbitrage. Replication refers to the possibility of constructing combinations of assets that reproduce or replicate the cash flow of another asset. The cash flows of a coupon bond, for example, can be a combination of zeros. Arbitrage refers to the process of buying an asset at a low price and selling an equivalent asset for a higher price, to make a profit. ·????Zeros and Coupon Bonds Bond Maturity Coupon Rate Price($) (Years) A 0.5 none 96.00 B 1.0 none 91.00 C 0.5 8 99.84 D 1.0 6 98.00 Consider the possibility of replicating the cash flows of D from the two zeros. We buy(say) na units of A and nb units of B, generating cash flows of na*100 in 0.5 year and nb*100 in a year. For these to equal the cash flows of bond D, we need 3= na*100, 103=nb*100, implying na=0.03 and nb=1.03. Thus we have replicated D with a combination of A and B. The next question is whether the cost of the synthetic version of D sells the same price as D. The cost is na*96.00+nb*91.00=96.61. Since this is lower then the quoted price of D, we would buy the synthetic and sell short D pocketing the profit of 1.39. ·?? Linear Programming Problem Consider a collection of bonds, indexed by i =1,…I. Each bond i can be described in terms of its price, pi, and its cash flow over T periods, (c-1i, c2i, …,cTi), with T set at the maximum maturity of I bonds. Problem: min sum(n*p, i=1,..T) (by choosing ni, i=1,…,I) subject to sum(ni*cti,i=1,..I) =0, for each t=1,…T If this problem has a minimum zero, then these bonds are immune to arbitrage. But if the answer has negative cost, we have found a pure arbitrage opportunity: we sell the overpriced bonds(ni0) and buy the under priced ones. ·????Common yield fallacies Yiel