貨幣時間價值與利率期限結構清華大學絕版金融工程(文件)
【正文】 8 — Shapes of Yield Curve upward flat downward ? Some theories for the shapes of yield curve — Unbiased expectations theory — Liquidity preference theory — Market segment theory — Preferred habitat theory 19 1 1 5$%)151(1 0 0$ ????F . One year’s riskfree rate Forward Interest — There is a nodividend stock and its expected return is 15%. The current price is A mini case: 100$0 ?S%5?fr . What is one year’s forward price of this stock? ? 20 Position Immediate Cash Flow Cash Flow in the Future Replicating Stock Using riskfree bond and forward contract Suppose forward price F = $106 per share Short sell $100 riskfree bond Short sell one stock forward at $106 per share Buy one stock at $100 per share +$100 ? $105 0 106 – S1 ? $100 S1 Net Cash Flow 0 $1 Arbitrage Stock forward price = $105 per share 21 Forward price of a risky asset is not the expectation of the future spot price of the asset. Proposition! 22 The Forward Price for a Traded Asset ? The forward price for a traded asset without interim ine is: F=SerT ? The forward price for a traded asset with deterministic dividend rate is: F=Se(rq)T ? The above equation can be obtained through the following arbitrage strategy: – Buy spot eqT of the asset and reinvest ine from the asset in the asset. – Short a forward contract on one unit of the asset. 23 The Forward Price for a Traded Asset ? The holding of the asset grows at rate q so that eqT x eqT ,or exactly one unit of the asset, is held at time T. Under the terms of the forward contract, the asset is sold for F at time T, leading to the following cash flow: 0 T SeqT F SeqT=FerT F=Se(rq)T 24 ? Forward interest rates are the expectation of future riskfree spot interest rates. 0 1 2 3 n — Zerocoupon rates amp。 Deposition 。 forward interest rates v r ttt? ?11? ?v rt t t? ?11f vv mj jj? ????? ????? 1 1 ,r t vtt? ???? ???1 1 1r vttt? ?1 1v0 1?vvfmjjj??????????111Discount factors tvForward rates jfZerocoupon rates tr
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