Explain the idea of valuing a fixed-income instrument so that no arbitrage is possible
The idea
An arbitrage-free value is the price that leaves no riskless profit available. Two instruments with identical cash flows must have the same price, and any bond is worth the sum of its cash flows each valued at the spot rate for its date, which is the price of the matching zero-coupon strip. If a coupon bond trades below the value of its strips, buy the bond and sell the strips; if above, do the reverse. Either trade needs no net investment and carries no risk. Trading pressure removes such gaps, which is why models are calibrated to reproduce market prices. The common error is getting the direction of the trade backwards.
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- Work out the arbitrage-free value of a straight fixed-coupon bond
- Explain the framework of a binomial tree for interest rates
- Explain how a binomial interest rate tree is calibrated so that it fits a given term structure
- Explain valuation by backward induction, and use it to value a fixed-income instrument from its cash flow at every node
- Contrast valuing with the zero-coupon yield curve and valuing with an arbitrage-free binomial lattice
- Explain pathwise valuation within a binomial interest rate model, and use it to value a fixed-income instrument from its cash flows on every path
- Explain how a Monte Carlo simulation of forward rates works and where it is applied
- Explain term structure models and the uses they are put to