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Risk Neutral Pricing and Financial Mathematics: A Primer by John L. Teall, Peter M. Knopf

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Chapter 8

Mean-Reverting Processes and Term Structure Modeling

The mean-reverting Ornstein–Uhlenbeck process is discussed and then applied to interest rates (the Vasicek model). We derive the pricing of zero-coupon bonds driven by a common single factor interest rate model. To accomplish this task, a no-arbitrage argument is used to derive a differential equation for the bond price. The general form of the solution is derived in the appendix. In the text, we give a heuristic treatment of the martingale method of solution. The yield curve is discussed and derived in a Vasicek setting. We examine the specific solutions of the bond price and term structure obtained for various types of single factor interest rate models such as the Vasicek model, ...

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