Derivative Valuation in Fixed Income Markets
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This work studies asset pricing in interest rate markets. A key input for valuation models is the term structure of interest rates constructed from forward rate curves. Because bonds are issued at discrete maturities, building these curves requires smoothing across observed prices. We compare standard static parameterizations (including Nelson-Siegel, Svensson, and cubic splines), and introduce a dynamically consistent approach. We evaluate each method by its ability to fit market bond prices and show that cubic splines and our dynamic specification generally outperform the traditional static models. We then examine interest rate swaps. Since their introduction in October 2018, SOFR swap rates have traded below U.S. Treasury yields, posing a puzzling arbitrage opportunity because swaps can be replicated using bonds and repo transactions. We develop an arbitrage-free replication framework in the SOFR setting to quantify the sources of this spread. We show that the gap between swap and Treasury rates can be explained by Treasury market pricing, repo transaction costs, and regulatory constraints under Basel III. Next, we examine bank certificates of deposit (CDs). CDs offer fixed rates over a stated term and often include embedded options, such as early withdrawal or rate increase features. Using an arbitrage-free pricing framework, we show that CDs are frequently mispriced relative to the U.S. Treasury curve and to the banks’ own competing CD offerings. Our results suggest that consumers do not always exercise embedded options optimally and that bank CD rates can deviate from arbitrage-free values. Finally, we analyze callable brokered CDs and the exercise decision from the bank’s perspective. We compute arbitrage-free values and characterize the optimal call policy implied by our valuation model. Comparing model values with market prices, we document spreads that are related to bank funding needs, contractual features, and market frictions. We find that callable CDs are rarely overvalued in the market, and banks typically call close to the optimal boundary. However, deviations are more common among banks with limited callable CD issuance, perhaps due to different funding needs.