These study notes cover Tuckman, Fixed Income Securities, 3rd & 4th Editions:
Chapter 6: Regression Hedging and Principal Component Analysis – 4th Edition
Explain the drawback to using a DV01-neutral hedge for a bond position.
Describe a regression hedge and explain how it can improve a standard DV01-neutral hedge.
Calculate the regression hedge adjustment factor, beta.
Calculate the face value of an offsetting position needed to carry out a regression hedge.
Calculate the face value of multiple offsetting swap positions needed to carry out a two-variable regression hedge.
Compare and contrast level and change regressions.
Explain why and how a regression hedge differs from a hedge based on a reverse regression.
Describe principal component analysis and explain how it is applied to constructing a hedging portfolio.
Chapter 7: Arbitrage Pricing with Term Structure Models – 4th Edition
Calculate the expected discounted value of a zero-coupon security using a binomial tree.
Construct and apply an arbitrage argument to price a call option on a zero-coupon security using replicating portfolios.
Define risk-neutral pricing and apply it to option pricing.
Explain the difference between true and risk-neutral probabilities, and apply this difference to interest rate drift.
Explain how the principles of arbitrage pricing of derivatives on fixed income securities can be extended over multiple periods.
Define option-adjusted spread (OAS) and apply it to security pricing.
Describe the rationale behind the use of recombining trees in option pricing.
Calculate the value of a constant maturity Treasury swap, given an interest rate tree and the risk-neutral probabilities.
Evaluate the advantages and disadvantages of reducing the size of the time steps on the pricing of derivatives on fixed income securities.
Evaluate the appropriateness of the Black-Scholes-Merton model when valuing derivatives on fixed income securities.
Chapter 8: Expectations, Risk Premium, Convexity and the Shape of the Term Structure – 4th Edition
Explain the role of interest rate expectations in determining the shape of the term structure.
Apply a risk-neutral interest rate tree to assess the effect of volatility on the shape of the term structure.
Estimate the convexity effect using Jensen’s inequality.
Identify the components into which the return on a bond can be decomposed, and calculate the expected return on a bond for a risk-averse investor.
Chapter 9: The Vasicek and Gauss+ Models – 4th Edition
Describe the structure of the Gauss+ model and discuss the implications of this structure for the model’s ability to replicate empirically observed interest rate dynamics.
Compare and contrast the dynamics, features, and applications of the Vasicek model and the Gauss+ model.
Calculate changes in the short-term, medium-term, and long-term interest rate factors under the Gauss+ model.
Explain how the parameters of the Gauss+ model can be estimated from empirical data.
Chapter 9: The Art of Term Structure Models: Drift – 3rd Edition
Construct and describe the effectiveness of a short-term interest rate tree assuming normally distributed rates, both with and without drift.
Calculate the short-term rate change and standard deviation of the rate change using a model with normally distributed rates and no drift.
Describe methods for addressing the possibility of negative short-term rates in term structure models.
Construct a short-term rate tree under the Ho-Lee Model with time-dependent drift
Describe uses and benefits of the arbitrage-free models and assess the issue of fitting models to market prices.
Describe the process of constructing a simple and recombining tree for a short-term rate under the Vasicek Model with mean reversion.
Calculate the Vasicek Model rate change, standard deviation of the rate change, expected rate in T years, and half-life.
Describe the effectiveness of the Vasicek Model.
Chapter 10: The Art of Term Structure Models: Volatility and Distribution – 3rd Edition
Describe the short-term rate process under a model with time-dependent volatility.
Calculate the short-term rate change and determine the behavior of the standard deviation of the rate change using a model with time dependent volatility.
Assess the efficacy of time-dependent volatility models.
Describe the short-term rate process under the Cox-Ingersoll-Ross(CIR) and lognormal models.
Calculate the short-term rate change and describe the basis point volatility using the CIR and lognormal models.
Describe lognormal models with deterministic drift and mean reversion.