- Why Finance?
- Utilities, Endowments, and Equilibrium
- Computing Equilibrium
- Efficiency, Assets, and Time
- Present Value Prices and the Real Rate of Interest
- Irving Fisher's Impatience Theory of Interest
- Shakespeare's Merchant of Venice and Collateral, Present Value and the Vocabulary of Finance
- How a Long-Lived Institution Figures an Annual Budget Yield
- Yield Curve Arbitrage
- Dynamic Present Value
- Financial Implications of US Social Security System
- Overlapping Generations Models of the Economy
- Will the Stock Market Decline when the Baby Boomers Retire?
- Quantifying Uncertainty and Risk
- Uncertainty and the Rational Expectations Hypothesis
- Backward Induction and Optimal Stopping Times
- Callable Bonds and the Mortgage Prepayment Option
- Modeling Mortgage Prepayments and Valuing Mortgages
- Dynamic Hedging
- Dynamic Hedging and Average Life
- Risk Aversion and CAPM
- The Mutual Fund Theorem and Covariance Pricing Theorems
- Risk, Return, and Social Security
- Leverage Cycle and the Subprime Mortgage Crisis
- Shadow Banking: Parallel and Growing?

# Callable Bonds and the Mortgage Prepayment Option

This lecture is about optimal exercise strategies for callable bonds, which are bonds bundled with an option that allows the borrower to pay back the loan early, if she chooses. Using backward induction, we calculate the borrower's optimal strategy and the value of the option. As with the simple examples in the previous lecture, the option value turns out to be very large. The most important callable bond is the fixed rate amortizing mortgage; calling a mortgage means prepaying your remaining balance. We examine how high bankers must set the mortgage rate in order to compensate for the prepayment option they give homeowners. Looking at data on mortgage rates we see that mortgage borrowers often fail to prepay optimally.

*Source: Open Yale Courses*

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