- 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?

# Dynamic Present Value

In this lecture we move from present values to dynamic present values. If interest rates evolve along the forward curve, then the present value of the remaining cash flows of any instrument will evolve in a predictable trajectory. The fastest way to compute these is by backward induction. Dynamic present values help us understand the returns of various trading strategies, and how marking-to-market can prevent some subtle abuses of the system. They explain how mortgages work, why they're called amortizing, and what is meant by the remaining balance. In the second half of the lecture we turn to an important application of present value thinking: an analysis of the troubles facing the Social Security system.

*Source: Yale Open Courses*

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