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7.6 Monte Carlo Forward-Rate Simulation and Its Application

  • The Monte Carlo method is an alternative method for simulating a sufficiently large number of potential interest rate paths in an effort to discover how a value of a security is affected.
  • This method involves randomly selecting paths in an effort to approximate the results of a complete pathwise valuation.
  • Monte Carlo methods are often used when a security's cash flows are path dependent (e.g., asset-backed securities).
  • "Interest-rate path dependent" means that the cash flow received in one period is determined not only by the current interest rate level but also by the path that interest rates took to get to the current level.
  • For example, for a 30-year bond with monthly coupon payments, the following steps are taken:

(1) Simulate numerous (say, 500) paths of one-month interest rates under some volatility assumption and probability distribution, (2) generate spot rates from the simulated future one- month interest rates, (3) determine the cash flow along each interest rate path, (4) calculate the present value for each path, and (5) calculate the average present value across all interest rate paths.

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Lesson Wrap-Up

This lesson should leave you able to explain the monte carlo forward-rate simulation and its application in a fixed-income context and connect it to the decisions made by issuers, investors, or analysts.

Review Prompts

  1. Explain monte carlo forward-rate simulation and its application in your own words.
  2. State one exam-style risk, valuation, or market implication of the monte carlo forward-rate simulation and its application.