How to Simulate House Prices for Mortgage Risk

TL;DR

House prices can be simulated for mortgage risk by generating many possible price paths, converting adjusted random numbers into annual percentage changes, and averaging the resulting default experience. The example assumes a 2% mean annual increase, a 3% standard deviation, and an initial $100,000 house price, while emphasizing that these assumptions remain highly uncertain. Read on for the calculation steps, key assumptions, and limits of the approach.

Transcript

okay the topic for this talk is simulating house prices it's a very important topic it's the process of simulating house prices is very important to the process of pricing mortgage risk of estimating expected default costs for different kinds of mortgages but I want you to take away from this that even though I think this is the best approach for U... Read More

Key Insights

• Simulating house prices involves creating multiple paths and averaging their outcomes.
• Assumptions include average annual price increase and standard deviation, often using a normal distribution.
• Random numbers are adjusted for assumed mean and standard deviation to simulate price changes.
• The simulation helps in estimating mortgage default risks, though with significant uncertainty.
• Two types of uncertainty affect simulations: future price trends and variation around the average.
• It's crucial to consider whether house price changes are independent or accumulate over time.
• The tail of the distribution, where prices fall, is most important for assessing default risk.
• Despite its limitations, simulation offers a better risk assessment than no analysis at all.

Questions & Answers

Q: How do you simulate house prices for mortgage risk?

Generate many possible paths for house prices, translate each path into possible mortgage defaults, and average the default experience across the paths. The example creates annual percentage changes by adjusting normally distributed random numbers for an assumed mean and standard deviation.

Q: How are random numbers adjusted to simulate annual house-price changes?

Start with random numbers having a mean of zero and a standard deviation of one. Multiply each number by the assumed standard deviation of 3% and then add the assumed mean of 2% to obtain the simulated percentage change.

Q: What assumptions are used in the example house-price simulation?

The example assumes annual house-price changes are normally distributed with a mean increase of 2% and a standard deviation of 3%. It applies the adjusted percentage changes to an initial house price of $100,000 over six years.

Q: What price-change ranges follow from the example's normal-distribution assumptions?

With a 2% mean and 3% standard deviation, the annual change falls between a 1% decline and a 5% increase two-thirds of the time. It falls between a 3% decline and an 8% increase 95% of the time under the stated assumptions.

Q: How many simulated house-price paths should be used?

The method can use hundreds or even thousands of different random-number paths. Results are averaged across those paths to estimate overall default experience rather than relying on a single possible future.

Q: Why do simulated house-price paths produce different mortgage-default outcomes?

Some paths keep the house price fairly high and therefore imply few defaults, while other paths may produce many defaults. Still other paths can imply essentially zero chance of default, so the simulation averages across all of them.

Q: What are the two main sources of uncertainty in the simulation assumptions?

The first is uncertainty about average house prices over a future period such as 10 or 30 years. The second is how an individual home's price varies around the national average because of local conditions, maintenance, and similar factors.

Q: How precise are stochastic house-price simulations for estimating mortgage risk?

The approach is computationally intensive and may look highly scientific, but its estimates remain limited in precision. Its assumed mean and standard deviation are uncertain, yet the method still provides a rational basis for differentiating mortgages by expected default cost.

Summary & Key Takeaways

• Simulating house prices is essential for evaluating mortgage risks, though it involves considerable uncertainty. The process uses random numbers adjusted for assumed mean and standard deviation to predict price changes. Despite its computational intensity and unreliable assumptions, this method offers a clearer picture of relative default risks compared to doing nothing.

• The simulation requires assumptions about average price changes and their variability, often modeled with a normal distribution. It helps estimate default risks by simulating multiple paths and averaging outcomes. However, the accuracy of forecasts is limited by the inherent uncertainty in future price trends and regional variations.

• Key challenges include deciding if price changes are independent or cumulative and focusing on the distribution's tail, where prices fall. While not precise, the simulation provides a reasonable basis for comparing risks of different mortgage scenarios, such as varying down payment sizes, despite its reliance on uncertain assumptions.