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this is my first question and I hope I get everything right. The problem I have to solve is the following: a bank is offering its customers "pre-validated" mortgages of up to a certain amount (for example, a client may receive the offer for a pre-validated mortgage up to $500,000). How can I calculate the price elasticity for the mortgage?

I have two different approaches in mind, but I am no expert. One approach is at the individual client level and the other one uses aggregate data.

Individual client level I imagine I can segment rating classes (to account for risk) in different segments identifying clients with different "propensity" to buy mortgages, price notwithstanding. After that, I was thinking of the right model to apply for each client: from a preliminary search, it seems to me that a logit regression could work. The response variable would then be "Accepted the offer (binomial)" and the main explanatory variable would be the offered price. Am I going in the right direction or am I completely lost?

Aggregate level After segmenting rating classes as before to identify clients with different "buying behavior", I could use as observations the different campaigns for each segment by aggregating them. In this case, my observations will include some variables to account for seasonality (e.g. month of the campaign) as well. With this approach, I believe that a multiplicative regression could be the appropriate solution. In this case, the response variable would be the total volume of mortgages sold (or would it be better to have the number of mortgages sold?) and the main explanatory one would still be the price.

Now, my questions are the following: - What are the fatal flaws in my reasoning? - Is there anything that makes sense in what I wrote? - Which approach could yield the better results? - Are there any other approaches I should consider?

Thank you very much for the support!

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  • $\begingroup$ This is a tough, interesting question. First, for anyone to be able to answer you need to define how you are operationalizing or defining price. I would question the value of segmenting customers by risk (FICO score?) vs treating risk continuously. At a minimum, price elasticity requires information related to choice (purchase) at differing, possible price points while controlling for relevant factors such as the value or amount of the loan, the interest rate-fixed or adjustable-as well as things like the originating conditions of the offer. ctd.>> $\endgroup$ – DJohnson Jun 28 '18 at 18:47
  • $\begingroup$ <<ctd. E.g., is it based on an RFI from a customer? Was it made online? f2f with a bank rep? over the phone? a direct marketing campaign drawn from pre-existing bank customers or a list of prospects? All of these factors (and more) can impact responsiveness or price elasticity. You also need to identify the point in the loan approval value chain where elasticity will be evaluated. Next, based on an offer, how many customers respond? Offers are frequently teasers requiring later customer vetting for approval. How many responders obtain approval? Of those approved, how many obtain a loan? ctd.>> $\endgroup$ – DJohnson Jun 28 '18 at 18:48
  • $\begingroup$ Finally, consideration should be given to how you structure the matrix of data for analysis. Some variant of discrete choice modeling would be the most informative. $\endgroup$ – DJohnson Jun 28 '18 at 18:49

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