Greetings,
I apologize in advance if this question is less "coherent" or well-formed than I would prefer, but I am hoping someone on the list can offer suggestions on the following topic.
Briefly, I am working on a research problem in quantitative finance involving the use of options models to value mortgages written on large commercial real estate properties. Options model (such as the famous Black-Scholes equation) require the user to specify a "volatility parameter", which is related to the variance of the value of the asset one is trying to model. Often one would simply calculate the standard deviation of historical prices on the asset (e.g., historical stock market prices) and use this estimate as the input into the model.
For my particular problem, I have a large sample of data on commercial real estate sales for major cities in the United States. Each record is geocoded by the lat-long coordinate of the building. I have successfully built SAR models based upon Delaunay triangulation for the spatial matrix, so the data supports some reasonable geo-statistical modeling. Experience and past research suggests that the value of the mortgages is closely tied to the value of the properties, which show a significant degree of spatial correlation (on a city-by-city basis).
I am trying to determine a way to estimate a vector of "intra-city" volatility parameters that reflect the underlying spatial correlation of the real estate data. I should also point out that this data is skewed and fat-tailed, so a reasonably flexible distribution would be ideal.
Thanks in advance for any help that may be offered; and again I apologize if my inquiry is less than fully thought-out.
Regards,
Mark
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