[ai-geostats] Help on estimating "spatial volatilities"
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
Thanks in advance for any help that may be offered; and again I
apologize if my inquiry is less than fully thought-out.