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[ai-geostats] Help on estimating "spatial volatilities"

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  • Mark Coleman
    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
    Message 1 of 1 , Aug 7, 2004
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      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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