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Hello all,I am trying to implement implied trinomial trees, and the literature I have found so far does not do a very good job at explaining how to obtain the option prices for the list of strikes and tenures represented in the nodes of the tree. Perhaps someone here can help.In all examples I have run into, authors suggest interpolating option prices based on the few options that may be available in the market. This is because of the impossibility of finding option quotes for the Strike/Maturity combinations required by the tree for purposes of calibration. Some suggest interpolating implied volatility and then reverting to prices as needed.After looking around at option quotes, I can only say that, typically, a very small number of options are available to be used for tree calibration. Consequently, interpolating and, even worse, extrapolating, with a reasonable degree of confidence becomes nearly impossible. The question I have is, then, how to address this issue.I was wondering if either the option price (or implied volatility) surfaces can be parameterized, such that a reasonable representation of the surface can be achieved from a small number of data points. Is there a general equation that we can use to fit the data against? If not, how can one come up with reasonable prices - or implied volatilities – for the Strike/Maturity pairs demanded by the nodes of the tree?Thanks in advance,-LB