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The issue of developing simple Black-Scholes type approximations for pricingEuropean options with large discrete dividends was popular since early 2000'swith a few different approaches reported during the last 10 years. Moreover, ithas been claimed that at least some of the resulting expressions representhigh-quality approximations which closely match results obtained by the use ofnumerics.  In this paper we review, on the one hand, these previously suggestedBlack-Scholes type approximations and, on the other hand, different versions ofthe corresponding Crank-Nicolson numerical schemes with a primary focus ontheir boundary condition variations. Unexpectedly we often observe substantialdeviations between the analytical and numerical results which may be especiallypronounced for European Puts. Moreover, our analysis demonstrates that anyBlack-Scholes type approximation which adjusts Put parameters identically toCall parameters has an inherent problem of failing to detect a little knownPut-Call Parity violation phenomenon. To address this issue we derive a newanalytic approximation which is in a better agreement with the correspondingnumerical results in comparison with any of the previously known analyticapproaches for European Calls and Puts with large discrete dividends.

New analytic approach to address Put - Call parity violation due to discrete dividends