I work at an accountancy firm and we use Black-Scholes to value equity in private companies that has option like features. The equity we typically value is akin to deeply out of the money European call options and we source volatility using historical share price volatilities of quoted comparable volatilities.
It's a very rudimentary approach which I'm hoping to improve given all the problems associated with Black-Scholes (my primary concern being the volatility skew). I've done a bit of research on local vol and stochastic vol models (a lot of which went over my head) and I'm not sure which would work best given this fact pattern. I understand you need to calibrate these models to market data, which we obviously do not have for private companies. Unless it would be reasonable to calibrate the model to comparable companies (though many of these do not have traded options), or are there some 'general' parameters which could be used? It would also need to be implemented in Excel.
Any ideas for what would work best given this fact pattern? Ideally something which would address the volatility skew given the equity is deeply out of the money and therefore using constant volatility is overvaluing the equity. The simpler the better really. Bonus if there's an template excel model I could download!
Note I have no quant experience, but do have a math degree from many years ago, so I'm somewhat mathematically literate. Thanks in advance.