On the pricing of illiquid options with Black-Scholes formula

Detecting the fair, ie. no-arbitrage, price of an option is a very interesting and challenging task of quantitative finance. It results mostly from the fact that the option payoff is nonlinear and the price can be very sensitive to the changes of underlying factors (especially ATM options). From the other point of view, ATM vanilla options are often traded and liquid, while deep ITM and OTM options are mostly illiquid and it is difficult to estimate the model parameters. Another issue is how to obtain the market assumptions about riskless rate relevant for the option maturity and the future expected dividends. In this paper we focus on a particular problem of extracting parameters to value options on dividend paying stocks via BS model using real data from German option market.