Option Pricing: Examples and Open Problems

The option pricing problem is equivalent with the hedging problem of the option, i.e. what the writer should do in order to hedge the risk that she undertakes selling a contract and moreover what is the probability of profit selling at a specific price. The probability of profit is also a useful information for the buyer. The hedging strategy should be practically possible for the writer otherwise has no meaning. In this note we will discuss the option pricing problem and in particular the effect of the volatility on the binomial model which is a way to hedge practically a specific option in contrast to every pricing model that assumes rebuilding of the replicating portfolio continuously in time. In order to use the binomial model we have to modified it accordingly as we have seen in a previous paper. We also point out three open problems regarding the binomial option pricing model.