ABC Corp. European Options Evaluation

ABC Corp. is considering two different strategies involving options on its stock. The stock has a current price of $50 and follows a binomial model with an up factor of 1.2 and a down factor of 0.8 over a single period. The risk-free interest rate is 5%. ABC Corp. is particularly interested in establishing the value of a European call option with a strike price of $52. The company also wants to compare this with a European put option with the same strike price.

Using the binomial model, calculate the fair price of the European call option and the European put option, then determine which option is overpriced based on the derived values.