A risk manager for Bank ABS is considering writing a 6-month American put option on a non-dividend paying stock XYZ. The current stock price is $50, and the strike price of the option is $52. In order to find the no-arbitrage price of the option, the manager uses a two-step binomial tree model. The stock price can go up or down by 20% each period. The managers view is that the stock price has an 80% probability of going up each period and a 20% probability of going down. The annual risk-free rate is 12% with continuous compounding. a) What is the risk-neutral probability of the stock price going up in a single step? b) What is no-arbitrage price of the option?