You own Macquarie Group Shares (MQG) currently valued at $170 per share, and believe the recent weakness in the banking system may present some downside risks. As a result, you decide to purchase a 2-month 'at-the-money' Put Option on MQG shares to protect your risk. The volatility of MQG shares is 25%, and the Shares pay a dividend of $5 at the end of month 1. The risk free rate is 4.5% for all maturities. All variables are required to be calculated using continuous compounding (recall use of e^rt). Show all workings and calculate:

The up movement factor and down movement factor when a one-month time step is used?

The up movement probability (Pu) and down movement probability (Pd) when a one-month time step is used?