Consider an American put option with the following features:

1. The initial stock price is 80.
2. The option expires in 6 months
3. Use a two-step binomial tree.
4. Stock pays 2 percent continuous dividend.
5. Strike price of the option is 85.
6. The continuously compounded risk free interest rate is 0.05.
7. At any given 3 month-period, the stock prices will either increase by 15 percent or decrease by 12 percent.

Estimate the annual theta at the initial node