The stock of R$$o Hondo Inc. is currently trading at $$100$ and doesn't pay dividends. Thanks to the COVID$-19$ pandemic, the risk$-$free rate has gone

down to zero.

You are interested in buying an American call option on R$$o Hondo's stock, expiring $9$ months from now with a strike price of $$125.$ Unfortunately, R$$o

Hondo is a new venture so there are no options on the market. You approach your local investment bank who is willing to sell you the option.

You and the bank both know that R$$o Hondo's stock evolves according to the following binomial tree. Each period represents $3$ months, so the end of

the tree is $9$ months from now.

What market price will you and the bank agree on for the option? Assume there are no transactions costs.