The current price of a non$-$dividend paying stock is $$30.$ Use a two$-$step tree to value a put option on the stock with a strike price of $$32$ that expires in $6$ months. Each step is $3$ months, and in each step the stock price either moves up by $10\%$ or moves down by $10\%.$ Suppose that the risk free rate is $8\%$ per annum with continuous compounding. Please answer the following $3$ questions

What should be the EUROPEAN PUT option price today?

What should be the EUROPEAN PUT option price today?

$$1\mathrm{.}25$

$$2\mathrm{.}24$

$$0\mathrm{.}90$

$$4\mathrm{.}36$

If it was an AMERICAN PUT option, what should be the option price today?

If it was an AMERICAN PUT option, what should be the option price today?

$$4\mathrm{.}48$

$$2\mathrm{.}49$

$$1\mathrm{.}40$

$$0\mathrm{.}95$

If the volatility was given as $30\%,$ how would this change the AMERICAN PUT option price today?

If the volatility was given as $30\%,$ how would this change the AMERICAN PUT option price today?

$$6\mathrm{.}63$

$$3\mathrm{.}33$

$$4\mathrm{.}23$

$$2\mathrm{.}13$