The stock of Heptad Inc. is priced at $41 per share today. No dividend is expected from this…

The stock of Heptad Inc. is priced at $41 per share today. No dividend is expected from this company within a few years. Based on the historical data, analysts estimate that the volatility of the stock price is 70% per annum. The interest rate is 2%. A put option on the stock strikes at 40 and matures in exactly 14 months from now.

-Suppose the put is European. What is the value of the put if you value it in a seven-step binomial model? Display the binomial tree in your answer.

-Now, suppose the put is American and value it again using a seven-step binomial model. By how much is the American put value higher than its European version? Indicate the nodes on which the American put will be exercised.

-If the volatility jumps instantaneously to 90% per annum today, will the European put value increase or decrease according to your seven-step binomial model? By how much? What if the put is American?

-If the European put is quoted for $11.51 in the exchange now, with what volatility will your seven-step binomial model give the option price quoted in the market? (This volatility is called the implied volatility of this put option; it is implied by the premium quoted or traded for in the market.) What if the put is American?