Question:

Please try to make two-branch binomial tree for a stock price.

Assume a 1-year option expiry.

Using a volatility of 25%

Assume the stock price (spot and forward) is 200

What is the probability up and down for each step? What are your up and down amounts?

What would the price of a call option struck at 110% of the forward cost? (Hint: Recall risk neutral means you care only about expected payoffs. So just calculate a payoff and probability at the end of the tree.)

Now let's make this a one-branch normal model (so two outcomes at the end). Suppose forward interest rates are 2% and volatility is 1%. Time is 1 year. What is the up move and down move? Is the probability of 1% higher, the same, or more than the probability of 3%? What is the value of a 2% floor (payoff = max(2% - rate, 0)?

7. [10 points] Consider a malicious node that wants to perform a DNS poisoning attack. Would their attack have more impact if they poisoned a root server or a top level domain server? 8. [10 points] When an attacker is performing an ARP spoofing attack they are trying to poison the ARP tables. Suppose the LAN has a total of 8 devices, including one that is a malicious agent. Our example in class discussed poisoning the ARP table of two nodes on the LAN. What would be the maximum number of ARP tables that the malicious node can poison? Briefly explain your answer.Consider three urns, one colored red, one white, and one blue. The red urn contains 1 red and 4 blue balls; the white urn contains 3 white balls, 2 red balls, and 2 blue balls; the blue urn contains 4 white balls, 3 red balls, and 2 blue balls. At the initial stage, a ball is randomly selected from the urn whose color is the same as that of the ball previously selected and is then returned to that urn. Let X,, be the color of the ball in the ath draw. (a) What is the state space? (b) Construct the transition matrix P for the Markov chain. (c) Is the Markove chain irreducible? Aperiodic? (d) Compute the limiting distribution of the Markov chain. (Use your computer) (e) Find the stationary distribution for the Markov chain. (f) In the long run, what proportion of the selected balls are red? What proportion are white? What proportion are blue