Suppose a stock has an expected return of 10% per year and a return volatility of 28% per year and equally likely transitions (i.e. with probability 1/2). The risk-free rate is 4% per year. The stock has a current price of $100 and has declared dividends of $2.04 to be paid at the end of each six-month period.

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Construct a binomial model for the stock price of ABC with 2 semi-annual periods.?

Find the value of a European call option expiring in 1 year with a strike price of $104 using the binomial model.?

Find the value of a European put option expiring in 1 year with a strike price of $104 using the binomial model.?

Find the value of an American call option expiring in 1 year with a strike price of $104 using the binomial model.?

Find the value of an American put option expiring in 1 year with a strike price of $104 using the binomial model.?

1. One-dimensional random walk. There is a one-dimensional lattice with lattice constant a as shown in Figure 1. An atom is initially at the origin :1: = E] and transits from a site to a nearest-neighbor site every 1" seconds. The probabilities of transiting to the right and left are p and q = 1p, respectively. Let a be the number of transitions to the right, and \"It" the number of transitions to the left. The total number of transitions is thus N = n + of. v F' (\"N/W ii, 00000000 0 Figure 1: A 1D lattice with an atom hopping on it. (a) Where is the atom at t = NT in terms of N, n, and a? That is, what is the displacement :r of the atom after N transitions? (b) What is the probability of the displacement in (a)? (c) What are the pollible values of n? (d) What is the average value of a and the displacement a after N transitions? (e) 'What is the average displacement in one transitions? (f) Compare the results from (d) and (e) and show that they are consistent with the central limit theorem by noting that the total The Metropolis-Hastings algorithm is used to simulate a binomial random vari- able with parameters n = 4 and p = 1/4. The proposal distribution is simple symmetric random walk on {0, 1, 2, 3, 4} with reflecting boundaries. (a) Exhibit the T matrix. (b) Exhibit the transition matrix for the Markov chain created by the Metropolis-Hastings algorithm.Design Transitions Animations Slide Show Review View Help A Search 3 term 171 By using the binomial series, the coefficient of * in the power series rep- resentation of v4 + x2, is Linged Stakes