5. Consider a binomial tree model for a stock price, S(n) as above. Find a probability...
3. Let K(1)., K(n) be independent identically distributed one step returns rates on a binomial tree model for a stock price, S(n). Here K(1) = u with probability p and K(1) with probability 1 p. For which values of n and what conditions on u and d can (n) S(0)
Consider a binomial tree model for a stock price, S(n). Let r be the risk free rate of interest and p∗ the probability for which E∗(K(1)) =r. Find the conditional expectation E∗(S(n)|S(1)) for any value of n.
Consider the following one-period binomial model for stock price. At t = 0 the stock price is $80 and at t = 1 (t is in years) it could be $70 with probability p > 0 and $y with probability 1 − p. The interest rate is assumed to be 8%. (1) Determine the range of values for y that precludes arbitrage in this model. (2) Assume that y = $83. Construct an arbitrage strategy for this model.1
Consider the binomial model for an American call and put on a stock whose price is $90. The exercise price for both the put and the call is $65. The standard deviation of the stock returns is 25 percent per annum, and the risk-free rate is 6 percent per annum. The options expire in 120 days. The stock will pay a dividend equal to 4 percent of its value in 60 days. (a) Draw the three-period stock tree and the...
2. Consider a two-period (T = 2) binomial model with initial stock price So = $8, u= 2, d=1/2, and “real world” up probability p=1/3. (a) Draw the binary tree illustrating the possible paths followed by the stock price process. (b) The sample space for this problem can be listed as N = {dd, jdu, ud, uu}. List the probabilities associated with the individual elements of the sample space 12. (c) List the events (i.e., the subsets of N2) making...
5. Consider the single period binomial model as in Section 1.2.2. Suppose that d <1+r <u. Show that if there exists an arbitrage opportunity (as in Definition 1.5), then one can find an arbitrage opportunity with V = 0. This means that there is no net cash flow at time 0. (Note: This is a step in the proof of Proposition 1.7 which you should go through carefully.) 1.2.2 Formal logical content The theory we build will be a mathematical...
Problem 5. Indicator variables S points possible (graded) Consider a sequence of n 1 independent tosses of a biased coin, at times k = 0,1,2,...,n On each toss, the probability of Heads is p, and the probability of Tails is 1 -p {1,2,.., at time for E resulted in Tails and the toss at time - 1 resulted in A reward of one unit is given if the toss at time Heads. Otherwise, no reward is given at time Let...
Q8-Part I (6 marks) The current price of a non-dividend-paying stock is $42. Over the next year it is expected to rise to-$44. or fall to $39. An investor buys put options with a strike price of $43. To hedge the position, should (and by how many) the investor buy or sell the underlying share (s) for each put option purchased? (6 marks) 08-Part II (9 marks) The current price of a non-dividend paying stock is $49. Use a two-step...
Black-Scholes 1. C8: Provide a formula for the forward price based on the stock price S, the risk-free rate r and the time to expiration T. 2. Columns N, O: Provide formulas for the future value (at expiration) value of the option premiums using the BlackScholes option prices C(K,T) and P(K,T), the risk free rate r and the time to expiration T. Black-Scholes 2.45-Y 100% Q- Search in Sheet Home Layout Tables Charts SmartArt Formulas Data Review Edit Font Number...
1. Consider the following discrete time one-period market model. The savings account is given by Bo 1 and B1 1.1. The stock price is given by So 1 and S,-ξ where ξ is a random variable taking two possible values u 1.2 and d = 0.9. Consider a put option whose payoff at time l is P = (1-S)+. (a) Find a replicating strategy for this option. By considering the value of the replicating strategy, find the time 0 price...