Yes, there is an abritrage opportunity
as d > (1+r)
Take S0 loan from bank/other and take long position on S
after 1 period
S1 will be S0 * d or S0 * u
Now note that
both S0*d and S0 * u > S0 (1+r)
You can repay the loan by giving S0 (1+r)
now you can have
i) S0 u - S0(1+r)
= S0 (u- (1+r)
or ii) S0(d - (1+r) )
both are > 0
hence there is arbitrage
1. Consider the one period binomial model and assume 0 < So< 00, S1(H) -- uSo...
1. Consider the one period binomial model and assume 0 < So< 00, S1(H) -- uSo and Si (Τ)-dSo for some 0 〈 1 + r 〈 d 〈 u. P is an arbitrage oportunity. rove or disprove There
2. Let So and Si be the prices of a stock at t = 0. 1 in the one-period binomial model. Assume the no-arbitrage condition 0 〈 d 〈 1 + r < u, and assume P(H)-p. We define θ-up + d(1-p)-1. Show that the expected value at t 0 of is 1S 1+θ Si 1+θ Eo =So-
4. Consider the one-period binomial model, and let V1 S1- That is, the derivative security pays the stock price at time t-1. Find the time t = 0 no-arbitrage price of the derivative, Vo
4. Consider the one-period binomial model, and let V1 S1- That is, the derivative security pays the stock price at time t-1. Find the time t = 0 no-arbitrage price of the derivative, Vo
1.1. Suppose that you have a stock in the one-period binomial model with fixed u, d, and r such that 0< d< 1 +r < u. Suppose that there are positive numbers pi and such that pi, qi < 1, pi + q-1, and (1 + r)So = PiSi (H) + qi Si (T). Show that pi = p ad qi = q. Hint: You know that the risk-neutral probabilities satisfy these equations as well.
1.2. You have a stock in the one-period binomial model such that So and r= 4, S1(H) = 8, S, (T) = 2, 1.5. (a) Show that this setup violates the no-arbitrage assumption. (b) Show that there is a portfolio in the one-period model such that Xo X1 > 0. Such a portfolio is an example of arbitrage extraction. 0, Ao #0, and %3D 1.3. With the same stock as in problem 1.2 but with r = 0.25, suppose that...
2. Consider the N-step binomial asset pricing model with 0 < d<1< u (a) Assume N-3. Sİ,-100, r-0.05, u-1.10, and d-0.90. Calculate the price at time (b) If the observed market price of the option in part (a) is $25 give a specific arbitrage trading (c) Suppose you wish to earn a profit of $100,000 from implementing your arbitrage trading zero, VO, of the European call-option with strike price K = 87.00. strategy to take advantage of any potential mis-pricing....
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
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...
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...