Binomial model

By

QUESTION
 
1. Consider the single period binomial model with d < 1 + r < u. Prove from first principles (i.e., without using the fundamental theorems of asset pricing) that there is a unique equivalent martingale measure. 2. Consider the single period binomial model. Suppose r = 0.02, u = 1.05, d = 0.9 and S0 = 50. Consider a put option on the stock with strike price K = 49. (a) Compute the equivalent martingale measure (qu, qd). (b) Find the no-arbitrage price of the claim at time 0. (c) Find the replicating portfolio. 3. Consider a single period binomial model which satisfies the no-arbitrage condition d < 1 + r < u. Consider two contingent claims C and C 0 where (cu, cd) = (1, 2) and (c 0 u , c0 d ) = (1, 4). You are given that the no-arbitrage price of C is 1.5, and the no-arbitrage price of C 0 is 2. (a) Find the interest rate r. Hint: Use the two given claims to generate other cashflows. (b) Find the risk-neutral probabilities qu and qd. 4. Write down two different sets of parameters (u, d, r, S0) of the single period binomial model which give the same equivalent martingale probabilities. Must they give the same prices for all contingent claims? Explain your reasoning. 5. Consider the trinomial model in Example 2.1 of the lecture notes: r = 0, S0 = 1, u = 3, m = 2 and d = 1/2. Characterize all contingent claims that can be replicated. That is, give a general expression of the payoffs cu, cm, cd that can be replicated. 6. Consider a single-period model with 4 states and 3 risky assets (apart from the risk-free asset). Write Ω = {ω1, ω2, ω3, ω4}. Assume that (S j 0 )0≤j≤3 = 1 1.7 2 2 and (S j 1 (ωi))1≤i≤4,0≤j≤3 =     1 1 3 1 1 2 3 3 1 2 1 1 1 1 1 3     . 1 (Here the column index j runs from 0 to 3. So the risk-free interest rate is 0.) (a) Show that the model is arbitrage-free and complete. (b) Consider the contingent claim (C(ωi))1≤i≤4 =     1 0 0 1     . Find the no-arbitrage price of C at time 0 and find a replicating portfolio. Is the replicating portfolio unique? 7. Consider the gambling strategy in Example 3.2 of the lecture notes, where the initial wealth is 0. Find the exact distribution of the wealth M10 at time t. (This means finding the probability mass function P(M10 = x) for the possible values of x.) Verify numerically that E[M10] = 0.   Sample Solutions Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Phasellus hendrerit. Pellentesque aliquet nibh nec urna. In nisi neque, aliquet vel, dapibus id, mattis vel, nisi. Sed pretium, ligula sollicitudin laoreet viverra, tortor libero sodales leo, eget blandit nunc tortor eu nibh. Nullam mollis. Ut justo. Suspendisse potenti. Get sample solution Order Now Sed egestas, ante et vulputate volutpat, eros pede semper est, vitae luctus metus libero eu augue. Morbi purus libero, faucibus adipiscing, commodo quis, gravida id, est. Sed lectus. Praesent elementum hendrerit tortor. Sed semper lorem at felis. Vestibulum volutpat, lacus a ultrices sagittis, mi neque euismod dui, eu pulvinar nunc sapien ornare nisl. Phasellus pede arcu, dapibus eu, fermentum et, dapibus sed, urna. Morbi interdum mollis sapien. Sed ac risus. Phasellus lacinia, magna a ullamcorper laoreet, lectus arcu pulvinar risus, vitae facilisis libero dolor a purus. Sed vel lacus. Mauris nibh felis, adipiscing varius, adipiscing in, lacinia vel, tellus. Suspendisse ac urna. Etiam pellentesque mauris ut lectus. Nunc tellus ante, mattis eget, gravida vitae, ultricies ac, leo. Integer leo pede, ornare a, lacinia eu, vulputate vel, nisl. Suspendisse mauris. Fusce accumsan mollis eros. Pellentesque a diam sit amet mi ullamcorper vehicula. Integer adipiscing risus a sem. Nullam quis massa sit amet nibh viverra malesuada. Nunc sem lacus, accumsan quis, faucibus non, congue vel, arcu. Ut scelerisque hendrerit tellus. Integer sagittis. Vivamus a mauris eget arcu gravida tristique. Nunc iaculis mi in ante. Vivamus imperdiet nibh feugiat est. Ut convallis, sem sit amet interdum consectetuer, odio augue aliquam leo, nec dapibus tortor nibh sed augue. Integer eu magna sit amet metus fermentum posuere. Morbi sit amet nulla sed dolor elementum imperdiet. Quisque fermentum. Cum sociis natoque penatibus et magnis xdis parturient montes, nascetur ridiculus mus. Pellentesque adipiscing eros ut libero. Ut condimentum mi vel tellus. Suspendisse laoreet. Fusce ut est sed dolor gravida convallis. Morbi vitae ante. Vivamus ultrices luctus nunc. Suspendisse et dolor. Etiam dignissim. Proin malesuada adipiscing lacus. Donec metus. Curabitur gravida

How to create Testimonial Carousel using Bootstrap5

Clients' Reviews about Our Services