QuestionQuestion

Transcribed TextTranscribed Text

1. Binomial Lattice Model (BLM): Sn+1 = SnYn+1, 72 >0. Suppose that So = 50 (dollars per share), u = 1.3, d = .90, and p = 0.6. (a) For T 20, and K = 60, you are to estimate the expected payoff E(G) of an Asian call option, with payoff T Cr = n-1 Using Monte Carlo simulation: Generate 72 (large) ind copies of CT. denoted by X1 Xr and use the estimate Use n = 100, n = 1000, n = 10,000. (b) Suppose the risk-free interest rate r = 0.05. Compute the risk-neutral probability p* d)/(a d) and use it to estimate (via Monte Carlo) the price of this option; 1 Co E*(CT). (1+r) Use n = 10,000 iid copies of G. (c) Consider a barrier call option in which the payoff at time T = 12 is (S10 - 60)+ as long as the price Sn never falls below (c) 43 at specific times 72 = 2,4,6. Otherwise the payoff is 0. Thus the payoff C12 can be written as C12 = (S10 - 60)+ I{S 43, and S4 43, and S6 43}, where I(A} denotes the indicator rv for the event A. i. Use Monte-Carlo simulation to estimate the probability that the payoff is O: P(G1=0). Use 12 = 10,000 for the number of copies generated. ii. Suppose the risk-free interest rate r = 0.05. Estimate (via Monte Carlo) the price of this option; 1 Co (1++) E*(CT). Use 12 = 10,000 for the number of copies generated. 2. You will simulate the following simple (irreducible) Markov chain in what follows. The Markov chain {Xn 72 \0} has three states, S = {0,1,2}, and transition matrix 0.30 0 0.70 P 0 0.20 0.80 0.60 0.30 0.10 1 (a) With Xo = 0, simulate out to 72 = 1000 and estimate the long-run average: 1 N a lim N->oo N n-1 by using as an estimate 1000 1 [x 1000 n-1 Solve x = mP, for the limiting (stationary) distribution IT = and compare your estimate with the exact answer Einj. i-D (b) Solve x = wP, for the limiting (stationary) distribution IT = and compare your estimate in (a) with the exact answer (the mean of the limiting distribution) 2 [in, i=0 2

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

clear; clc; close all;
%Solution to 1(a)
u=1.3; d=0.9; p=0.6;
S0=50; n=[100 1000 10000];
T=20; K=60;
E=expayoff(n,T,K,p,u,d,S0);
fprintf('\n\n(a) Expected payoff of Asian Call Option is as follows for different number of tials.\n');
[n' E']
%Solution to 1(b)
r=0.05;
pstar=(1+r-d)/(u-d);
C0=(1/power(1+r,T))*expayoff(n(3),T,K,pstar,u,d,S0);
fprintf('\n\n(b) Price of the option considerng risk neutral probability is %8.4f(n=10000)\n',C0);
%Solution to 1(c)(i)
P=prob0_barrier(n(3),p,u,d,S0);
fprintf('\n(c)(i) Probability for zero payoff under barrier call option is %8.4f(n=10000)',P);
%Solution to 1(c)(ii)
C0_barrier=(1/power(1+r,12))*expayoff_barrier(n(3),pstar,u,d,S0);
fprintf('\n\n(c)(ii) Price of the option considerng risk neutral probability is %8.4f(n=10000)\n\n',C0_barrier);...

By purchasing this solution you'll be able to access the following files:
Solution.zip.

$90.00
for this solution

or FREE if you
register a new account!

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

Find A Tutor

View available MATLAB for Engineering Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.

Decision:
Upload a file
Continue without uploading

SUBMIT YOUR HOMEWORK
We couldn't find that subject.
Please select the best match from the list below.

We'll send you an email right away. If it's not in your inbox, check your spam folder.

  • 1
  • 2
  • 3
Live Chats