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Show that if spot and volatility are uncorrelated then the risk-neutral density of spot can be written as an integral over log-normal densities. How would you use Monte Carlo to estimate this density?
Engineering Mathematics, Engineering
Assignment - 1. Let (T, ∧, ∨,', 0, 1) be a Boolean Algebra. Define ∗ : T × T → T and o : T × T → T as follows: x ∗ y := (x ∨ y)' x o y := (x ∧ y)' (a) Show, using the laws of Boolean Algebra, how to define x ∗ y using on ...
Question : (a) Suppose that you are given an instance of the MST problem on a graph G, with edge weights that are all positive and distinct. Let T be the minimum spanning tree for G returned by Kruskal's algorithm. Now s ...
(1) This problem concerns of the proof of the NP-completeness of 300L a) Convert the formula F into a 300L graph b) Find a solution for the 300L instance of F and verify that it is a solution for F F = (Z 1 V Z 2 ) ^ (z ...
Problem # 1: Given a sequence x(n) for 0≤n≤3, where x(0) = 1, x(1) = 1, x(2) = -1, and x(3) = 0, compute its DFT X(k). (Use DFT formula, don't use MATLAB function) Use inverse DFT and apply it on the Fourier components X ...
(SHOW ALL YOUR WORK, not just the answers) When you multiply: 21 x 68 you most likely do: 8x1 + 8x20 + 60x1 + 60x20 = 1, 428 So, there are 4 multiplications and then 3 additions. How long would it take a computer to do t ...
Question : Suppose that G is a directed graph. In class we discussed an algorithm that will determine whether a given vertex can reach every other vertex in the graph (this is the 1-to-many reachability problem). Conside ...
Question : What is the signed binary sum of 1011100 and 1110101 in decimal? Show all of your work. What is the hexadecimal sum of 9A88 and 4AF6 in hexadecimal and decimal? Show all of your work.
Numerical Analysis Assignment - Q1. Define the following terms: (i) Truncation error (ii) Round-off error Q2. Show that if f(x) = logx, then the condition number, c(x) = |1/logx|. Hence show that log x is ill-conditioned ...
ANALYTICAL METHODS FOR ENGINEERS ASSIGNMENT - CALCULUS This assignment assesses Outcome - Analyse and model engineering situations and solve problems using calculus. Questions - Q1. Differentiate the following functions ...
Math Assignment - Q1. Let f(x) = -x 3 -cos(x), and p 0 = 1. Use Newton's method to find p 2 . Could p0=0 be used? Q2. Perform two iterations by Newton's method and the secant method to each of the following: a. e x + 2 - ...
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