Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Assume the following (idealized) annual return estimates (, 2 ) from a dataset. Arithmetic: (0.08, 0.20 2 ), Continuous: (0.06, 0.20 2 ) note the

  1. Assume the following (idealized) annual return estimates (, 2) from a dataset. Arithmetic: (0.08, 0.202), Continuous: (0.06, 0.202) note the perfect mean shift for continuous returns. In the lectures we saw two binomial models, the Hull model with simplified u/d formulas and more complicated p*, and the general u/d formulas with p*=1/2. In theory, both binomial models converge to the same lognormal model. With S0=100 and T=1, confirm one example of convergence, comparing Pr(S1>110) from these binomials (Hull and General) as t0 to the theoretical lognormal.

Hint: Given n, let t=1/n and note that in either binomial model

S1= 100ukdn-k=100dn(u/d)k where k is between 0 and n. Algebraically translate Pr(S1>110) into a statement about k (which has a binomial distribution), and then evaluate with Excels BINOM function since you have p* (note that these models have different u/d definitions, different p* values, and these all change with n). Compare these probabilities as n increases to exact Pr(S1>110) calculated with the limiting lognormal distribution. Try n=50, 500, 1000, 100000.

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Equity Valuation And Portfolio Management

Authors: Frank J. Fabozzi, Harry M. Markowitz

1st Edition

047092991X, 9780470929919

More Books

Students also viewed these Finance questions

Question

What are the different techniques used in decision making?

Answered: 1 week ago

Question

Discuss the concept of ethics in the management of human resources.

Answered: 1 week ago

Question

Define organizational culture.

Answered: 1 week ago