Derivatives Assignment

Satisfactory Essays
Chapter 14
14.3.
Explain the principle of risk-neutral valuation.

The price of an option or other derivative when expressed in terms of the price of the underlying stock is independent of risk preferences. Options therefore have the same value in a risk-neutral world as they do in the real world. We may therefore assume that the world is risk neutral for the purposes of valuing options. This simplifies the analysis. In a risk-neutral world all securities have an expected return equal to risk-free interest rate. Also, in a risk-neutral world, the appropriate discount rate to use for expected future cash flows is the risk-free interest rate.

14.6.
What is implied volatility? How can it be calculated?

The implied volatility is the volatility that makes the Black–Scholes-Merton price of an option equal to its market price. The implied volatility is calculated using an iterative procedure. A simple approach is the following. Suppose we have two volatilities one too high (i.e., giving an option price greater than the market price) and the other too low (i.e., giving an option price lower than the market price). By testing the volatility that is half way between the two, we get a new too-high volatility or a new too-low volatility. If we search initially for two volatilities, one too high and the other too low we can use this procedure repeatedly to bisect the range and converge on the correct implied volatility. Other more sophisticated approaches (e.g., involving the Newton-Raphson procedure) are used in practice.

14.7.
A stock price is currently $40. Assume that the expected return from the stock is 15% and its volatility is 25%. What is the probability distribution for the rate of return (with continuous compounding) earned over a two-year period?

In this case and . From equation (15.7) the probability distribution for the rate of return over a two-year period with continuous compounding is:

i.e.,

The expected value of the return is 11.875%

You May Also Find These Documents Helpful

  • Satisfactory Essays

    BUSN3031/9244 Derivatives and Risk Management Assignment 1 (due March 19) Each question is worth 1 point. The assignment consists of 10 questions. Please write your name and student number on top of the first page of the assignment. Please provide the relevant calculations. Assignment is individual. Assignments should be lodged at the next lecture (if you intend not to attend the lecture but would like to submit assignment, contact topic coordinator). Emailing…

    • 573 Words
    • 3 Pages
    Satisfactory Essays
  • Powerful Essays

    Derivatives

    • 8087 Words
    • 33 Pages

    thank GOD almighty for giving us strength to complete this project. Introduction A derivative is a financial contract which derives its value from the performance of another entity such as an asset, index, or interest rate, called the "underlying". Derivatives are one of the three main categories of financial instruments, the other two being equities (i.e. stocks) and debt (i.e. bonds and mortgages). Derivatives include a variety of financial contracts, including futures, forwards, swaps, options…

    • 8087 Words
    • 33 Pages
    Powerful Essays
  • Satisfactory Essays

    derivatives

    • 13995 Words
    • 56 Pages

    Derivatives in Financial Market Development Rangarajan K. Sundaram New York University (contact: rsundara@stern.nyu.edu) (contact: ) February 2013 Derivatives in Financial Market Development Rangarajan K. Sundaram Stern School of Business, New York University http://pages.stern.nyu.edu/ rsundara 13 September 2012 Contents Executive Summary ii 1 Introduction 2 2 The World Derivatives Market 2 2.1 Basic Derivative Instruments . . . . . . . . . . . . . . .…

    • 13995 Words
    • 56 Pages
    Satisfactory Essays
  • Powerful Essays

    Derivatives

    • 58054 Words
    • 233 Pages

    Contents 1 Introduction to derivatives 1.1 Derivatives defined . . . . . . . . . . . . . . . . 1.2 Products, participants and functions . . . . . . . 1.3 Derivatives markets . . . . . . . . . . . . . . . . 1.3.1 Spot versus forward transaction . . . . . 1.3.2 Exchange traded versus OTC derivatives . 1.3.3 Some commonly used derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .…

    • 58054 Words
    • 233 Pages
    Powerful Essays
  • Better Essays

    Derivative

    • 889 Words
    • 4 Pages

    ------------------------------------------------- ------------------------------------------------- ASSIGNMENT ON DERIVATIVES ------------------------------------------------- ------------------------------------------------- Presentation on Derivatives ------------------------------------------------- ------------------------------------------------- DERIVATIVES Definition: A derivative is a complicated financial contract that gets (derives) its value from an underlying asset. It is an agreement…

    • 889 Words
    • 4 Pages
    Better Essays
  • Satisfactory Essays

    Derivatives

    • 3438 Words
    • 14 Pages

    www.edupristine.com Derivatives- I Mapping to Curriculum • Reading 60: Derivative Markets and Instruments • Reading 61: Forward Markets and Contracts • Reading 62: Future Markets and Contracts Expect around 6 questions in the exam from today’s lecture © Neev Knowledge Management – Pristine 2 www.edupristine.com Key Concepts • Difference Between OTC And Exchange Traded Contracts • Payoffs of Futures and Forwards • FRA‘s • Margins • Types of Futures © Neev Knowledge Management…

    • 3438 Words
    • 14 Pages
    Satisfactory Essays
  • Good Essays

    Derivative

    • 1092 Words
    • 5 Pages

    Financial Derivatives DERIVATIVE SECURITY: A derivative security is a security whose value is contingent on the value of other more basic underlying variables. Hence derivatives are also known as contingent claims. Very often the variables underlying derivatives securities are the prices of traded securities. For example, stock option. Futures and Options ⇒⇒⇒⇒⇒⇒ actively traded on the many different exchanges. Forward Contracts, Swaps ⇒⇒⇒⇒⇒ traded outside of exchanges by financial Institutions…

    • 1092 Words
    • 5 Pages
    Good Essays
  • Good Essays

    derivatives

    • 772 Words
    • 4 Pages

    Financial Derivatives Market in India This research study encompasses in its scope an analysis of historical roots of derivative trading, types of derivative products, regulation and policy developments, trend and growth, future prospects and challenges of derivative market in India. The study is organized into three sections. Section I deals with the concept, definition, features and types of financial derivatives. Section II has been devoted to a discussion of the growth of derivatives market…

    • 772 Words
    • 4 Pages
    Good Essays
  • Powerful Essays

    Derivatives

    • 27261 Words
    • 110 Pages

    BASICS OF DERIVATIVES © Copyright 2002 India Infoline Ltd. All rights reserved. Regd. Off: 24, Nirlon Complex, Off W E Highway, Goregaon(E) Mumbai-400 063. Tel.: +(91 22) 685 0101/0505 Fax: 685 0585 BASICS OF DERIVATIVES CONTENTS FOREWORD ...................................................................................................................... 3 1.INTRODUCTION.......................................................................................................... 5 2. FUTURES…

    • 27261 Words
    • 110 Pages
    Powerful Essays
  • Good Essays

    derivatives

    • 672 Words
    • 3 Pages

    date=12/11/2003&story=1&title=Your-perception-of-derivatives-instrument-is With an assortment of investment instruments available in the financial markets, derivatives have caught the attention of investors and their volumes are on the rise. However, since this market is relatively more complicated than the cash market awareness and participation continues to be low as far as retail investors are concerned. Therefore, in order to know as to what an average investor feels about derivatives we conducted a poll and the…

    • 672 Words
    • 3 Pages
    Good Essays