Example 6.5.2 CIR interest rate model. CIR interest rate model (continue 1)

Slides:

Advertisements

Similar presentations

Options Markets: Introduction Faculty of Economics & Business The University of Sydney Shino Takayama.

Advertisements

Financial Innovation & Product Design II Dr. Helmut Elsinger « Options, Futures and Other Derivatives », John Hull, Chapter 22 BIART Sébastien The Standard.

Black-Scholes Equation April 15, Contents Options Black Scholes PDE Solution Method.

Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull Mechanics of Options Markets Chapter 8.

Chapter 9 Mechanics of Options Markets Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull

A New View of Mortgages (and life). Scene 1 A farmer owns a horse farm outside Lexington on Richmond Road. Demographic trends indicate that this part.

Bond Prices Zero-coupon bonds: promise a single future payment, e.g., a U.S. Treasury Bill. Fixed payment loans, e.g., conventional mortgages. Coupon Bonds:

Interest-Rate Risk II. Duration Rules Rule 1: Zero Coupon Bonds What is the duration of a zero-coupon bond? Cash is received at one time t=maturity weight.

Stochastic Calculus for Finance II Steven E. Shreve 6.5 Interest Rate Models (1) 交大財金所碩一許嵐鈞.

Financial options1 From financial options to real options 2. Financial options Prof. André Farber Solvay Business School ESCP March 10,2000.

Table 13.1: Cash Flow from a Floating Rate Loan of a dollar (the Principal), with maturity date T.

7.1 Mechanics of Options Markets Chapter Types of Options A call is an option to buy A put is an option to sell A European option can be exercised.

Bond Portfolio Management: Extra b How can you tell bond yields of different maturities are mis-aligned? Maturity T 1 yr. 5 yrs10 yrs30 yrs Yield.

Options An Introduction to Derivative Securities.

Zvi WienerContTimeFin - 10 slide 1 Financial Engineering Interest Rate Models Zvi Wiener tel: following Hull and White.

Asset Pricing Theory Option A right to buy (or sell) an underlying asset. Strike price: K Maturity date: T. Price of the underlying asset: S(t)

Mechanics of Options Markets

OPTIONS AND CORPORATE SECURITIES Chapter 25. Chapter Outline Options: The Basics Option Payoffs Employee Stock Options Equity as a Call Option on the.

5.6 Forwards and Futures 鄭凱允 Forward Contracts Let S(t),, be an asset price process, and let R(t),, be an interest rate process. We consider will.

Théorie Financière Financial Options Professeur André Farber.

9.4 Forward Measure Forward Price Zero-Coupon Bond as Numeraire Theorem

Corporate Finance Options Prof. André Farber SOLVAY BUSINESS SCHOOL UNIVERSITÉ LIBRE DE BRUXELLES.

Lecture 7: Measuring interest rate

Foreign Currency Options A foreign currency option is a contract giving the option purchaser (the buyer) –the right, but not the obligation, –to buy.

McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved Corporate Finance Ross  Westerfield  Jaffe Seventh Edition.

Introduction to options

Mechanics of Options Markets Chapter Assets Underlying Exchange-Traded Options Page Stocks Stock Indices Futures Foreign Currency Bond.

OPTIONS MARKETS: INTRODUCTION Derivative Securities Option contracts are written on common stock, stock indexes, foreign exchange, agricultural commodities,

Interest Rates Finance (Derivative Securities) 312 Tuesday, 8 August 2006 Readings: Chapter 4.

Chapter 10 Properties of Stock Options

Options An Introduction to Derivative Securities.

0 Forwards, futures swaps and options WORKBOOK By Ramon Rabinovitch.

“A derivative is a financial instrument that is derived from some other asset, index, event, value or condition (known as the underlying asset)”

Fundamentals of Futures and Options Markets, 7th Ed, Ch 9, Copyright © John C. Hull 2010 Mechanics of Options Markets Chapter 9 1.

8.1 Mechanics of Options Markets Chapter Types of Options A call is an option to buy A put is an option to sell A European option can be exercised.

C2: Change of Base of Logarithms Learning Objective: to understand that the base of a logarithm may need changing to be able to solve an equation.

Monte Carlo: Option Pricing

A Short Primer of Options. Options Options give the holders a right to buy or sell the underlying asset by a certain date for a certain price. Four key.

A different kind of Tree Using trees to help price options. Using trees to help price options. Some of the ideas behind Black-Scholes. Some of the ideas.

© Prentice Hall, Corporate Financial Management 3e Emery Finnerty Stowe Derivatives Applications.

Computational Finance

11.1 Introduction to Futures and Options Markets, 3rd Edition © 1997 by John C. Hull Volatility Problem Suppose that observations on a stock price (in.

Logic – the study of argumentsarguments "the tool for distinguishing between the true and the false;“ "the Science, as well as the Art, of reasoning” inductive.

Lecture 2.  Option - Gives the holder the right to buy or sell a security at a specified price during a specified period of time.  Call Option - The.

Economics 434 Financial Markets Professor Burton University of Virginia Fall 2015 December 1, 2015.

© 2003 The McGraw-Hill Companies, Inc. All rights reserved. Basics of Financial Options.

Chapter 24 Interest Rate Models.

Mechanics of Options Markets Chapter 8 Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull

Mechanics of Options Markets Chapter 7. Types of Options A call is an option to buy A put is an option to sell A European option can be exercised only.

Chapter 8 Swaps. © 2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.8-2 Introduction to Swaps A swap is a contract calling.

11.1 Options and Swaps LECTURE Aims and Learning Objectives By the end of this session students should be able to: Understand how the market.

Chapter 9 Mechanics of Options Markets Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull

Principles of Finance with Excel, 2 nd edition Instructor materials Chapter 15 Bond valuation.

Learning Objectives LO 1: Explain the basic characteristics and terminology of options. LO 2: Determine the intrinsic value of options at expiration date.

P(T1, T2) - F(t, T1: T2) P(T1, T2) F(t, T1: T2) F(t, T1: T2) Figure 3.1: Payoff Diagram for a Forward Contract with Delivery.

Financial Market Theory

Chapter 9 Mechanics of Options Markets

Chapter 10 Mechanics of Options Markets

Let {image} Use substitution to determine which elements of S satisfy the inequality {image} Select the correct answer(s): {image}

Chapter Eleven Asset Markets.

A. Caggia, M. Armanini Financial Investments & Pricing 2015/2016

Financial Market Theory

Théorie Financière Financial Options

Thing / Person:____________________ Dates:_________________

Théorie Financière Financial Options

Presentation transcript:

Example CIR interest rate model

CIR interest rate model (continue 1)

CIR interest rate model (continue 2)

CIR interest rate model (continue 3)

CIR interest rate model (continue 4)

CIR interest rate model (continue)

Example Option on a bond Consider the general short-rate model (6.5.1). Let 0 ≦ t ≦ T 1 <T 2 be given. In this example, the fixed time T 2 is the maturity date for a zero-coupon bond. The fixed time T 1 is the expiration date for a European call on this bond. We wish to determine the value of this call at time t. Suppose we have solved for the function f(t,r) satisfying (6.5.4) together with the terminal condition (6.5.5). This gives us the price of the zero-coupon bond as a function of the underlying interest rate.

Option on a bond (continue)