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V. Black-Scholes Model: Derivation and Solution
V. Black-Scholes model: Derivation and solution Beáta Stehlíková Financial derivatives, winter term 2014/2015 Faculty of Mathematics, Physics and Informatics Comenius University, Bratislava V. Black-Scholes model: Derivation and solution – p.1/36 Content Black-Scholes model: • Suppose that stock price follows a geometric ◦ S Brownian motion dS = µSdt + σSdw + other assumptions (in a moment) We derive a partial differential equation for the price of ◦ a derivative Two ways of derivations: • due to Black and Scholes ◦ due to Merton ◦ Explicit solution for European call and put options • V. Black-Scholes model: Derivation and solution – p.2/36 Assumptions Further assumptions (besides GBP): • constant riskless interest rate ◦ r no transaction costs ◦ it is possible to buy/sell any (also fractional) number of ◦ stocks; similarly with the cash no restrictions on short selling ◦ option is of European type ◦ Firstly, let us consider the case of a non-dividend paying • stock V. Black-Scholes model: Derivation and solution – p.3/36 Derivation I. - due to Black and Scholes Notation: • S = stock price, t =time V = V (S, t)= option price Portfolio: 1 option, stocks • δ P = value of the portfolio: P = V + δS Change in the portfolio value: • dP = dV + δdS From the assumptions: From the It¯o • dS = µSdt + σSdw, ∂V ∂V 1 2 2 ∂2V ∂V lemma: dV = ∂t + µS ∂S + 2 σ S ∂S2 dt + σS ∂S dw Therefore: • ∂V ∂V 1 ∂2V dP = + µS + σ2S2 + δµS dt ∂t ∂S 2 ∂S2 ∂V + σS + δσS dw ∂S V. Black-Scholes model: Derivation and solution – p.4/36 Derivation I. -
Computation of Binomial Option Pricing Model with Parallel
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by KHALSA PUBLICATIONS I S S N 2 2 7 8 - 5 6 1 2 Volume 11 Number 5 International Journal of Management and Information T e c h n o l o g y Computation Of Binomial Option Pricing Model With Parallel Processing On A Linux Cluster Harya Widiputra Faculty of Information Technology, Perbanas Institute Jakarta, Indonesia [email protected] ABSTRACT Binary Option Pricing Model (BOPM) is one approach that can be utilized to calculate the value of either call or put option. BOPM generally works by building a binomial tree diagram, also known as lattice diagram to explore all possible option values that occur based on the intrinsic price of the underlying asset in a range of specific time period. Due to its basic characteristics BOPM is renowned for its longer lead times in calculating option values while also acknowledged as a technique that can provide an assessment of the most fair option value. Therefore, this study aims to shorten the BOPM completion time of calculating the value of an option by building a computer cluster and presently implement the BOPM algorithm into a form that can be run in parallel processing. As an outcome, a Linux-based computer cluster has been built and conversion of BOPM algorithm so that it can be executed in parallel has been performed and also implemented using Python in this research. Conclusively, results of conducted experiments confirm that the implementation of BOPM algorithm in a form that can be executed in parallel and its application on a computer cluster was able to limit the growth of the completion time whilst at the same time maintain quality of calculated option values. -
Opposition, CFTC V. Banc De Binary
Case 2:13-cv-00992-MMD-VCF Document 37 Filed 08/08/13 Page 1 of 30 Kathleen Banar, Chief Trial Attorney (IL Bar No. 6200597) David Slovick, Senior Trial Attorney (IL Bar No. 6257290) Margaret Aisenbrey, Trial Attorney (Mo Bar No. 59560) U.S. Commodity Futures Trading Commission 1155 21 St. NW Washington, DC 20581 [email protected], [email protected], [email protected] (202) 418-5335 (202) 418-5987 (facsimile) Blaine T. Welsh (NV Bar No. 4790) Assistant United States Attorney United States Attorney’s Office 333 Las Vegas Boulevard, Suite 5000 Las Vegas, Nevada 89101 [email protected] (702) 388-6336 (702) 388-6787 (facsimile) UNITED STATES DISTRICT COURT DISTRICT OF NEVADA ) U.S. COMMODITY FUTURES TRADING ) COMMISSION, ) ) Case No. 2:13-cv-00992-MMD-VCF Plaintiff, ) ) PLAINTIFF’S OPPOSITION TO v. ) DEFENDANT’S MOTION TO ) DISMISS COUNTS ONE, THREE ) AND FOUR OF THE COMPLAINT BANC DE BINARY LTD. (A/K/A E.T. ) BINARY OPTIONS LTD.), ) ) Defendant. ) ) 1 Case 2:13-cv-00992-MMD-VCF Document 37 Filed 08/08/13 Page 2 of 30 The United States Commodity Futures Trading Commission (“CFTC” or “Commission”) opposes Banc de Binary’s Motion to Dismiss Counts I, III and IV of the Complaint (“Defendant’s Motion”),1 and states as follows: I. SUMMARY Since at least May 2012 Banc de Binary Ltd. (A/K/A E.T. Binary Options) (“Banc de Binary” or “Defendant”) has been violating the CFTC’s long-standing ban on trading options contracts with persons located in the United States off of a contract market designated by the CFTC for that purpose (i.e., “off-exchange”). -
Decreto Del Direttore Amministrativo N
Corso di Laurea magistrale (ordinamento ex D.M. 270/2004) in Economia e Finanza Tesi di Laurea Gli strumenti derivati ed il loro utilizzo in azienda: l’importanza di gestirne i vantaggi e le complessità Relatore Prof. Guido Massimiliano Mantovani Laureando Ambra Moschini Matricola:835318 Anno Accademico 2013 / 2014 Sessione straordinaria 2 Indice Indice delle Figure ....................................................................................................................... 6 Indice delle Tavole ...................................................................................................................... 7 Introduzione ................................................................................................................................. 8 Capitolo 1 - Il concetto di rischio ............................................................................................. 11 1.1. Definizione .................................................................................................................. 12 1.2. La percezione del rischio in azienda ........................................................................... 16 1.3. Identificazione delle categorie di rischio .................................................................... 24 1.3.1. Rischi finanziari .................................................................................................. 26 1.3.1.1. Rischio di mercato ............................................................................................... 28 1.3.1.1.1. Rischio di -
What Are Binary Options?
PA R T I Introduction to Binary Options his section will provide you with an overview and discussion of the T main benefi ts of binary option trading. What You Will Learn: • What are binary options? • How do binary options differ from traditional options? • Which underlying instruments are binary options available to trade on? • Where can youhttp://www.pbookshop.com trade binary options? • What are the benefi ts of trading binary options? • What makes binary options unique compared to other instruments and options? COPYRIGHTED MATERIAL When you complete this section you should have a basic understand- ing of what binary options are and be familiar with their main advantages. 1 c01.indd 1 11/8/2012 4:12:44 PM http://www.pbookshop.com c01.indd 2 11/8/2012 4:12:44 PM CH A P T E R 1 What Are Binary Options? inary options are also known as digital options or all‐or‐nothing options. They are derivative instruments that can be considered a B yes‐or‐no proposition—either the event happens or it does not. Binary options are considered binary because there are only two po- tential outcomes at expiration: 0 or 100; 0 and 100 refer to the settlement value of a binary option and could be viewed in dollars. At expiration, if you are incorrect, you do not make anything ($0), and if you are correct, you make up to $100. The next section will go into further detail on the set- tlement value of binary options. ON WHAT ASSEThttp://www.pbookshop.com CLASSES ARE BINARY OPTIONS AVAILABLE? Binary options are available on four different asset classes. -
CHARACTERISTICS and RISKS of STANDARDIZED OPTIONS TABLE of CONTENTS Page CHAPTER I—INTRODUCTION
CHARACTERISTICS AND RISKS OF STANDARDIZED OPTIONS February 1994 1997 through 2018 Supplements included BATS Exchange, Inc. 8050 Marshall Drive Lexena, Kansas 66214 C2 OPTIONS EXCHANGE, INCORPORATED 400 South LaSalle Street Chicago, Illinois 60605 CHICAGO BOARD OPTIONS EXCHANGE, INCORPORATED 400 South LaSalle Street Chicago, Illinois 60605 INTERNATIONAL SECURITIES EXCHANGE, LLC 60 Broad Street New York, New York 10004 NASDAQ OMX BX, INC. 101 Arch Street Boston, Massachusetts 02110 NASDAQ OMX PHLX, INC. 1900 Market Street Philadelphia, Pennsylvania 19103 NASDAQ STOCK MARKET, LLC One Liberty Plaza 165 Broadway New York, New York 10006 NYSE AMEX LLC 11 Wall Street New York, New York 10005 NYSE ARCA, INC. 100 South Wacker Drive Chicago, Illinois 60606 ȴ 1994 American Stock Exchange, LLC, Chicago Board Options Exchange, Incorporated, New York Stock Exchange, Inc., NYSE Arca, Inc. and Philadelphia Stock Exchange, Inc. CHARACTERISTICS AND RISKS OF STANDARDIZED OPTIONS TABLE OF CONTENTS Page CHAPTER I—INTRODUCTION .............. 1 CHAPTER II—OPTIONS NOMENCLATURE ...... 5 CHAPTER III—OPTIONS ON EQUITY SECURITIES 18 Features of Stock Options ................. 18 CHAPTER IV—INDEX OPTIONS ............. 23 About Indexes ........................ 23 Features of Index Options ................. 26 CHAPTER V—DEBT OPTIONS .............. 29 Rates, Yields and Prices of Debt Securities ....... 29 Treasury Securities ...................... 31 Yield-Based Options ..................... 32 CHAPTER VI—FOREIGN CURRENCY OPTIONS . 35 Market for Foreign Currencies ............... 36 Special Characteristics of Foreign Currency Options .37 Special Features of Dollar-Denominated Foreign Currency Options ..................... 38 Cross-Rate Foreign Currency Options .......... 41 Special Features of Cross-Rate Options ......... 42 Cash-Settled Foreign Currency Options ......... 43 CHAPTER VII—FLEXIBLY STRUCTURED OPTIONS 45 Special Features of Flexibly Structured Options .... 46 CHAPTER VIII—EXERCISE AND SETTLEMENT . -
United States Securities and Exchange Commission Form
Table of Contents UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 ____________________________________________________________________________ FORM 10-K ý ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934 For the fiscal year ended December 31, 2016 or o TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934 For the transition period from to Commission File No. 0-51754 ____________________________________________________________________________ CROCS, INC. (Exact name of registrant as specified in its charter) Delaware 20-2164234 (State or other jurisdiction of (I.R.S. Employer incorporation or organization) Identification No.) 7477 East Dry Creek Parkway Niwot, Colorado 80503 (303) 848-7000 (Address, including zip code and telephone number, including area code, of registrant's principal executive offices) Securities registered pursuant to Section 12(b) of the Act: Title of each class: Name of each exchange on which registered: Common Stock, par value $0.001 per share The NASDAQ Global Select Market Securities registered pursuant to Section 12(g) of the Act: None ____________________________________________________________________________ Indicate by check mark if the registrant is a well-known seasoned issuer, as defined in Rule 405 of the Securities Act. Yes o No ý Indicate by check mark if the registrant is not required to file reports pursuant to Section 13 or Section 15(d) of the Act. Yes o No ý Indicate by check mark whether the registrant (1) has filed all reports required to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during the preceding 12 months (or for such shorter period that the registrant was required to file such reports), and (2) has been subject to such filing requirements for the past 90 days. -
The National Conference of Insurance Legislators' Model CDS Bill
The National Conference of Insurance Legislators’ Model CDS Bill June 3, 2009 Table of Contents Introduction The National Conference of Insurance Legislators (“NCOIL”) is drafting Introduction .........................................1 model legislation (the “Model Bill”) that would subject credit default swaps (“CDS”) to a state regulatory regime closely modeled on that regulating CDS and Insurance Law: The Current State of Play .....................................1 financial guaranty insurance in New York. This memorandum discusses NCOIL’s plans for a state CDS regulatory regime and explores the Overview of the NCOIL Model Bill ..........2 implications of such a regime on the CDS market. Analysis of the Model Bill ......................3 Licensing Requirements .......................3 CDS and Insurance Law: The Current State of Play Requirement of a “Material Interest” in the Reference Security.......................4 In a typical credit default swap, one party (the “protection buyer”) makes a Capital Requirements...........................4 Financial Guaranty Insurance Payout stream of payments to the other (the “protection seller”) so long as no negative Method Versus Acceleration ...............5 credit event occurs with respect to one or more specified obligors. Negative Applicability of Other Insurance Law ......5 credit events include a failure by the obligor to make payments on an Additional Questions Raised by the underlying reference obligation (a “reference security”) and bankruptcy. If a Model Bill.........................................5 -
The Uses and the Valuation Methods of Credit Default Swaps
UNIVERSITY OF PIRAEUS DEPARTMENT OF BANKING AND FINANCIAL MANAGEMENT The uses and the valuation methods of Credit Default Swaps Theodore Chantzis MXAN1228 February 2014 Supervisor: M. Anthropelos Examination Committee: A. Antzoulatos, N. Egglezos 1 Contents 1. Introduction ..................................................................................................................2 2. Credit Derivatives .........................................................................................................3 3. Credit Default Swaps ....................................................................................................7 3.1. Definition and Structure .........................................................................................7 3.2. Credit Default Swap Market Today ...................................................................... 10 3.3. Credit Default Swap Documentation .................................................................... 13 Definition of Credit Events and CDS Triggering ............................................................. 17 Credit Default Events since 1997..................................................................................... 22 Macroeconomic Drivers of Sovereign CDS Spread ......................................................... 23 European Debt Crisis ...................................................................................................... 27 Greece Debt Restructuring in 2012 ................................................................................. -
How to Trade Binary Options Successfully
How to Trade Binary Options Successfully A Complete Guide to Binary Options Trading By Meir Liraz ___________________________________________________________________ Revealed At Last! The Best Kept Secret Among Successful Binary Options and Forex Traders The Easiest Way to Make Money Trading Online ___________________________________________________________________ Published by BizMove Binary Options Trading Center Copyright © Meir Liraz. All Rights Reserved. Our Preferred Binary Options Broker We currently trade at this broker. After testing several Binary Options and Forex platforms we find this one to be the best. What made the difference is a unique feature that allow us to watch and copy the strategies and trades of the best performing traders on the platform. You can actually see each move the "Guru" traders make. This method works nicely for us. Since we started trading at this broker we noticed an increase of our successful trades and profits when compared to our former brokers. Having said that, please note that all trading involves risk. Only risk capital you're prepared to lose. Past performance does not guarantee future results. This post is for educational purposes and should not be considered as investment advice. Table of Contents 1. The Single Most Critical Factor to Binary Options Trading Success 2. What are Binary Options 3. The Flow of Decisions in a Binary Options Trade 4. Advantages and Disadvantages of Binary Options Trading 5. Binary Trading Risk Management 6. What You Need to Succeed in Binary Options 7. How Much Money You Need to Start Trading 8. Technical Analysis As a Tool for Binary Trading Success 9. Developing a Binary Options Strategy and Entry Signals 10. -
On Black-Scholes Equation, Black- Scholes Formula and Binary Option Price
On Black-Scholes Equation, Black- Scholes Formula and Binary Option Price Chi Gao 12/15/2013 Abstract: I. Black-Scholes Equation is derived using two methods: (1) risk-neutral measure; (2) - hedge. II. The Black-Scholes Formula (the price of European call option is calculated) is calculated using two methods: (1) risk-neutral pricing formula (expected discounted payoff) (2) directly solving the Black-Scholes equation with boundary conditions III. The two methods in II are proved to be essentially equivalent. The Black-Scholes formula for European call option is tested to be the solution of Black-Scholes equation. IV. The value of digital options and share digitals are calculated. The European call and put options are be replicated by digital options and share digitals, thus the prices of call and put options can be derived from the values of digitals. The put-call parity relation is given. 1. The derivation(s) of Black-Scholes Equation Black Scholes model has several assumptions: 1. Constant risk-free interest rate: r 2. Constant drift and volatility of stock price: 3. The stock doesn’t pay dividend 4. No arbitrage 5. No transaction fee or cost 6. Possible to borrow and lend any amount (even fractional) of cash at the riskless rate 7. Possible to buy and sell any amount (even fractional) of stock A typical way to derive the Black-Scholes equation is to claim that under the measure that no arbitrage is allowed (risk-neutral measure), the drift of stock price equal to the risk-free interest rate . That is (usually under risk-neutral measure, we write Brownian motion as , here we remove Q subscript for convenience ) (1) Then apply Ito’s lemma to the discounted price of derivatives , we get [ ] [( ) ] (2) Still, under risk-neutral measure we can argue that is martingale. -
Introduction Section 4000.1
Introduction Section 4000.1 This section contains product profiles of finan- Each product profile contains a general cial instruments that examiners may encounter description of the product, its basic character- during the course of their review of capital- istics and features, a depiction of the market- markets and trading activities. Knowledge of place, market transparency, and the product’s specific financial instruments is essential for uses. The profiles also discuss pricing conven- examiners’ successful review of these activities. tions, hedging issues, risks, accounting, risk- These product profiles are intended as a general based capital treatments, and legal limitations. reference for examiners; they are not intended to Finally, each profile contains references for be independently comprehensive but are struc- more information. tured to give a basic overview of the instruments. Trading and Capital-Markets Activities Manual February 1998 Page 1 Federal Funds Section 4005.1 GENERAL DESCRIPTION commonly used to transfer funds between depository institutions: Federal funds (fed funds) are reserves held in a bank’s Federal Reserve Bank account. If a bank • The selling institution authorizes its district holds more fed funds than is required to cover Federal Reserve Bank to debit its reserve its Regulation D reserve requirement, those account and credit the reserve account of the excess reserves may be lent to another financial buying institution. Fedwire, the Federal institution with an account at a Federal Reserve Reserve’s electronic funds and securities trans- Bank. To the borrowing institution, these funds fer network, is used to complete the transfer are fed funds purchased. To the lending institu- with immediate settlement.