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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. -
Section 1256 and Foreign Currency Derivatives
Section 1256 and Foreign Currency Derivatives Viva Hammer1 Mark-to-market taxation was considered “a fundamental departure from the concept of income realization in the U.S. tax law”2 when it was introduced in 1981. Congress was only game to propose the concept because of rampant “straddle” shelters that were undermining the U.S. tax system and commodities derivatives markets. Early in tax history, the Supreme Court articulated the realization principle as a Constitutional limitation on Congress’ taxing power. But in 1981, lawmakers makers felt confident imposing mark-to-market on exchange traded futures contracts because of the exchanges’ system of variation margin. However, when in 1982 non-exchange foreign currency traders asked to come within the ambit of mark-to-market taxation, Congress acceded to their demands even though this market had no equivalent to variation margin. This opportunistic rather than policy-driven history has spawned a great debate amongst tax practitioners as to the scope of the mark-to-market rule governing foreign currency contracts. Several recent cases have added fuel to the debate. The Straddle Shelters of the 1970s Straddle shelters were developed to exploit several structural flaws in the U.S. tax system: (1) the vast gulf between ordinary income tax rate (maximum 70%) and long term capital gain rate (28%), (2) the arbitrary distinction between capital gain and ordinary income, making it relatively easy to convert one to the other, and (3) the non- economic tax treatment of derivative contracts. Straddle shelters were so pervasive that in 1978 it was estimated that more than 75% of the open interest in silver futures were entered into to accommodate tax straddles and demand for U.S. -
Tracking and Trading Volatility 155
ffirs.qxd 9/12/06 2:37 PM Page i The Index Trading Course Workbook www.rasabourse.com ffirs.qxd 9/12/06 2:37 PM Page ii Founded in 1807, John Wiley & Sons is the oldest independent publishing company in the United States. With offices in North America, Europe, Aus- tralia, and Asia, Wiley is globally committed to developing and marketing print and electronic products and services for our customers’ professional and personal knowledge and understanding. The Wiley Trading series features books by traders who have survived the market’s ever changing temperament and have prospered—some by reinventing systems, others by getting back to basics. Whether a novice trader, professional, or somewhere in-between, these books will provide the advice and strategies needed to prosper today and well into the future. For a list of available titles, visit our web site at www.WileyFinance.com. www.rasabourse.com ffirs.qxd 9/12/06 2:37 PM Page iii The Index Trading Course Workbook Step-by-Step Exercises and Tests to Help You Master The Index Trading Course GEORGE A. FONTANILLS TOM GENTILE John Wiley & Sons, Inc. www.rasabourse.com ffirs.qxd 9/12/06 2:37 PM Page iv Copyright © 2006 by George A. Fontanills, Tom Gentile, and Richard Cawood. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the web at www.copyright.com. -
Seeking Income: Cash Flow Distribution Analysis of S&P 500
RESEARCH Income CONTRIBUTORS Berlinda Liu Seeking Income: Cash Flow Director Global Research & Design Distribution Analysis of S&P [email protected] ® Ryan Poirier, FRM 500 Buy-Write Strategies Senior Analyst Global Research & Design EXECUTIVE SUMMARY [email protected] In recent years, income-seeking market participants have shown increased interest in buy-write strategies that exchange upside potential for upfront option premium. Our empirical study investigated popular buy-write benchmarks, as well as other alternative strategies with varied strike selection, option maturity, and underlying equity instruments, and made the following observations in terms of distribution capabilities. Although the CBOE S&P 500 BuyWrite Index (BXM), the leading buy-write benchmark, writes at-the-money (ATM) monthly options, a market participant may be better off selling out-of-the-money (OTM) options and allowing the equity portfolio to grow. Equity growth serves as another source of distribution if the option premium does not meet the distribution target, and it prevents the equity portfolio from being liquidated too quickly due to cash settlement of the expiring options. Given a predetermined distribution goal, a market participant may consider an option based on its premium rather than its moneyness. This alternative approach tends to generate a more steady income stream, thus reducing trading cost. However, just as with the traditional approach that chooses options by moneyness, a high target premium may suffocate equity growth and result in either less income or quick equity depletion. Compared with monthly standard options, selling quarterly options may reduce the loss from the cash settlement of expiring calls, while selling weekly options could incur more loss. -
Buying Options on Futures Contracts. a Guide to Uses
NATIONAL FUTURES ASSOCIATION Buying Options on Futures Contracts A Guide to Uses and Risks Table of Contents 4 Introduction 6 Part One: The Vocabulary of Options Trading 10 Part Two: The Arithmetic of Option Premiums 10 Intrinsic Value 10 Time Value 12 Part Three: The Mechanics of Buying and Writing Options 12 Commission Charges 13 Leverage 13 The First Step: Calculate the Break-Even Price 15 Factors Affecting the Choice of an Option 18 After You Buy an Option: What Then? 21 Who Writes Options and Why 22 Risk Caution 23 Part Four: A Pre-Investment Checklist 25 NFA Information and Resources Buying Options on Futures Contracts: A Guide to Uses and Risks National Futures Association is a Congressionally authorized self- regulatory organization of the United States futures industry. Its mission is to provide innovative regulatory pro- grams and services that ensure futures industry integrity, protect market par- ticipants and help NFA Members meet their regulatory responsibilities. This booklet has been prepared as a part of NFA’s continuing public educa- tion efforts to provide information about the futures industry to potential investors. Disclaimer: This brochure only discusses the most common type of commodity options traded in the U.S.—options on futures contracts traded on a regulated exchange and exercisable at any time before they expire. If you are considering trading options on the underlying commodity itself or options that can only be exercised at or near their expiration date, ask your broker for more information. 3 Introduction Although futures contracts have been traded on U.S. exchanges since 1865, options on futures contracts were not introduced until 1982. -
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. -
Implied Volatility Modeling
Implied Volatility Modeling Sarves Verma, Gunhan Mehmet Ertosun, Wei Wang, Benjamin Ambruster, Kay Giesecke I Introduction Although Black-Scholes formula is very popular among market practitioners, when applied to call and put options, it often reduces to a means of quoting options in terms of another parameter, the implied volatility. Further, the function σ BS TK ),(: ⎯⎯→ σ BS TK ),( t t ………………………………(1) is called the implied volatility surface. Two significant features of the surface is worth mentioning”: a) the non-flat profile of the surface which is often called the ‘smile’or the ‘skew’ suggests that the Black-Scholes formula is inefficient to price options b) the level of implied volatilities changes with time thus deforming it continuously. Since, the black- scholes model fails to model volatility, modeling implied volatility has become an active area of research. At present, volatility is modeled in primarily four different ways which are : a) The stochastic volatility model which assumes a stochastic nature of volatility [1]. The problem with this approach often lies in finding the market price of volatility risk which can’t be observed in the market. b) The deterministic volatility function (DVF) which assumes that volatility is a function of time alone and is completely deterministic [2,3]. This fails because as mentioned before the implied volatility surface changes with time continuously and is unpredictable at a given point of time. Ergo, the lattice model [2] & the Dupire approach [3] often fail[4] c) a factor based approach which assumes that implied volatility can be constructed by forming basis vectors. Further, one can use implied volatility as a mean reverting Ornstein-Ulhenbeck process for estimating implied volatility[5]. -
Show Me the Money: Option Moneyness Concentration and Future Stock Returns Kelley Bergsma Assistant Professor of Finance Ohio Un
Show Me the Money: Option Moneyness Concentration and Future Stock Returns Kelley Bergsma Assistant Professor of Finance Ohio University Vivien Csapi Assistant Professor of Finance University of Pecs Dean Diavatopoulos* Assistant Professor of Finance Seattle University Andy Fodor Professor of Finance Ohio University Keywords: option moneyness, implied volatility, open interest, stock returns JEL Classifications: G11, G12, G13 *Communications Author Address: Albers School of Business and Economics Department of Finance 901 12th Avenue Seattle, WA 98122 Phone: 206-265-1929 Email: [email protected] Show Me the Money: Option Moneyness Concentration and Future Stock Returns Abstract Informed traders often use options that are not in-the-money because these options offer higher potential gains for a smaller upfront cost. Since leverage is monotonically related to option moneyness (K/S), it follows that a higher concentration of trading in options of certain moneyness levels indicates more informed trading. Using a measure of stock-level dollar volume weighted average moneyness (AveMoney), we find that stock returns increase with AveMoney, suggesting more trading activity in options with higher leverage is a signal for future stock returns. The economic impact of AveMoney is strongest among stocks with high implied volatility, which reflects greater investor uncertainty and thus higher potential rewards for informed option traders. AveMoney also has greater predictive power as open interest increases. Our results hold at the portfolio level as well as cross-sectionally after controlling for liquidity and risk. When AveMoney is calculated with calls, a portfolio long high AveMoney stocks and short low AveMoney stocks yields a Fama-French five-factor alpha of 12% per year for all stocks and 33% per year using stocks with high implied volatility. -
A Fundamental Introduction to Japanese Candlestick Charting
© Copyright 2018 TheoTrade, LLC. All Rights Reserved 1 TRADE LIKE THE FLOUNDER An overview to Matt’s trading style, methods, thoughts, and insights © Copyright 2018 TheoTrade, LLC. All Rights Reserved 2 Acronyms and Shorthand Cheat Sheet • PnL – Profit and Loss (P. and L. → P n L) • IV – implied volatility • IRA – Individual Retirement Account • Vol – Volatility (typically, IMPLIED volatility) • DTE – Days to Expiration • Roll – move an option from one strike and/or expiration to a different strike and/or expiration • ATM/ITM/OTM/DITM – At the Money, In the Money, Out of the Money, DEEP in the Money • Legging – trading a piece of a spread by itself instead of the whole spread • Skew – the difference between supply/demand (or IV) at different strikes or expirations • Front month – the shorter-dated contract of a multiple-expiration spread • Back month – the longer-dated contract of a multiple-expiration spread • Opex – Option expiration © Copyright 2018 TheoTrade, LLC. All Rights Reserved 3 PART 1 – WHAT KIND OF TRADER AM I? Vehicle, products, time frames, structures, targets, etc. © Copyright 2018 TheoTrade, LLC. All Rights Reserved 4 What do I prefer to trade? Ask most people that question, they will tell you what PRODUCTS they like to trade (GOOG, AAPL, VIX, etc.) but before you settle on a product, learn WHAT you’re trading. Things you can trade: Direction (up or down) Volatility (IV vs. HV) Correlation/Relative Strength/Beta (Pairs Trading) Mispricing/Difference in pricing (Pure arbitrage) Order Flow (HFT) M&A/Special Situations (Merger Arb) Almost ALL retail traders trade direction. I primarily trade volatility. -
Asian Journal of Comparative Law
Asian Journal of Comparative Law Volume 5, Issue 1 2010 Article 8 Financial Regulation in Hong Kong: Time for a Change Douglas W. Arner, University of Hong Kong Berry F.C. Hsu, University of Hong Kong Antonio M. Da Roza, University of Hong Kong Recommended Citation: Douglas W. Arner, Berry F.C. Hsu, and Antonio M. Da Roza (2010) "Financial Regulation in Hong Kong: Time for a Change," Asian Journal of Comparative Law: Vol. 5 : Iss. 1, Article 8. Available at: http://www.bepress.com/asjcl/vol5/iss1/art8 DOI: 10.2202/1932-0205.1238 ©2010 Berkeley Electronic Press. All rights reserved. Financial Regulation in Hong Kong: Time for a Change Douglas W. Arner, Berry F.C. Hsu, and Antonio M. Da Roza Abstract The global financial system experienced its first systemic crisis since the 1930s in autumn 2008, with the failure of major financial institutions in the United States and Europe and the seizure of global credit markets. Although Hong Kong was not at the epicentre of this crisis, it was nonetheless affected. Following an overview of Hong Kong's existing financial regulatory framework, the article discusses the global financial crisis and its impact in Hong Kong, as well as regulatory responses to date. From this basis, the article discusses recommendations for reforms in Hong Kong to address weaknesses highlighted by the crisis, focusing on issues relating to Lehman Brothers "Minibonds." The article concludes by looking forward, recommending that the crisis be taken not only as the catalyst to resolve existing weaknesses but also to strengthen and enhance Hong Kong's role and competitiveness as China's premier international financial centre. -
OPTIONS on MONEY MARKET FUTURES Anatoli Kuprianov
Page 218 The information in this chapter was last updated in 1993. Since the money market evolves very rapidly, recent developments may have superseded some of the content of this chapter. Federal Reserve Bank of Richmond Richmond, Virginia 1998 Chapter 15 OPTIONS ON MONEY MARKET FUTURES Anatoli Kuprianov INTRODUCTION Options are contracts that give their buyers the right, but not the obligation, to buy or sell a specified item at a set price within some predetermined time period. Options on futures contracts, known as futures options, are standardized option contracts traded on futures exchanges. Although an active over-the-counter market in stock options has existed in the United States for almost a century, the advent of exchange-traded options is a more recent development. Standardized options began trading on organized exchanges in 1973, when the Chicago Board Options Exchange (CBOE) was organized. The American and Philadelphia Stock Exchanges soon followed suit by listing stock options in 1975, followed one year later by the Pacific Stock Exchange. Today a wide variety of options trade on virtually all major stock and futures exchanges, including stock options, foreign currency options, and futures options. Options on three different short-term interest rate futures are traded actively at present. The International Monetary Market (IMM) division of the Chicago Mercantile Exchange (CME) began listing options on three-month Eurodollar time deposit futures in March of 1985, and on 13-week Treasury bill futures a year later. Trading in options on IMM One-Month LIBOR futures began in 1991. The London International Financial Futures Exchange also lists options on its Eurodollar futures contract, but the IMM contract is the more actively traded of the two by a substantial margin. -
A Glossary of Securities and Financial Terms
A Glossary of Securities and Financial Terms (English to Traditional Chinese) 9-times Restriction Rule 九倍限制規則 24-spread rule 24 個價位規則 1 A AAAC see Academic and Accreditation Advisory Committee【SFC】 ABS see asset-backed securities ACCA see Association of Chartered Certified Accountants, The ACG see Asia-Pacific Central Securities Depository Group ACIHK see ACI-The Financial Markets of Hong Kong ADB see Asian Development Bank ADR see American depositary receipt AFTA see ASEAN Free Trade Area AGM see annual general meeting AIB see Audit Investigation Board AIM see Alternative Investment Market【UK】 AIMR see Association for Investment Management and Research AMCHAM see American Chamber of Commerce AMEX see American Stock Exchange AMS see Automatic Order Matching and Execution System AMS/2 see Automatic Order Matching and Execution System / Second Generation AMS/3 see Automatic Order Matching and Execution System / Third Generation ANNA see Association of National Numbering Agencies AOI see All Ordinaries Index AOSEF see Asian and Oceanian Stock Exchanges Federation APEC see Asia Pacific Economic Cooperation API see Application Programming Interface APRC see Asia Pacific Regional Committee of IOSCO ARM see adjustable rate mortgage ASAC see Asian Securities' Analysts Council ASC see Accounting Society of China 2 ASEAN see Association of South-East Asian Nations ASIC see Australian Securities and Investments Commission AST system see automated screen trading system ASX see Australian Stock Exchange ATI see Account Transfer Instruction ABF Hong