Smile Arbitrage: Analysis and Valuing
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Machine Learning Based Intraday Calibration of End of Day Implied Volatility Surfaces
DEGREE PROJECT IN MATHEMATICS, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2020 Machine Learning Based Intraday Calibration of End of Day Implied Volatility Surfaces CHRISTOPHER HERRON ANDRÉ ZACHRISSON KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES Machine Learning Based Intraday Calibration of End of Day Implied Volatility Surfaces CHRISTOPHER HERRON ANDRÉ ZACHRISSON Degree Projects in Mathematical Statistics (30 ECTS credits) Master's Programme in Applied and Computational Mathematics (120 credits) KTH Royal Institute of Technology year 2020 Supervisor at Nasdaq Technology AB: Sebastian Lindberg Supervisor at KTH: Fredrik Viklund Examiner at KTH: Fredrik Viklund TRITA-SCI-GRU 2020:081 MAT-E 2020:044 Royal Institute of Technology School of Engineering Sciences KTH SCI SE-100 44 Stockholm, Sweden URL: www.kth.se/sci Abstract The implied volatility surface plays an important role for Front office and Risk Manage- ment functions at Nasdaq and other financial institutions which require mark-to-market of derivative books intraday in order to properly value their instruments and measure risk in trading activities. Based on the aforementioned business needs, being able to calibrate an end of day implied volatility surface based on new market information is a sought after trait. In this thesis a statistical learning approach is used to calibrate the implied volatility surface intraday. This is done by using OMXS30-2019 implied volatil- ity surface data in combination with market information from close to at the money options and feeding it into 3 Machine Learning models. The models, including Feed For- ward Neural Network, Recurrent Neural Network and Gaussian Process, were compared based on optimal input and data preprocessing steps. -
Module 6 Option Strategies.Pdf
zerodha.com/varsity TABLE OF CONTENTS 1 Orientation 1 1.1 Setting the context 1 1.2 What should you know? 3 2 Bull Call Spread 6 2.1 Background 6 2.2 Strategy notes 8 2.3 Strike selection 14 3 Bull Put spread 22 3.1 Why Bull Put Spread? 22 3.2 Strategy notes 23 3.3 Other strike combinations 28 4 Call ratio back spread 32 4.1 Background 32 4.2 Strategy notes 33 4.3 Strategy generalization 38 4.4 Welcome back the Greeks 39 5 Bear call ladder 46 5.1 Background 46 5.2 Strategy notes 46 5.3 Strategy generalization 52 5.4 Effect of Greeks 54 6 Synthetic long & arbitrage 57 6.1 Background 57 zerodha.com/varsity 6.2 Strategy notes 58 6.3 The Fish market Arbitrage 62 6.4 The options arbitrage 65 7 Bear put spread 70 7.1 Spreads versus naked positions 70 7.2 Strategy notes 71 7.3 Strategy critical levels 75 7.4 Quick notes on Delta 76 7.5 Strike selection and effect of volatility 78 8 Bear call spread 83 8.1 Choosing Calls over Puts 83 8.2 Strategy notes 84 8.3 Strategy generalization 88 8.4 Strike selection and impact of volatility 88 9 Put ratio back spread 94 9.1 Background 94 9.2 Strategy notes 95 9.3 Strategy generalization 99 9.4 Delta, strike selection, and effect of volatility 100 10 The long straddle 104 10.1 The directional dilemma 104 10.2 Long straddle 105 10.3 Volatility matters 109 10.4 What can go wrong with the straddle? 111 zerodha.com/varsity 11 The short straddle 113 11.1 Context 113 11.2 The short straddle 114 11.3 Case study 116 11.4 The Greeks 119 12 The long & short straddle 121 12.1 Background 121 12.2 Strategy notes 122 12..3 Delta and Vega 128 12.4 Short strangle 129 13 Max pain & PCR ratio 130 13.1 My experience with option theory 130 13.2 Max pain theory 130 13.3 Max pain calculation 132 13.4 A few modifications 137 13.5 The put call ratio 138 13.6 Final thoughts 140 zerodha.com/varsity CHAPTER 1 Orientation 1.1 – Setting the context Before we start this module on Option Strategy, I would like to share with you a Behavioral Finance article I read couple of years ago. -
Users/Robertjfrey/Documents/Work
AMS 511.01 - Foundations Class 11A Robert J. Frey Research Professor Stony Brook University, Applied Mathematics and Statistics [email protected] http://www.ams.sunysb.edu/~frey/ In this lecture we will cover the pricing and use of derivative securities, covering Chapters 10 and 12 in Luenberger’s text. April, 2007 1. The Binomial Option Pricing Model 1.1 – General Single Step Solution The geometric binomial model has many advantages. First, over a reasonable number of steps it represents a surprisingly realistic model of price dynamics. Second, the state price equations at each step can be expressed in a form indpendent of S(t) and those equations are simple enough to solve in closed form. 1+r D-1 u 1 1 + r D 1 + r D y y ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ = u fl u = 1+r D u-1 u 1+r-u 1 u 1 u yd yd ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ1+r D ÅÅÅÅÅÅÅÅ1 uêÅÅÅÅ-ÅÅÅÅu ÅÅ H L H ê L i y As we will see shortlyH weL Hwill solveL the general problemj by solving a zsequence of single step problems on the lattice. That K O K O K O K O j H L H ê L z sequence solutions can be efficientlyê computed because wej only have to zsolve for the state prices once. k { 1.2 – Valuing an Option with One Period to Expiration Let the current value of a stock be S(t) = 105 and let there be a call option with unknown price C(t) on the stock with a strike price of 100 that expires the next three month period. -
VERTICAL SPREADS: Taking Advantage of Intrinsic Option Value
Advanced Option Trading Strategies: Lecture 1 Vertical Spreads – The simplest spread consists of buying one option and selling another to reduce the cost of the trade and participate in the directional movement of an underlying security. These trades are considered to be the easiest to implement and monitor. A vertical spread is intended to offer an improved opportunity to profit with reduced risk to the options trader. A vertical spread may be one of two basic types: (1) a debit vertical spread or (2) a credit vertical spread. Each of these two basic types can be written as either bullish or bearish positions. A debit spread is written when you expect the stock movement to occur over an intermediate or long- term period [60 to 120 days], whereas a credit spread is typically used when you want to take advantage of a short term stock price movement [60 days or less]. VERTICAL SPREADS: Taking Advantage of Intrinsic Option Value Debit Vertical Spreads Bull Call Spread During March, you decide that PFE is going to make a large up move over the next four months going into the Summer. This position is due to your research on the portfolio of drugs now in the pipeline and recent phase 3 trials that are going through FDA approval. PFE is currently trading at $27.92 [on March 12, 2013] per share, and you believe it will be at least $30 by June 21st, 2013. The following is the option chain listing on March 12th for PFE. View By Expiration: Mar 13 | Apr 13 | May 13 | Jun 13 | Sep 13 | Dec 13 | Jan 14 | Jan 15 Call Options Expire at close Friday, -
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 -
Risk and Return in Yield Curve Arbitrage
Norwegian School of Economics Bergen, Fall 2020 Risk and Return in Yield Curve Arbitrage A Survey of the USD and EUR Interest Rate Swap Markets Brage Ager-Wick and Ngan Luong Supervisor: Petter Bjerksund Master’s Thesis, Financial Economics NORWEGIAN SCHOOL OF ECONOMICS This thesis was written as a part of the Master of Science in Economics and Business Administration at NHH. Please note that neither the institution nor the examiners are responsible – through the approval of this thesis – for the theories and methods used, or results and conclusions drawn in this work. Acknowledgements We would like to thank Petter Bjerksund for his patient guidance and valuable insights. The empirical work for this thesis was conducted in . -scripts can be shared upon request. 2 Abstract This thesis extends the research of Duarte, Longstaff and Yu (2007) by looking at the risk and return characteristics of yield curve arbitrage. Like in Duarte et al., return indexes are created by implementing a particular version of the strategy on historical data. We extend the analysis to include both USD and EUR swap markets. The sample period is from 2006-2020, which is more recent than in Duarte et al. (1988-2004). While the USD strategy produces risk-adjusted excess returns of over five percent per year, the EUR strategy underperforms, which we argue is a result of the term structure model not being well suited to describe the abnormal shape of the EUR swap curve that manifests over much of the sample period. For both USD and EUR, performance is much better over the first half of the sample (2006-2012) than over the second half (2013-2020), which coincides with a fall in swap rate volatility. -
The Impact of Implied Volatility Fluctuations on Vertical Spread Option Strategies: the Case of WTI Crude Oil Market
energies Article The Impact of Implied Volatility Fluctuations on Vertical Spread Option Strategies: The Case of WTI Crude Oil Market Bartosz Łamasz * and Natalia Iwaszczuk Faculty of Management, AGH University of Science and Technology, 30-059 Cracow, Poland; [email protected] * Correspondence: [email protected]; Tel.: +48-696-668-417 Received: 31 July 2020; Accepted: 7 October 2020; Published: 13 October 2020 Abstract: This paper aims to analyze the impact of implied volatility on the costs, break-even points (BEPs), and the final results of the vertical spread option strategies (vertical spreads). We considered two main groups of vertical spreads: with limited and unlimited profits. The strategy with limited profits was divided into net credit spread and net debit spread. The analysis takes into account West Texas Intermediate (WTI) crude oil options listed on New York Mercantile Exchange (NYMEX) from 17 November 2008 to 15 April 2020. Our findings suggest that the unlimited vertical spreads were executed with profits less frequently than the limited vertical spreads in each of the considered categories of implied volatility. Nonetheless, the advantage of unlimited strategies was observed for substantial oil price movements (above 10%) when the rates of return on these strategies were higher than for limited strategies. With small price movements (lower than 5%), the net credit spread strategies were by far the best choice and generated profits in the widest price ranges in each category of implied volatility. This study bridges the gap between option strategies trading, implied volatility and WTI crude oil market. The obtained results may be a source of information in hedging against oil price fluctuations. -
Copyrighted Material
Index AA estimate, 68–69 At-the-money (ATM) SPX variance Affine jump diffusion (AJD), 15–16 levels/skews, 39f AJD. See Affine jump diffusion Avellaneda, Marco, 114, 163 Alfonsi, Aurelien,´ 163 American Airlines (AMR), negative book Bakshi, Gurdip, 66, 163 value, 84 Bakshi-Cao-Chen (BCC) parameters, 40, 66, American implied volatilities, 82 67f, 70f, 146, 152, 154f American options, 82 Barrier level, Amortizing options, 135 distribution, 86 Andersen, Leif, 24, 67, 68, 163 equal to strike, 108–109 Andreasen, Jesper, 67, 68, 163 Barrier options, 107, 114. See also Annualized Heston convexity adjustment, Out-of-the-money barrier options 145f applications, 120 Annualized Heston VXB convexity barrier window, 120 adjustment, 160f definitions, 107–108 Ansatz, 32–33 discrete monitoring, adjustment, 117–119 application, 34 knock-in options, 107 Arbitrage, 78–79. See also Capital structure knock-out options, 107, 108 arbitrage limiting cases, 108–109 avoidance, 26 live-out options, 116, 117f calendar spread arbitrage, 26 one-touch options, 110, 111f, 112f, 115 vertical spread arbitrage, 26, 78 out-of-the-money barrier, 114–115 Arrow-Debreu prices, 8–9 Parisian options, 120 Asymptotics, summary, 100 rebate, 108 Benaim, Shalom, 98, 163 At-the-money (ATM) implied volatility (or Berestycki, Henri, 26, 163 variance), 34, 37, 39, 79, 104 Bessel functions, 23, 151. See also Modified structure, computation, 60 Bessel function At-the-money (ATM) lookback (hindsight) weights, 149 option, 119 Bid/offer spread, 26 At-the-money (ATM) option, 70, 78, 126, minimization, -
CAIA® Level I Workbook
CAIA® Level I Workbook Practice questions, exercises, and keywords to test your knowledge SEPTEMBER 2021 CAIA Level I Workbook, September 2021 CAIA Level I Workbook Table of Contents Preface ........................................................................................................................................... 3 Workbook ...................................................................................................................................................................... 3 September 2021 Level I Study Guide ....................................................................................................................... 3 Errata Sheet .................................................................................................................................................................... 3 The Level II Examination and Completion of the Program ................................................................................. 3 Review Questions & Answers ................................................................................................. 4 Chapter 1 What is an Alternative Investment? ......................................................................................... 4 Chapter 2 The Environment of Alternative Investments ........................................................................... 6 Chapter 3 Quantitative Foundations ........................................................................................................ 8 Chapter 4 Statistical Foundations ...........................................................................................................10 -
Volatility Risk Premium: New Dimensions
Deutsche Bank Markets Research Europe Derivatives Strategy Date 20 April 2017 Derivatives Spotlight Caio Natividade Volatility Risk Premium: New [email protected] Dimensions Silvia Stanescu [email protected] Vivek Anand Today's Derivatives Spotlight delves into systematic options research. It is the first in a series of collaborative reports between our derivatives and [email protected] quantitative research teams that aim to systematically identify and capture value across global volatility markets. Paul Ward, Ph.D [email protected] This edition zooms into the volatility risk premia (VRP), one of the key sources of return in options markets. VRP strategies are popular across the investor Simon Carter community, but suffer from structural shortcomings. This report looks to [email protected] improve on those. Going beyond traditional methods, we introduce a P-distribution that best Pam Finelli represents our projected future returns and associated probabilities, based on [email protected] their drivers. Other topics are also highlighted as we construct our P- distribution, namely a new multivariate volatility risk factor model, our Global Spyros Mesomeris, Ph.D Sentiment Indicator, and the treatment of event-based versus non-event based [email protected] returns. +44 20 754 52198 We formulate a strategy which should improve the way in which the VRP is harnessed. It utilizes alternative delta hedging methods and timing. Risk Statement: while this report does not explicitly recommend specific options, we note that there are risks to trading derivatives. The loss from long options positions is limited to the net premium paid, but the loss from short option positions can be unlimited. -
A Brief Analysis of Option Implied Volatility and Strategies
Economics World, July-Aug. 2018, Vol. 6, No. 4, 331-336 doi: 10.17265/2328-7144/2018.04.009 D DAVID PUBLISHING A Brief Analysis of Option Implied Volatility and Strategies Zhou Heng University of Adelaide, Adelaide, Australia With the implementation of reform of financial system and the opening-up of financial market in China, knowing and properly utilizing financial derivatives becomes an inevitable road. The phenomenon of B-S-M option pricing model underpricing deep-in/out option prices is called volatility smile. The substantial reasons are conflicts between model’s presumptions and reality; moreover, the market trading mechanism brings extra uncertainties and risks to option writers when doing delta hedging. Implied volatility research and random volatility research have been modifying B-S-M model. Giving a practical case may let reader have an intuitive and in-depth understanding. Keywords: financial derivatives, option pricing, option strategies Introduction Since the first standardized “exchanged-traded” forward contracts were successfully traded in 1864, more and more financial institutions and companies were starting to use financial derivatives not only for generating revenue, but also aiming for controlling the risk exposure. Currently, derivatives can be divided into four categories which are forwards, options, futures, and swaps. This essay will mainly focus on options and further discussing what causes the option’s implied volatility and how to utilize implied volatility in a practical way. Causing the Implied Volatility Implied volatility plays an important role in valuing an option, and it is derived from Black-Scholes option pricing model. Several theories explained the reason. Market Trading Mechanism Basically, deep-out of money options have less probability to get valuable comparing with less deep-out of money options and at-the money options at expiration date. -
Applications of Realized Volatility, Local Volatility and Implied Volatility Surface in Accuracy Enhancement of Derivative Pricing Model
APPLICATIONS OF REALIZED VOLATILITY, LOCAL VOLATILITY AND IMPLIED VOLATILITY SURFACE IN ACCURACY ENHANCEMENT OF DERIVATIVE PRICING MODEL by Keyang Yan B. E. in Financial Engineering, South-Central University for Nationalities, 2015 and Feifan Zhang B. Comm. in Information Management, Guangdong University of Finance, 2016 B. E. in Finance, Guangdong University of Finance, 2016 PROJECT SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN FINANCE In the Master of Science in Finance Program of the Faculty of Business Administration © Keyang Yan, Feifan Zhang, 2017 SIMON FRASER UNIVERSITY Term Fall 2017 All rights reserved. However, in accordance with the Copyright Act of Canada, this work may be reproduced, without authorization, under the conditions for Fair Dealing. Therefore, limited reproduction of this work for the purposes of private study, research, criticism, review and news reporting is likely to be in accordance with the law, particularly if cited appropriately. Approval Name: Keyang Yan, Feifan Zhang Degree: Master of Science in Finance Title of Project: Applications of Realized Volatility, Local Volatility and Implied Volatility Surface in Accuracy Enhancement of Derivative Pricing Model Supervisory Committee: Associate Professor Christina Atanasova _____ Professor Andrey Pavlov ____________ Date Approved: ___________________________________________ ii Abstract In this research paper, a pricing method on derivatives, here taking European options on Dow Jones index as an example, is put forth with higher level of precision. This method is able to price options with a narrower deviation scope from intrinsic value of options. The finding of this pricing method starts with testing the features of implied volatility surface. Two of three axles in constructed three-dimensional surface are respectively dynamic strike price at a given time point and the decreasing time to maturity within the life duration of one strike-specified option.