FOREIGN EXCHANGE DERIVATIVES: Effective Theoretical and Practical Techniques for Trading, Hedging and Managing FX Derivatives by Dr. A. A. Kotze´ Financial Chaos Theory Pty. Ltd. March 2011 http:nnwww.quantonline.co.za Philosophy is written in that great book whichever lies before our gaze | I mean the universe | but we cannot understand if we do not first learn the language and grasp the symbols in which it is written. The book is written in the mathematical language, and the symbols are triangle, circles and other geometrical figures, without the help of which it is impossible to conceive a single word of it, and without which one wonders in vain through a dark labyrinth. Galileo Galilei (1564-1642) Abstract Instruments traded in the financial markets are getting more and more complex. This leads to more complex derivative structures that are harder to analyse and risk managed. These instruments cannot be traded or managed without the relevant systems and numerical techniques. The global economy is becoming more and more interlinked with trading between countries skyrocketing. Due to the world trade, foreign exchange forwards, futures, options and exotics are becoming increasingly commonplace in today's capital mar- kets. The objective of these notes is to let the reader develop a solid understanding of the current currency derivatives used in international treasury management with an emphasis on the African continent. This will give participants the mathematical and practical background necessary to deal with all the products on the market. Before I came here I was confused about the subject. Having listened to your lecture I am still confused. But on a higher level. Enrico Fermi (1901-1954) Financial Chaos Theory Pty. Ltd. Illuminating OTC and listed Derivatives through: consulting services training workshops/seminars In-house training quantitative analysis research modeling complex optionality model building software products and development risk management and analysis structured products Financial Chaos Theory PO Box 16185 Doornfontein 2028 South Africa [email protected] But the creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed. Albert Einstein Contents 1 Introduction 12 1.1 Introduction . 14 1.2 A History of Derivatives . 15 1.3 A History of Option Valuation . 17 1.4 A Word on Modeling . 19 1.5 Payoff Diagrams . 20 1.6 Understanding the Foreign Exchange Markets . 22 1.6.1 The Gold Standard . 22 1.6.2 Uniqueness of the Market . 22 1.6.3 Size of the Market . 23 1.6.4 Growth in the FX Market . 26 1.6.5 Emerging Markets: Growth in Derivatives Activity . 28 1.6.6 Currency Composition of OTC Derivatives in Emerging Markets 30 1.7 Why Trade FX? . 33 1.8 Where is the Spot Traded . 34 1.9 Quotation Styles . 37 1.10 Jargon: Nicknames . 38 1.11 Settlement Rules . 38 1.11.1 Banking Holidays . 38 1.11.2 Islamic Currencies . 39 1.12 Pips and Big Figures . 40 1.13 Major, Minor and Exotic Currencies . 41 1.13.1 Most Heavily traded Currencies . 41 1.13.2 Circulating Currencies . 42 1.13.3 Groups of Currencies . 44 1.14 What is a Hard Currency? . 45 1.15 Cross Currencies . 48 1.16 Currency Indices: Rand Currency Index . 49 2 Foreign Exchange Risk and Hedging 53 2.1 Introduction . 53 2.2 FX Market Participants . 55 1 2.3 Risks in Forex Trading . 55 2.4 Modern Corporate Risk Management . 57 2.5 What is FX Risk Management? . 57 2.6 The Great Equiliser . 59 2.7 How to Minimise Foreign Exchange Risks? . 60 2.7.1 Foreign Exchange Forward Contracts . 60 2.7.2 Currency Options . 61 2.7.3 Cross Currency Swaps . 61 2.8 Hedging FX Exposures in Emerging Markets . 61 2.9 Hedging and Profit Opportunities . 64 2.10 Fundamental en Technical Analysis . 65 2.11 Hedging Policy Principles . 66 2.12 Regulatory and Accounting Initiatives . 68 2.12.1 Basel Accords . 69 2.12.2 Regulatory Reform of OTC Derivatives . 71 2.12.3 Accounting Reforms . 72 3 Capital Markets in Africa 74 3.1 Introduction . 74 3.2 Time Value of Money . 75 3.2.1 Day Count . 76 3.2.2 Simple Interest Rate Calculations . 76 3.2.3 Zero-Coupon Bond . 77 3.2.4 Discount Factors . 77 3.2.5 Compounding Periods . 78 3.2.6 Compounded Rates . 78 3.2.7 Forward Rates . 80 3.2.8 Converting between Rates . 81 3.2.9 Nominal and Effective Rates . 81 3.3 Modern Capital Markets . 82 3.4 African Equity and Bond Markets . 84 3.4.1 South Africa . 86 3.4.2 Kenya . 90 3.4.3 Nigeria . 91 3.4.4 Mauritius . 93 3.4.5 Egypt . 94 3.5 The Zero-Coupon Yield Curve . 94 3.6 From Spot to Derivatives . 96 3.6.1 The Spot Price . 99 3.6.2 Simple Derivatives . 99 3.6.3 The Forward Contract . 100 3.6.4 The Futures Contract . 102 2 3.6.5 Cash Flow Differences . 102 3.7 Arbitrage-free Pricing of Forwards and Futures . 103 3.7.1 What is Arbitrage? . 103 3.7.2 Box Diagrams . 105 3.7.3 Carry Cost and Forward Points . 107 3.7.4 Trading Futures on Exchange . 110 3.8 Non-Deliverable Forwards . 110 3.9 Contango and Backwardation . 111 3.10 Forward Prices versus Futures Prices . 113 3.11 Trading African Currency Derivatives . 114 4 Properties of Options Prices 116 4.1 Introduction . 116 4.2 The Two Types of Derivatives . 117 4.3 Option Basics . 117 4.4 Exchange Traded Options . 118 4.5 Over-the-Counter Options . 118 4.6 Why trade FX Options versus the Spot FX? . 119 4.7 The Benefits of the Black & Scholes Model . 121 4.8 Black, Scholes and Merton did not invent any Formula! . 122 4.9 The Black & Scholes Environment . 125 4.10 The Black & Scholes Analysis . 128 4.10.1 The Option Payoff . 128 4.10.2 The Black & Scholes Hedging Strategy: a Replicating Portfolio 128 4.11 The Seminal Formula . 130 4.12 The Intuitive Black & Scholes . 132 4.12.1 As a Replicating Portfolio - Delta Hedging . 132 4.12.2 As a Present Value of Risk-neutral Expectation . 133 4.13 A Currency Option Model . 133 4.14 Options on Forwards and Futures . 134 4.15 Settlement Adjustments . 135 4.16 Option Pricing in Excel . 136 4.17 Option Sensitivities . 136 5 The Mechanics of Option Prices 139 5.1 Introduction . 139 5.2 Payoff Profiles . 139 5.3 Building Blocks . 140 5.4 Put-Call-Parity . 141 5.5 Option Dynamics and Risk Managements . 143 5.5.1 Asymptotics . 144 5.5.2 The Greeks . 145 3 5.5.3 The Gamma and Theta Relationship . 149 5.5.4 Intrinsic and Time Value . 149 5.6 Some more Basic Concepts . 152 5.7 Useful Relationships . 153 5.7.1 Identities . 153 5.7.2 Symmetries . 153 5.7.3 Put-Call-Delta Parity . 154 5.7.4 Symmetries for Currency Options . ..