DOCSLIB.ORG

FINANCIAL RISK the GREEKS the Whole of This Presentation Is As A

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
FINANCIAL RISK the GREEKS the Whole of This Presentation Is As A FINANCIAL RISK THE GREEKS The whole of this presentation is as a result of the collective efforts of both participants. MICHAEL AGYAPONG BOATENG Email: [email protected] MAVIS ASSIBEY-YEBOAH Email: [email protected] DECEMBER 1, 2011 Contents 1. INTRODUCTION 3 2. THE BLACK-SCHOLES MODEL 3 3. THE GREEKS 4 4. HIGHER-ORDER GREEKS 7 5. CONCLUSION 8 6. STUDY GUIDE 8 7. REFERENCES 8 2 1. INTRODUCTION The price of a single option or a position involving multiple options as the market changes is very difficult to predict. This results from the fact that price does not always move in correspondence with the price of the underlying asset. As such, it is of major interest to understand factors that contribute to the movement in price of an option, and what effect they have. Most option traders therefore turn to the Greeks which provide a means in measuring the sensitivity of an option price by quantifying the factors. The Greeks are so named because they are often denoted by Greek letters. The Greeks, as vital tools in risk management measures sensitivity of the value of the portfolio relative to a small change in a given underlying parameter. This treats accompanying risks in isolation to rebalance the portfolio accordingly so as to achieve a desirable exposure. In this project, the derivation and analysis of the Greeks will be based on the Black-Scholes model. This is because, they are easy to calculate, and are very useful for derivatives traders, especially those who seek to hedge their portfolios from adverse changes in market conditions. The most commonly used Greeks are the delta, vega, theta, rho and gamma out of which we give an insight into delta hedging and how it works. The first four are first order derivatives whilst gamma is of second-order. Some higher order Greeks will be discussed as well. 2. THE BLACK-SCHOLES MODEL The definition of compound interest satisfies the ordinary differential equation (ODE) dx(t)/x(t)= rdt (r is the interest rate). In the case where rate is uncertain, it is believed to be perturbed by the noise r + ξ(t) which results in the following stochastic differential equation (SDE) dX(t) = (r + σξ(t))X(t). dt This means that (1) dX(t)= rX(t)dt + σX(t)dB(t). When there is no noise, that is σ = 0, we recover the deterministic equation whose solution is obtained by separating variables as x(t) = ert. The solution to (1) is governed by a geometric Brownian motion and it is given by (r σ2/2)t+σB(t) X(t)= e − . Now, let us consider a capital market consisting of a stock, a bond and options on the stock. We assume that the riskless interest rate is a constant r, µ is the mean rate of return and σ is the volatility where σ(S(t)) = σS(t). The stock price process S(t) satisfies the SDE (2) dS(t)= µS(t)dt + σS(t)dB(t). Using Itˆo’s formula with f(x)= ln(x) we find that a strong solution for (2) is obtained as 3 (µ σ2/2)t+σB(t) S(t)= S(0)e − . Furthermore, (B(t))t 0 is the bond price process given by ≥ B(t)= B(0)ert. where r > 0 is a constant. At time 0, the asset prices S(0) and B(0) are known strictly positive real numbers. Through a series of calculations, which we will not bore you with, we arrive at the natural price of a simple European contingent claim with the payoff g(S(T )) at time of maturity T ]0, [ which also happens to be the Black-Scholes equation. The equation is shown below ∈ ∞ 2 rτ (r σ )τ+σ√τG υ(t,s)= e− E[g(se − 2 )] where G N(0, 1), 0 t<T , and τ = T t. ∈ ≤ − Hence, Black and Scholes derived the price at time 0 of a European call with strike price K and termination date T in 1973 as follows S(0) σ2 S(0) σ2 ln K + (r + 2 )T rT ln K + (r 2 )T (3) c(0,S(0),K,T )= S(0)φ( ) Ke− φ( − ). σ√T − σ√T S 2 S 2 ln (0) +(r+ σ )T ln (0) +(r σ )T We make the following denotions; d = ( K 2 ) and d = ( K − 2 ) 1 σ√T 2 σ√T 3. THE GREEKS As mentioned earlier in the introduction, the Greeks of an option measure the sensitivity of the option price from its parameters. In mathematical notations, a simple European option on a stock S with payoff function (S(T ) K)+) at time of maturity T has the price υ(t,S(t) expressed as − 2 rτ (r σ )τ+σ√τG (4) υ(t,s)= e− E[g(se − 2 )] at time t<T . The partial derivatives of (4) with respect to (t,s,r,σ) evaluated at the point (t,S(t)) are called the Greeks of the option. DELTA In options trading, delta is the measure of how the value of an option changes with respect to changes in the value of the underlying asset. It is denoted by the Greek letter ∆. It measures the sensitivity of an option to a change in the price of the underlying parameter. Delta is a number 4 between negative one and one (or in trading jargon, between 100 and +100) which shows the amount of money one losses or gains in the market. In general,− ∂υ ∆= ∂S where υ is the price of the option and S is the stock price. The Black-Scholes model analysis has a close relationship with ∆ in that it constructs a riskless portfolio made up of a position in the option on the stock and a position in the stock. Hence, for a European call option on a non-dividend paying stock, the delta of a call is given by ∂c = φ(d ) ∂S 1 PROOF The call price formula is given by (3). Taking its derivative with respect to the stock price gives ∂c ∂d1 rτ ∂d2 = φ(d )+ S(ϕ) Ke− ϕ(d ) ∂S 1 ∂S − 2 ∂S ∂d ∂d 1 = 2 ∂S ∂S ∂c ∂d1 rτ = φ(d )+ (S(ϕ) Ke− ϕ(d ) ⇒ ∂S 1 ∂S − 2 rτ (S(ϕ) Ke− ϕ(d )=0 − 2 ∂c = φ(d ) ∂S 1 In a call option, an increase in the price of the underlying asset increases the value of the option by an amount equal to the delta of the option. The opposite occurs when there is a decrease in the underlying asset’s price. This scenario exists when the investor takes a long position in the call option as the delta of the call option is a positive number ranging between 0 and 1. Put option on the other hand has a negative delta ranging between 1 and 0. Due to the inverse relationship between the underlying asset and the option price in a− put option, there is a decrease in the option’s price by an amount equal to the delta of the option whenever the underlying asset’s price increases. Also, a decrease in the price of the underlying asset causes the price of the option to increase. The delta for a European put is also given below without proof ∂c = φ( d ) ∂S − − 1 For a portfolio of options with a single asset price as S, the delta of the portfolio is given by ∂π ∂S where π is the value of the portfolio. The delta of the portfolio is the sum of the individual options in the portfolio. A portfolio consisting of a quantity x of option i(1 i n) has a delta i ≤ ≤ n ∆= X xi∆i i=1 where ∆i is the delta of the ith position. A delta neutral portfolio is the position in the price of the underlying asset necessary to make the delta of the portfolio zero. Because delta changes, the ability to make the portfolio delta neutral can exist for a short period of time and the investor has to adjust his position regularly in order to adapt to this changing atmosphere and this is referred to as rebalancing. 5 DELTA AS A HEDGING STRATEGY First of all, hedging can be thought of as an insurance. When individuals decide to hedge, they are insuring themselves against a negative event and this does not necessarily prevent the occurence of a negative event. But when it does happen and one is properly hedged, the impact of the event is essentially reduced. Hedging occurs in our everyday lives. As an example, when one buys a health insurance, unforseen disasters in ones’ health is hedged against. If we assume that we have a portfolio of options with V (t) as the value of the portfolio at time t, then V (t)= n1c + n2S + B where c is the value of a single option, S represents the underlying share’s value, B is the bond invested in a riskless asset and n1 and n2 are the number of options and shares respectively. If n1 is negative, it implies we have a short position in the option whilst a positive value of n1 means we have a long position. The delta of the portfolio will then be ∂V ∂c (5) = n + n ∂S 1 ∂S 2 For this portfolio to be made delta neutral (insensitive to minimal changes in the value of the underlying parameter), we set the left hand side of (5) to zero.
Load more

Recommended publications
  • University of Illinois at Urbana-Champaign Department of Mathematics
    University of Illinois at Urbana-Champaign Department of Mathematics ASRM 410 Investments and Financial Markets Fall 2018 Chapter 5 Option Greeks and Risk Management by Alfred Chong Learning Objectives: 5.1 Option Greeks: Black-Scholes valuation formula at time t, observed values, model inputs, option characteristics, option Greeks, partial derivatives, sensitivity, change infinitesimally, Delta, Gamma, theta, Vega, rho, Psi, option Greek of portfolio, absolute change, option elasticity, percentage change, option elasticity of portfolio. 5.2 Applications of Option Greeks: risk management via hedging, immunization, adverse market changes, delta-neutrality, delta-hedging, local, re-balance, from- time-to-time, holding profit, delta-hedging, first order, prudent, delta-gamma- hedging, gamma-neutrality, option value approximation, observed values change inevitably, Taylor series expansion, second order approximation, delta-gamma- theta approximation, delta approximation, delta-gamma approximation. Further Exercises: SOA Advanced Derivatives Samples Question 9. 1 5.1 Option Greeks 5.1.1 Consider a continuous-time setting t ≥ 0. Assume that the Black-Scholes framework holds as in 4.2.2{4.2.4. 5.1.2 The time-0 Black-Scholes European call and put option valuation formula in 4.2.9 and 4.2.10 can be generalized to those at time t: −δ(T −t) −r(T −t) C (t; S; δ; r; σ; K; T ) = Se N (d1) − Ke N (d2) P = Ft;T N (d1) − PVt;T (K) N (d2); −r(T −t) −δ(T −t) P (t; S; δ; r; σ; K; T ) = Ke N (−d2) − Se N (−d1) P = PVt;T (K) N (−d2) − Ft;T N (−d1) ; where d1 and d2 are given by S 1 2 ln K + r − δ + 2 σ (T − t) d1 = p ; σ T − t S 1 2 p ln K + r − δ − 2 σ (T − t) d2 = p = d1 − σ T − t: σ T − t 5.1.3 The option value V is a function of observed values, t and S, model inputs, δ, r, and σ, as well as option characteristics, K and T .
    [Show full text]
  • Ice Crude Oil
    ICE CRUDE OIL Intercontinental Exchange® (ICE®) became a center for global petroleum risk management and trading with its acquisition of the International Petroleum Exchange® (IPE®) in June 2001, which is today known as ICE Futures Europe®. IPE was established in 1980 in response to the immense volatility that resulted from the oil price shocks of the 1970s. As IPE’s short-term physical markets evolved and the need to hedge emerged, the exchange offered its first contract, Gas Oil futures. In June 1988, the exchange successfully launched the Brent Crude futures contract. Today, ICE’s FSA-regulated energy futures exchange conducts nearly half the world’s trade in crude oil futures. Along with the benchmark Brent crude oil, West Texas Intermediate (WTI) crude oil and gasoil futures contracts, ICE Futures Europe also offers a full range of futures and options contracts on emissions, U.K. natural gas, U.K power and coal. THE BRENT CRUDE MARKET Brent has served as a leading global benchmark for Atlantic Oseberg-Ekofisk family of North Sea crude oils, each of which Basin crude oils in general, and low-sulfur (“sweet”) crude has a separate delivery point. Many of the crude oils traded oils in particular, since the commercialization of the U.K. and as a basis to Brent actually are traded as a basis to Dated Norwegian sectors of the North Sea in the 1970s. These crude Brent, a cargo loading within the next 10-21 days (23 days on oils include most grades produced from Nigeria and Angola, a Friday). In a circular turn, the active cash swap market for as well as U.S.
    [Show full text]
  • Yuichi Katsura
    P&TcrvvCJ Efficient ValtmVmm-and Hedging of Structured Credit Products Yuichi Katsura A thesis submitted for the degree of Doctor of Philosophy of the University of London May 2005 Centre for Quantitative Finance Imperial College London nit~ýl. ABSTRACT Structured credit derivatives such as synthetic collateralized debt obligations (CDO) have been the principal growth engine in the fixed income market over the last few years. Val- uation and risk management of structured credit products by meads of Monte Carlo sim- ulations tend to suffer from numerical instability and heavy computational time. After a brief description of single name credit derivatives that underlie structured credit deriva- tives, the factor model is introduced as the portfolio credit derivatives pricing tool. This thesis then describes the rapid pricing and hedging of portfolio credit derivatives using the analytical approximation model and semi-analytical models under several specifications of factor models. When a full correlation structure is assumed or the pricing of exotic structure credit products with non-linear pay-offs is involved, the semi-analytical tractability is lost and we have to resort to the time-consuming Monte Carlo method. As a Monte Carlo variance reduction technique we extend the importance sampling method introduced to credit risk modelling by Joshi [2004] to the general n-factor problem. The large homogeneouspool model is also applied to the method of control variates as a new variance reduction tech- niques for pricing structured credit products. The combination of both methods is examined and it turns out to be the optimal choice. We also show how sensitivities of a CDO tranche can be computed efficiently by semi-analytical and Monte Carlo framework.
    [Show full text]
  • RT Options Scanner Guide
    RT Options Scanner Introduction Our RT Options Scanner allows you to search in real-time through all publicly traded US equities and indexes options (more than 170,000 options contracts total) for trading opportunities involving strategies like: - Naked or Covered Write Protective Purchase, etc. - Any complex multi-leg option strategy – to find the “missing leg” - Calendar Spreads Search is performed against our Options Database that is updated in real-time and driven by HyperFeed’s Ticker-Plant and our Implied Volatility Calculation Engine. We offer both 20-minute delayed and real-time modes. Unlike other search engines using real-time quotes data only our system takes advantage of individual contracts Implied Volatilities calculated in real-time using our high-performance Volatility Engine. The Scanner is universal, that is, it is not confined to any special type of option strategy. Rather, it allows determining the option you need in the following terms: – Cost – Moneyness – Expiry – Liquidity – Risk The Scanner offers Basic and Advanced Search Interfaces. Basic interface can be used to find options contracts satisfying, for example, such requirements: “I need expensive Calls for Covered Call Write Strategy. They should expire soon and be slightly out of the money. Do not care much as far as liquidity, but do not like to bear high risk.” This can be done in five seconds - set the search filters to: Cost -> Dear Moneyness -> OTM Expiry -> Short term Liquidity -> Any Risk -> Moderate and press the “Search” button. It is that easy. In fact, if your request is exactly as above, you can just press the “Search” button - these values are the default filtering criteria.
    [Show full text]
  • Option Greeks Demystified
    Webinar Presentation Option Greeks Demystified Presented by Trading Strategy Desk 1 Fidelity Brokerage Services, Member NYSE, SIPC, 900 Salem Street, Smithfield, RI 02917. © 2016 FMR LLC. All rights reserved. 764207.1.0 Disclosures Options trading entails significant risk and is not appropriate for all investors. Certain complex options strategies carry additional risk. Before trading options, please read Characteristics and Risks of Standardized Options, and call 800-544- 5115 to be approved for options trading. Supporting documentation for any claims, if applicable, will be furnished upon request. Examples in this presentation do not include transaction costs (commissions, margin interest, fees) or tax implications, but they should be considered prior to entering into any transactions. The information in this presentation, including examples using actual securities and price data, is strictly for illustrative and educational purposes only and is not to be construed as an endorsement, recommendation. Active Trader Pro PlatformsSM is available to customers trading 36 times or more in a rolling 12-month period; customers who trade 120 times or more have access to Recognia anticipated events and Elliott Wave analysis. Greeks are mathematical calculations used to determine the effect of various factors on options. Goal of this webinar Demystify what Options Greeks are and explain how they are used in plain English. What we will cover: What the Greeks are What the Greeks tell us How the Greeks can help with planning option trades How the Greeks can help with managing option trades The Greeks What the Greeks are: • Delta • Gamma • Vega • Theta • Rho But what do they mean? Greeks What do they tell me? In simplest terms, Greeks give traders a theoretical way to judge their exposure to various options pricing inputs.
    [Show full text]
  • White Paper Volatility: Instruments and Strategies
    White Paper Volatility: Instruments and Strategies Clemens H. Glaffig Panathea Capital Partners GmbH & Co. KG, Freiburg, Germany July 30, 2019 This paper is for informational purposes only and is not intended to constitute an offer, advice, or recommendation in any way. Panathea assumes no responsibility for the content or completeness of the information contained in this document. Table of Contents 0. Introduction ......................................................................................................................................... 1 1. Ihe VIX Index .................................................................................................................................... 2 1.1 General Comments and Performance ......................................................................................... 2 What Does it mean to have a VIX of 20% .......................................................................... 2 A nerdy side note ................................................................................................................. 2 1.2 The Calculation of the VIX Index ............................................................................................. 4 1.3 Mathematical formalism: How to derive the VIX valuation formula ...................................... 5 1.4 VIX Futures .............................................................................................................................. 6 The Pricing of VIX Futures ................................................................................................
    [Show full text]
  • Straddles and Strangles to Help Manage Stock Events
    Webinar Presentation Using Straddles and Strangles to Help Manage Stock Events Presented by Trading Strategy Desk 1 Fidelity Brokerage Services LLC ("FBS"), Member NYSE, SIPC, 900 Salem Street, Smithfield, RI 02917 690099.3.0 Disclosures Options’ trading entails significant risk and is not appropriate for all investors. Certain complex options strategies carry additional risk. Before trading options, please read Characteristics and Risks of Standardized Options, and call 800-544- 5115 to be approved for options trading. Supporting documentation for any claims, if applicable, will be furnished upon request. Examples in this presentation do not include transaction costs (commissions, margin interest, fees) or tax implications, but they should be considered prior to entering into any transactions. The information in this presentation, including examples using actual securities and price data, is strictly for illustrative and educational purposes only and is not to be construed as an endorsement, or recommendation. 2 Disclosures (cont.) Greeks are mathematical calculations used to determine the effect of various factors on options. Active Trader Pro PlatformsSM is available to customers trading 36 times or more in a rolling 12-month period; customers who trade 120 times or more have access to Recognia anticipated events and Elliott Wave analysis. Technical analysis focuses on market action — specifically, volume and price. Technical analysis is only one approach to analyzing stocks. When considering which stocks to buy or sell, you should use the approach that you're most comfortable with. As with all your investments, you must make your own determination as to whether an investment in any particular security or securities is right for you based on your investment objectives, risk tolerance, and financial situation.
    [Show full text]
  • Greece's Sovereign Debt and Economic Realism
    abcd POLICY INSIGHT No.90 June 2017 Greece’s sovereign debt and economic realism Jeremy Bulow and John Geanakoplos Stanford Business School; Yale University Introduction still-unspecified debt relief measures that would The problem make the remaining debt repayable. Meanwhile, unrest and labour strife remain high in Greece, and reek unemployment currently stands at potential foreign investors are still scared off by the 23% (Hellencic Statistical Authority 2016), uncertainty surrounding the debt. The creditors Gand has exceeded 20% for five years. have yet to receive any net payments, and all the Greek GDP is down 25% from its peak in 2009, ministers of Europe are obliged to attend to the and infrastructure investment has been almost Greek debt problem, instead of to more pressing nonexistent over the ensuing seven years. Young issues like terrorism, Brexit, Putin, Trump, and the people have been emigrating in droves, exacerbating refugee crisis. More troubling, this is just a replay what was already one of the most alarming old/ of the same exhausting scenario we have seen young ratios in the world. Capital flight has cost repeated time and again. the banks roughly half their deposits, while half their loans are non-performing. The sovereign We present our analysis of how sophisticated and debt/GDP is almost 180%; worse, the debt is owed experienced negotiators like the IMF, the Eurozone almost entirely to foreigners, and GDP is stated leadership, and by now even the Greeks, could have in what, for Greece, is an over-valued currency.1 let negotiations drag out for so many years.
    [Show full text]
  • Value at Risk for Linear and Non-Linear Derivatives
    Value at Risk for Linear and Non-Linear Derivatives by Clemens U. Frei (Under the direction of John T. Scruggs) Abstract This paper examines the question whether standard parametric Value at Risk approaches, such as the delta-normal and the delta-gamma approach and their assumptions are appropriate for derivative positions such as forward and option contracts. The delta-normal and delta-gamma approaches are both methods based on a first-order or on a second-order Taylor series expansion. We will see that the delta-normal method is reliable for linear derivatives although it can lead to signif- icant approximation errors in the case of non-linearity. The delta-gamma method provides a better approximation because this method includes second order-effects. The main problem with delta-gamma methods is the estimation of the quantile of the profit and loss distribution. Empiric results by other authors suggest the use of a Cornish-Fisher expansion. The delta-gamma method when using a Cornish-Fisher expansion provides an approximation which is close to the results calculated by Monte Carlo Simulation methods but is computationally more efficient. Index words: Value at Risk, Variance-Covariance approach, Delta-Normal approach, Delta-Gamma approach, Market Risk, Derivatives, Taylor series expansion. Value at Risk for Linear and Non-Linear Derivatives by Clemens U. Frei Vordiplom, University of Bielefeld, Germany, 2000 A Thesis Submitted to the Graduate Faculty of The University of Georgia in Partial Fulfillment of the Requirements for the Degree Master of Arts Athens, Georgia 2003 °c 2003 Clemens U. Frei All Rights Reserved Value at Risk for Linear and Non-Linear Derivatives by Clemens U.
    [Show full text]
  • Volatile Markets Made Easy Trading Stocks and Options for Increased Profits
    Volatile Markets Made Easy Trading Stocks and Options for Increased Profits Guy Cohen Contents Foreword xiii Acknowledgments xiv About the Author xv Preface xvii chapter 1 Introduction to Options 1 Definition of an Option 1 Calls and Puts 2 Right Versus Obligation 2 Fixed Price 3 Expiration Date 4 The Valuation of Options 4 Intrinsic and Time Value for Calls 6 Intrinsic and Time Value for Puts 6 Why Trade Options? 8 Advantages of Trading Options 9 Risk Profile Charts 12 Long Call Risk Profile 15 Short Call Risk Profile 15 Long Put Risk Profile 17 Short Put Risk Profile 18 The Four Basic Risk Profiles Summarized 19 Options in the Marketplace 20 Option Contracts 20 Expiration Dates 20 Strike Prices 20 Option Ticker Symbols 20 Open Interest 22 Placing Your Trade 23 Other Market Considerations 26 Learning Points 26 viii Volatile Markets Made Easy chapter 2 Trends and Flags 27 A Common Mistake 28 Benefits of this Method 29 Trending Stocks 29 What Is a Trend? 30 The Challenge with Moving Averages 32 Trendlines 34 Consolidating Chart Patterns 35 Bull Flag 36 Bear Flag 36 Flags Within the Context of a Trend 38 Managing Your Profits 41 Rounded Tops and Flag Failures 48 Cup and Handle—Two Patterns in One 51 Finding Flag Patterns 55 Learning Points 55 chapter 3 Options and the Greeks 57 Delta 61 Why Does Speed Matter? 63 Delta Neutral Trading 64 Leverage and Gearing 64 Delta Neutral Trading for Hedging 65 Delta with Puts 70 Gamma 71 Theta 75 Vega 82 Implied Volatility 83 Theoretical Option Pricing 84 Rho 91 Learning Points 92 Contents ix chapter
    [Show full text]
  • Consolidated Policy on Valuation Adjustments Global Capital Markets
    Global Consolidated Policy on Valuation Adjustments Consolidated Policy on Valuation Adjustments Global Capital Markets September 2008 Version Number 2.35 Dilan Abeyratne, Emilie Pons, William Lee, Scott Goswami, Jerry Shi Author(s) Release Date September lOth 2008 Page 1 of98 CONFIDENTIAL TREATMENT REQUESTED BY BARCLAYS LBEX-BARFID 0011765 Global Consolidated Policy on Valuation Adjustments Version Control ............................................................................................................................. 9 4.10.4 Updated Bid-Offer Delta: ABS Credit SpreadDelta................................................................ lO Commodities for YH. Bid offer delta and vega .................................................................................. 10 Updated Muni section ........................................................................................................................... 10 Updated Section 13 ............................................................................................................................... 10 Deleted Section 20 ................................................................................................................................ 10 Added EMG Bid offer and updated London rates for all traded migrated out oflens ....................... 10 Europe Rates update ............................................................................................................................. 10 Europe Rates update continue .............................................................................................................
    [Show full text]
  • The Option Trader Handbook Strategies and Trade Adjustments
    The Option Trader Handbook Strategies and Trade Adjustments Second Edition GEORGE VI. JABBOIiR, PhD PHILIP H. BUDWICK, MsF WILEY John Wiley & Sons, Inc. Contents Preface to the First Edition xlli Preface to the Second Edition xvli CHAPTER 1 Trade and Risk Management 1 Introduction 1 The Philosophy of Risk 2 Truth About Reward 5 Risk Management 6 Risk 6 Reward 9 Breakeven Points , 11 Trade Management 11 Trading Theme 11 The Theme of Your Portfolio 14 Diversification and Flexibility 15 Trading as a Business 16 Start-Up Phase 16 Growth Phase 19 Mature Phase 20 Just Business, Nothing Personal 21 SCORE—The Formula for Trading Success 21 Select the Investment 22 Choose the Best Strategy 23 Open the Trade with a Plan v, 24 Remember Your Plan and Stick to It 26 Exit Your Trade 26 Vl CONTENTS CHAPTER 2 Tools of the Trader 29 Introduction 29 Option Value 30 Option Pricing 31 Stock Price 31 Strike Price 32 Time to Expiration 32 Volatility 33 Dividends 33 Interest Rates 33 Option Greeks and Risk Management 34 Time Decay 34 Trading Lessons Learned from Time Decay (Theta). 41 Delta/Gamma 43 Deep-in-the-Money Options 46 Implied Volatility 49 Early Assignment 63 Synthetic Positions 65 Synthetic Stock 66 Long Stock 66 Short Stock 67 Synthetic Call 68 Synthetic Put 70 Basic Strategies 71 Long Call , 71 Short Call . - 72 Long Put .' 73 Short Put 74 Basic Spreads and Combinations 75 Bull Call Spread 75 Bull Put Spread 76 Bear Call Spread 77 Bear Put Spread 78 Long Straddle 78 Long Strangle 79 Short Straddle 80 Short Strangle 81 Advanced Spreads 82 Call Ratio
    [Show full text]