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How to Calculate Options Prices and Their Greeks: Exploring the Black Scholes Model from Delta to Vega

Book Description

A unique, in-depth guide to options pricing and valuing their greeks, along with a four dimensional approach towards the impact of changing market circumstances on options

How to Calculate Options Prices and Their Greeks is the only book of its kind, showing you how to value options and the greeks according to the Black Scholes model but also how to do this without consulting a model. You'll build a solid understanding of options and hedging strategies as you explore the concepts of probability, volatility, and put call parity, then move into more advanced topics in combination with a four-dimensional approach of the change of the P&L of an option portfolio in relation to strike, underlying, volatility, and time to maturity. This informative guide fully explains the distribution of first and second order Greeks along the whole range wherein an option has optionality, and delves into trading strategies, including spreads, straddles, strangles, butterflies, kurtosis, vega-convexity, and more. Charts and tables illustrate how specific positions in a Greek evolve in relation to its parameters, and digital ancillaries allow you to see 3D representations using your own parameters and volumes.

The Black and Scholes model is the most widely used option model, appreciated for its simplicity and ability to generate a fair value for options pricing in all kinds of markets. This book shows you the ins and outs of the model, giving you the practical understanding you need for setting up and managing an option strategy.

  • Understand the Greeks, and how they make or break a strategy

  • See how the Greeks change with time, volatility, and underlying

  • Explore various trading strategies

  • Implement options positions, and more

  • Representations of option payoffs are too often based on a simple two-dimensional approach consisting of P&L versus underlying at expiry. This is misleading, as the Greeks can make a world of difference over the lifetime of a strategy. How to Calculate Options Prices and Their Greeks is a comprehensive, in-depth guide to a thorough and more effective understanding of options, their Greeks, and (hedging) option strategies.

    Table of Contents

    1. Title Page
    2. Copyright
    3. Preface
    4. Chapter 1: Introduction
    5. Chapter 2: The Normal Probability Distribution
      1. STANDARD DEVIATION IN A FINANCIAL MARKET
      2. THE IMPACT OF VOLATILITY AND TIME ON THE STANDARD DEVIATION
    6. Chapter 3: Volatility
      1. THE PROBABILITY DISTRIBUTION OF THE VALUE OF A FUTURE AFTER ONE YEAR OF TRADING
      2. NORMAL DISTRIBUTION VERSUS LOG-NORMAL DISTRIBUTION
      3. CALCULATING THE ANNUALISED VOLATILITY TRADITIONALLY
      4. <b xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ibooks="http://vocabulary.itunes.apple.com/rdf/ibooks/vocabulary-extensions-1.0">CALCULATING THE ANNUALISED VOLATILITY WITHOUT</b> &#956; μ
      5. CALCULATING THE ANNUALISED VOLATILITY APPLYING THE 16% RULE
      6. VARIATION IN TRADING DAYS
      7. APPROACH TOWARDS INTRADAY VOLATILITY
      8. HISTORICAL VERSUS IMPLIED VOLATILITY
    7. Chapter 4: Put Call Parity
      1. SYNTHETICALLY CREATING A FUTURE LONG POSITION, THE REVERSAL
      2. SYNTHETICALLY CREATING A FUTURE SHORT POSITION, THE CONVERSION
      3. SYNTHETIC OPTIONS
      4. COVERED CALL WRITING
      5. SHORT NOTE ON INTEREST RATES
    8. Chapter 5: Delta Δ
      1. CHANGE OF OPTION VALUE THROUGH THE DELTA
      2. DYNAMIC DELTA
      3. DELTA AT DIFFERENT MATURITIES
      4. DELTA AT DIFFERENT VOLATILITIES
      5. 20–80 DELTA REGION
      6. DELTA PER STRIKE
      7. DYNAMIC DELTA HEDGING
      8. THE AT THE MONEY DELTA
      9. DELTA CHANGES IN TIME
    9. Chapter 6: Pricing
      1. CALCULATING THE AT THE MONEY STRADDLE USING BLACK AND SCHOLES FORMULA
      2. DETERMINING THE VALUE OF AN AT THE MONEY STRADDLE
    10. Chapter 7: Delta II
      1. DETERMINING THE BOUNDARIES OF THE DELTA
      2. VALUATION OF THE AT THE MONEY DELTA
      3. DELTA DISTRIBUTION IN RELATION TO THE AT THE MONEY STRADDLE
      4. APPLICATION OF THE DELTA APPROACH, DETERMINING THE DELTA OF A CALL SPREAD
    11. Chapter 8: Gamma
      1. THE AGGREGATE GAMMA FOR A PORTFOLIO OF OPTIONS
      2. THE DELTA CHANGE OF AN OPTION
      3. THE GAMMA IS NOT A CONSTANT
      4. LONG TERM GAMMA EXAMPLE
      5. SHORT TERM GAMMA EXAMPLE
      6. VERY SHORT TERM GAMMA EXAMPLE
      7. DETERMINING THE BOUNDARIES OF GAMMA
      8. DETERMINING THE GAMMA VALUE OF AN AT THE MONEY STRADDLE
      9. GAMMA IN RELATION TO TIME TO MATURITY, VOLATILITY AND THE UNDERLYING LEVEL
      10. PRACTICAL EXAMPLE
      11. HEDGING THE GAMMA
      12. DETERMINING THE GAMMA OF OUT OF THE MONEY OPTIONS
      13. DERIVATIVES OF THE GAMMA
    12. Chapter 9: Vega
      1. DIFFERENT MATURITIES WILL DISPLAY DIFFERENT VOLATILITY REGIME CHANGES
      2. DETERMINING THE VEGA VALUE OF AT THE MONEY OPTIONS
      3. VEGA OF AT THE MONEY OPTIONS COMPARED TO VOLATILITY
      4. VEGA OF AT THE MONEY OPTIONS COMPARED TO TIME TO MATURITY
      5. VEGA OF AT THE MONEY OPTIONS COMPARED TO THE UNDERLYING LEVEL
      6. VEGA ON A 3-DIMENSIONAL SCALE, VEGA VS MATURITY AND VEGA VS VOLATILITY
      7. DETERMINING THE BOUNDARIES OF VEGA
      8. COMPARING THE BOUNDARIES OF VEGA WITH THE BOUNDARIES OF GAMMA
      9. DETERMINING VEGA VALUES OF OUT OF THE MONEY OPTIONS
      10. DERIVATIVES OF THE VEGA
      11. VOMMA
    13. Chapter 10: Theta
      1. A PRACTICAL EXAMPLE
      2. THETA IN RELATION TO VOLATILITY
      3. THETA IN RELATION TO TIME TO MATURITY
      4. THETA OF AT THE MONEY OPTIONS IN RELATION TO THE UNDERLYING LEVEL
      5. DETERMINING THE BOUNDARIES OF THETA
      6. THE GAMMA THETA RELATIONSHIP α
      7. THETA ON A 3-DIMENSIONAL SCALE, THETA VS MATURITY AND THETA VS VOLATILITY
      8. DETERMINING THE THETA VALUE OF AN AT THE MONEY STRADDLE
      9. DETERMINING THETA VALUES OF OUT OF THE MONEY OPTIONS
    14. Chapter 11: Skew
      1. VOLATILITY SMILES WITH DIFFERENT TIMES TO MATURITY
      2. STICKY AT THE MONEY VOLATILITY
    15. Chapter 12: Spreads
      1. CALL SPREAD (HORIZONTAL)
      2. PUT SPREAD (HORIZONTAL)
      3. BOXES
      4. APPLYING BOXES IN THE REAL MARKET
      5. THE GREEKS FOR HORIZONTAL SPREADS
      6. TIME SPREAD
      7. APPROXIMATION OF THE VALUE OF AT THE MONEY SPREADS
      8. RATIO SPREAD
    16. Chapter 13: Butterfly
      1. PUT CALL PARITY
      2. DISTRIBUTION OF THE BUTTERFLY
      3. BOUNDARIES OF THE BUTTERFLY
      4. METHOD FOR ESTIMATING AT THE MONEY BUTTERFLY VALUES
      5. ESTIMATING OUT OF THE MONEY BUTTERFLY VALUES
      6. BUTTERFLY IN RELATION TO VOLATILITY
      7. BUTTERFLY IN RELATION TO TIME TO MATURITY
      8. BUTTERFLY AS A STRATEGIC PLAY
      9. THE GREEKS OF A BUTTERFLY
      10. STRADDLE–STRANGLE OR THE “IRON FLY”
    17. Chapter 14: Strategies
      1. CALL
      2. PUT
      3. CALL SPREAD
      4. RATIO SPREAD
      5. STRADDLE
      6. STRANGLE
      7. COLLAR (RISK REVERSAL, FENCE)
      8. GAMMA PORTFOLIO
      9. GAMMA HEDGING STRATEGIES BASED ON MONTE CARLO SCENARIOS
      10. SETTING UP A GAMMA POSITION ON THE BACK OF PREVAILING KURTOSIS IN THE MARKET
      11. EXCESS KURTOSIS
      12. BENEFITTING FROM A PLATYKURTIC ENVIRONMENT
      13. THE MESOKURTIC MARKET
      14. THE LEPTOKURTIC MARKET
      15. TRANSITION FROM A PLATYKURTIC ENVIRONMENT TOWARDS A LEPTOKURTIC ENVIRONMENT
      16. WRONG HEDGING STRATEGY: KILLERGAMMA
      17. VEGA CONVEXITY/VOMMA
      18. VEGA CONVEXITY IN RELATION TO TIME/ VETA
    18. Index
    19. End User License Agreement