Оглавление
Ursone Pierino. How to Calculate Options Prices and Their Greeks
Preface
Chapter 1. Introduction
Chapter 2. The Normal Probability Distribution
STANDARD DEVIATION IN A FINANCIAL MARKET
THE IMPACT OF VOLATILITY AND TIME ON THE STANDARD DEVIATION
Chapter 3. Volatility
THE PROBABILITY DISTRIBUTION OF THE VALUE OF A FUTURE AFTER ONE YEAR OF TRADING
NORMAL DISTRIBUTION VERSUS LOG-NORMAL DISTRIBUTION
CALCULATING THE ANNUALISED VOLATILITY TRADITIONALLY
CALCULATING THE ANNUALISED VOLATILITY WITHOUT μ
CALCULATING THE ANNUALISED VOLATILITY APPLYING THE 16 % RULE
VARIATION IN TRADING DAYS
APPROACH TOWARDS INTRADAY VOLATILITY
HISTORICAL VERSUS IMPLIED VOLATILITY
Chapter 4. Put Call Parity
SYNTHETICALLY CREATING A FUTURE LONG POSITION, THE REVERSAL
SYNTHETICALLY CREATING A FUTURE SHORT POSITION, THE CONVERSION
SYNTHETIC OPTIONS
COVERED CALL WRITING
SHORT NOTE ON INTEREST RATES
Chapter 5. Delta Δ
CHANGE OF OPTION VALUE THROUGH THE DELTA
DYNAMIC DELTA
DELTA AT DIFFERENT MATURITIES
DELTA AT DIFFERENT VOLATILITIES
20–80 DELTA REGION
DELTA PER STRIKE
DYNAMIC DELTA HEDGING
THE AT THE MONEY DELTA
DELTA CHANGES IN TIME
Chapter 6. Pricing
CALCULATING THE AT THE MONEY STRADDLE USING BLACK AND SCHOLES FORMULA
DETERMINING THE VALUE OF AN AT THE MONEY STRADDLE
Chapter 7. Delta II
DETERMINING THE BOUNDARIES OF THE DELTA
VALUATION OF THE AT THE MONEY DELTA
DELTA DISTRIBUTION IN RELATION TO THE AT THE MONEY STRADDLE
APPLICATION OF THE DELTA APPROACH, DETERMINING THE DELTA OF A CALL SPREAD
Chapter 8. Gamma
THE AGGREGATE GAMMA FOR A PORTFOLIO OF OPTIONS
THE DELTA CHANGE OF AN OPTION
THE GAMMA IS NOT A CONSTANT
LONG TERM GAMMA EXAMPLE
SHORT TERM GAMMA EXAMPLE
VERY SHORT TERM GAMMA EXAMPLE
DETERMINING THE BOUNDARIES OF GAMMA
DETERMINING THE GAMMA VALUE OF AN AT THE MONEY STRADDLE
GAMMA IN RELATION TO TIME TO MATURITY, VOLATILITY AND THE UNDERLYING LEVEL
PRACTICAL EXAMPLE
HEDGING THE GAMMA
DETERMINING THE GAMMA OF OUT OF THE MONEY OPTIONS
DERIVATIVES OF THE GAMMA
Chapter 9. Vega
DIFFERENT MATURITIES WILL DISPLAY DIFFERENT VOLATILITY REGIME CHANGES
DETERMINING THE VEGA VALUE OF AT THE MONEY OPTIONS
VEGA OF AT THE MONEY OPTIONS COMPARED TO VOLATILITY
VEGA OF AT THE MONEY OPTIONS COMPARED TO TIME TO MATURITY
VEGA OF AT THE MONEY OPTIONS COMPARED TO THE UNDERLYING LEVEL
VEGA ON A 3-DIMENSIONAL SCALE, VEGA VS MATURITY AND VEGA VS VOLATILITY
DETERMINING THE BOUNDARIES OF VEGA
COMPARING THE BOUNDARIES OF VEGA WITH THE BOUNDARIES OF GAMMA
DETERMINING VEGA VALUES OF OUT OF THE MONEY OPTIONS
DERIVATIVES OF THE VEGA
VOMMA
Chapter 10. Theta
A PRACTICAL EXAMPLE
THETA IN RELATION TO VOLATILITY
THETA IN RELATION TO TIME TO MATURITY
THETA OF AT THE MONEY OPTIONS IN RELATION TO THE UNDERLYING LEVEL
DETERMINING THE BOUNDARIES OF THETA
THE GAMMA THETA RELATIONSHIP α
THETA ON A 3-DIMENSIONAL SCALE, THETA VS MATURITY AND THETA VS VOLATILITY
DETERMINING THE THETA VALUE OF AN AT THE MONEY STRADDLE
DETERMINING THETA VALUES OF OUT OF THE MONEY OPTIONS
Chapter 11. Skew
VOLATILITY SMILES WITH DIFFERENT TIMES TO MATURITY
STICKY AT THE MONEY VOLATILITY
Chapter 12. Spreads
CALL SPREAD (HORIZONTAL)
PUT SPREAD (HORIZONTAL)
BOXES
APPLYING BOXES IN THE REAL MARKET
THE GREEKS FOR HORIZONTAL SPREADS
TIME SPREAD
APPROXIMATION OF THE VALUE OF AT THE MONEY SPREADS
RATIO SPREAD
Chapter 13. Butterfly
PUT CALL PARITY
DISTRIBUTION OF THE BUTTERFLY
BOUNDARIES OF THE BUTTERFLY
METHOD FOR ESTIMATING AT THE MONEY BUTTERFLY VALUES
ESTIMATING OUT OF THE MONEY BUTTERFLY VALUES
BUTTERFLY IN RELATION TO VOLATILITY
BUTTERFLY IN RELATION TO TIME TO MATURITY
BUTTERFLY AS A STRATEGIC PLAY
THE GREEKS OF A BUTTERFLY
STRADDLE–STRANGLE OR THE “IRON FLY”
Chapter 14. Strategies
CALL
PUT
CALL SPREAD
RATIO SPREAD
STRADDLE
STRANGLE
COLLAR (RISK REVERSAL, FENCE)
GAMMA PORTFOLIO
GAMMA HEDGING STRATEGIES BASED ON MONTE CARLO SCENARIOS
SETTING UP A GAMMA POSITION ON THE BACK OF PREVAILING KURTOSIS IN THE MARKET
EXCESS KURTOSIS
BENEFITTING FROM A PLATYKURTIC ENVIRONMENT
THE MESOKURTIC MARKET
THE LEPTOKURTIC MARKET
TRANSITION FROM A PLATYKURTIC ENVIRONMENT TOWARDS A LEPTOKURTIC ENVIRONMENT
WRONG HEDGING STRATEGY: KILLERGAMMA
VEGA CONVEXITY/VOMMA
VEGA CONVEXITY IN RELATION TO TIME/VETA
WILEY END USER LICENSE AGREEMENT
Отрывок из книги
In September 1992 I joined a renowned and highly successful market-making company at the Amsterdam Options Exchange. The company early recognised the need for hiring option traders having had an academic education and being very strong in mental calculation. Option trading those days more and more professionalised and shifted away from “survival of the loudest and toughest guy” towards a more intellectual approach. Trading was a matter of speed, being the first in a deal. Strength in mental arithmetic gave one an edge. For instance, when trading option combinations, adding prices and subtracting prices – one at the bid price, the other for instance at the asking price – being the quickest brought high rewards.
After a thorough test of my mental maths skills, I was one of only two, of the many people tested, to be employed. There I stood, in my first few days in the open outcry pit, just briefly after September 16th 1992 (Black Wednesday). On that day the UK withdrew from the European EMS system (the forerunner of the Euro), the British pound collapsed, the FX market in general became heavily volatile – all around the time the management of the company had decided to let me start trading Dollar options.
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The problem the trader may have experienced, however, is that shortly after inception of the trade, the market came off rapidly towards the 42 level. As a result of the sharp drop in the underlying, the volatility may have jumped from 28 % to 40 %. The 40 put he sold at $1.50 suddenly had a value of $5.50, an unrealised loss of $4. It would have at least made the trader nervous, but most probably he would have bought back the option because it hit his stop loss level or he was forced by his broker, bank or clearing institution to deposit more margin; or even worse, the trade was stopped out by one of these institutions (at a bad price) when not adhering to the margin call.
So an adverse market move could have caused the trader to end up with a loss while being right in his strategy/view of the market. If he had anticipated the possibility of such a market move he might have sold less options or kept some cash for additional margin calls. Consequently, at expiry, he would have ended up with the $1.50 profit. Anticipation obviously can only be applied when understanding the consequences of changing option parameters with regards to the price of an option.
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