PowerPoint Presentation
IC315 Advanced Derivative Securities:
Hedging and Trading
January 2021
Dr Mike Smith
Where business comes to life
Course Notes
All course notes, exercises, answers to exercises, trading instructions etc are on Blackboard.
2
Course Structure
The course consists of 10 x 2hr lectures and 10 x 2hr trading seminars. The seminars will be a combination of face to face (in the dealing room) and online delivery (MS Teams) Please refer to your timetable. The main focus of the seminars is to manage equity option trading risk using the ICTrader trading simulation, but time will also be spent at the beginning of each seminar summarising the main points of that week’s lecture , and answering any related questions you may have.
3
Course Assessment
Assessment consists of 3 parts:
A 1.5 hour 20 question multiple choice test which will take place at the beginning of the summer term-this counts for 20% of the overall grade.
4
A 1 hour trading test on ICTrader (managing the risk of an equity options portfolio) which takes place at the end of the Spring term- this counts for 10% of the overall grade
5
A 1.5 hour final May/June exam consisting of 3 multiple part questions all of which must be answered- this counts for 70% of the overall grade.
6
During the semester we will go through a mock multiple choice paper, I will upload examples of past final exam papers, and you will be able to practice remotely on ICTrader for the trading test.
7
Office Hours- I will post office hours, both face to face and online (via MS Teams) in due course
You can also use the discussion board on Blackboard to ask any questions, or just email me:
m.j.smith@icmacentre.ac.uk
8
Books
S.Natenburg, Option Volatility and Pricing: Advanced Trading Strategies and Techniques: 2nd edition
J. Hull, Options, Futures and other Derivative Securities.
9
9
Software
ICTrader: Trading and hedging the risk of Equity options.
Option Strategist (Excel platform): Time characteristics of options and analysing the risk exposure of options using comprehensive case studies..
10
Topic 1: Review of Basic Concepts
Futures and forward contracts/markets
Review of basic option definitions/contract spec.
Overview of options markets
Premium strike relationships
Market exposure
Time value and intrinsic value
The probability of exercise
Some basic strategies
11
Futures and Forward Contracts
Options are really a more complicated version of futures and forward contracts, so a brief examination/review of these types of contract would probably be a good starting point for the course.
A futures contract is an exchange traded agreement/obligation to buy or sell an asset at a fixed point in time in the future at a fixed price.
A forward contract is an OTC market agreement/obligation to buy or sell an asset at a fixed point in time in the future at a fixed price.
12
Forward/Futures prices
The reason for reviewing forward/futures prices is to provide an intuitive insight into option pricing/payoff functions:
13
Forward/Futures payoff function
Forward contracts are settled at maturity, T.
ST Spot price of asset at time T
K Delivery price in forward contract
A long forward contract to buy one unit of an asset is worth
ST – K at maturity. This is the payoff from the contract.
Consider the following diagram:
14
15
Profit
0
K
The converse is true of a short forward contract- at maturity it will be worth K – ST because we are selling an asset at K when it is only worth ST :
16
17
Profit
0
K
Basic Option Concepts
Definition of puts and calls: the right but not the obligation to buy or sell the underlying at some point in the future.
American vs European Options
If you are short options is it still only a right?
This means that an option can either be worth something or nothing at expiry. Hence the following “kinked” diagrams:
18
Long a Call Option
19
10
Premium
Underlying
100
Long a Put Option
20
100
10
Premium
Underlying
Short a Call Option: Call Writer
21
10
100
Premium
Underlying
Short a Put Option: Put Writer
22
Premium
10
Underlying
100
“Kinked” Diagrams
Options have kinked payoff profiles because at expiry they can be either worth something or nothing.
Formally, for a call:
C = Max {S-X,0}
For a Put:
P = Max{X-S,0}
This point will be examined further below.
23
Payoff Functions
These diagrams can be expressed as option payoff functions (payoff to puts and calls at expiry):
Call Payoff Functions
IN THE MONEY (ITM): S > X.
AT THE MONEY (ATM): S = X .
OUT OF THE MONEY (OTM): S < X.
Does ATM really imply no loss at expiry?
24
24
Payoff Functions
Put Payoff Functions:
ITM: X > S
ATM: X =S
OTM: X < S 25 Strike/Premium Relationships Call option: The lower the strike the higher the premium. Reason ? Put option: The higher the strike the higher the premium. Reason? The lower the strike on the call the greater is the chance that the option will be exercised: The option is worth more. Vice versa for puts. The probability of ending up in the money and by how much is at the heart of option pricing and option price dynamics. 26 Writing (Short) Options From the payoff diagrams, short option positions appear to be risky: why do it? To earn premium Selling volatility (Covered in depth below) As a seller of options, are you expecting the market to be more or less volatile? 27 27 Writing (Short) Options Put differently: what level of probability are you assigning to the option ending In The Money? Selling “naked” options is a risky business. It is much less risky to sell the options “covered”(see covered call strategy, slide): If short calls, buy the underlying If short puts, sell the underlying 28 Market Exposure Understanding market exposure is crucial to understanding what you have bought or sold: What is your market exposure if you are long a call option? What is your market exposure if you are short a call option ? What is your market exposure if you are long a put option ? What is your market exposure if you are short a put option ? 29 Market Exposure What is your exposure if you are long a call and short a put option? What is your exposure if you are long a put and short a call option? 30 Long Synthetic Future 31 Long Call Short Put Long Synthetic Future Short Synthetic Future 32 Short Call Long Put Short Synthetic Future Basics of Option Valuation The price of an option is made up of two components: INTRINSIC VALUE AND TIME VALUE. The intrinsic value is the value of the option if it were exercised now. Intrinsic value cannot be negative: it is either positive or 0. 33 Basics of Option Valuation Formally, for a call: C = Max{S-X,0} for a put: P = Max{X-S,0} 34 Intrinsic Value Call option at expiry with a strike (X) of $100 Underlying (S) trading at $140 The intrinsic value of the option is S-X = $40. But, if the option is OTM and trading sometime prior to expiry, is it worthless? 35 Time Value If there is time left to expiry then an option is said to have time value (refer to option price curve on next page) Reason: there is a probability that the underlying may trade through the strike before expiry, giving the option value The probability is greater: The longer the remaining time to expiry The greater the volatility of the underlying 36 Time Value 37 Option Price Curve Intrinsic value Line Time Value 100 110 10 12 Premium Underlying Time Value Time value is greatest ATM If the option is deep OTM, there is a lower probability of the underlying trading through the strike: Lower time value If the option is deep ITM, the main component of its value is intrinsic value 38 Time Value Option premiums will decrease at an increasing rate over time Positive Time Decay (Diagram next page) To counteract time decay, we need underlying market direction and volatility If volatility increases, call and put premiums will increase 39 Positive Time Decay 40 : Call option value vs time to expiration Option 1 point in price 2.0 ATM 1 point out 1.0 0.0 -0.5 0 15 30 45 60 75 90 105 120 135 150 Time until expiration (days ) Time Decay If there is no volatility or direction in the underlying market, then at expiry the option price curve collapses into the intrinsic value line. Note: Time decay is covered in some depth in “the Greeks) 41 Time value Therefore, the “art and science” of pricing an option prior to maturity is really a question of pricing time value correctly. 42 Equity and Index Options U.K Equity Options These are options on specified actively traded stocks and are traded on LIFFE.(“traded options”) Fixed strikes and fixed quarterly expiry cycles For a full description of the contract specification go to www.liffe.com 43 U.K Equity Options In London the standard contract size is normally 1,000 shares. ( i.e one option gives you the right to buy or sell 1,000 of the underlying equity.) . In the U.S the contract gives you the right to buy or sell 100 shares. For a full description of U.S contract Specification, go to www.cbot.com The options are American style. e.g A “Boots July 420 call” with a premium of 15.5p (per share for 1000 shares ) would give you the right to buy Boots stock at £4.20 at any time until expiry which is July. What would you pay for the option? 44 U.K Equity Options The option costs £155 and had you bought the underlying outright it would have cost you £4,200. : Highly leveraged position in the underlying instrument. Consider the following option price quotation page from Bloomberg: 45 46 Synthetic Positions Recall that we can set up synthetic positions using combinations of options. We will examine this in a little more detail here. Say we have the choice of either buying a futures contract or creating a synthetic equivalent. Are they really the same thing? To create the synthetic we would buy a call and sell a put. If we sell a June put with a strike of 100, and buy a June call with a strike of 100, then this position should behave as if it were a futures contract locked in to buy the underlying at 100 47 Synthetic Positions If the underlying ends up above 100 at expiry, the trader could exercise the call and buy the underlying at 100 If the underlying ends up below 100 at expiry, then the put is assigned and the trader ends up long the underlying at 100 This is the same then as being long a futures contract. A synthetic short future is created when a put option is bought and a call option is sold, with the same strike and expiry (as above): 48 49 Long Call Short Put Long Synthetic Future 100 Synthetic Positions What about the delta exposure? If it is a synthetic future then the net delta should always be 1 If the delta exposure of the long June call is 75%, then the delta exposure of the short June put will be 25%. In other words, a one point rise in the underlying will result in a one point rise in the synthetic. The same applies to a short synthetic future. 50 Trading Synthetics: example1 We want long exposure to the underlying market June futures trading at 102 Could buy futures, or sell June put & buy June call June 100 call trading at $5, June 100 put trading at $3 Buy June call, sell June put = pay out $2 If at expiry, underlying trading at 110, exercise the call Make $10-$2 = $8 profit Same outcome if we had bought the futures contract 51 Trading Synthetics: example 2 June futures trading at 102 June 100 call trading at $4.90, June 100 put trading at $3.05 Sell put, buy call = payout $1.85 If underlying is 110 at expiry, Exercise call, make $10-$1.85 = $8.15 This is a better outcome than buying the futures contract 52 Trading Synthetics The difference between the call and put price is often referred to as the synthetic market. In general (in the absence of interest or dividend considerations), the synthetic market = Call price – put price = futures price-exercise price. If this equality holds, then there is no difference between a position in the futures vs a position in the synthetic future 53 Trading Synthetics In example 2, the synthetic market was: $4.90 - $3.05 = $1.85, Which is less than the difference between the futures (102), and the strike (100) = $2. The synthetic is cheaper, so a long synthetic is preferable to buying the future This implies that there must be arbitrage opportunities 54 Arbitrage: Conversions & Reversals June futures trading at 102 June 100 call trading at $5.10, June 100 put trading at $2.85 Synthetic market ($5.10-$2.85) = $2.25 Should be $2 (Underlying – exercise price) Sell synthetic = sell call and buy put Buy futures Lock in $0.25 55 Arbitrage: Conversions When the synthetic future is sold & the futures contract bought, It is known as a conversion: 56 57 0 Underlying 102 Short 100 call @ $5.10 Long 100 put @ $2.85 Long futures @ 102 Conversion P&L $0.25 Arbitrage: Reversals The opposite position, where the futures is sold & the synthetic futures bought, is known as a reversal: Futures trading at 102 June 100 call = $4.90, June 100 put = $3.05 Synthetic = $1.85, should be $2.00, Buy synthetic, sell futures = profit $0.15 58 59 0 Underlying 102 Long 100 call @ $4.90 Short 100 put @ $3.05 Short futures @ 102 Reversal P & L $0.15 Arbitrage: Conversions & Reversals Imbalances in the conversion/reversal market are usually small and rarely last very long. Option traders are therefore willing to execute conversions/reversals in very large size because of the low risk associated with these strategies. 60 Summary of some synthetic positions Synthetic long future = long call + short put Synthetic short future = long put + short call Synthetic long call = long future + long put Synthetic short call = short future + short put Synthetic long put = short future + long call Synthetic short put = long future + short call 61 Applied Exercises Option Strategist Exercise 1 62 62 Henley_Business_School_Logo_HYBRID T S /docProps/thumbnail.jpeg