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FREE SAMPLEOPTIONS EXPLAINEDSIMPLYTHE FUNDAMENTAL PRINCIPLES COURSEi

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FREE SAMPLEOPTIONS EXPLAINED SIMPLYTHE FUNDAMENTAL PRINCIPLES COURSEBALBINDER CHAGGER

Options Explained Simply - The Fundamental Principles CourseThis third edition published in 2021 by Balbinder ChaggerCopyright 2021 by Balbinder ChaggerAll rights reservedThe right of Balbinder Chagger to be identified as author of this work has beenasserted in accordance with the Copyright, Designs, and Patents Act 1988All rights reserved. This book or any portion thereof may not be reproduced or used inany manner whatsoever without the express written permission of the publisher exceptfor the use of brief quotations in a book review or scholarly journal.Every reasonable effort has been made to ensure the information contained in thispublication is accurate at the time of going to press, and the publisher and the authorcannot accept responsibility for any errors or omissions, however caused. Noresponsibility for loss or damage occasioned to any person or organisation acting, orrefraining from action, as a result of the material in this publication can be accepted bythe publisher or the author.Cover designs, typesetting, illustrations, and graphics by Balbinder mwww.OptionsExplainedSimply.comFirst Printing: 2021ISBN 979-8-519-59951-1

DEDICATIONSumitran & Harbhajanv

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ABOUT THE AUTHORBalbinder Chagger has a rigorous understanding of Futures andOptions, consolidated over thirteen years of professional practice in theMarket Risk and Product Control functions of several internationalinvestment banks.He has formally recognised teaching skills, acquired while studying aPGCE in Secondary School Mathematics at the UCL Institute ofEducation, London, and also while working as a mathematics teacher.His ability to teach simply enables you to understand easily.He is a Chartered Accountant of the ICAEW, has an MBA from CassBusiness School, London, and a BSc in Computer Engineering fromCity, University of London.Balbinder has also written two novels: Burden of Proof and Duty to Mitigate.vii

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PREFACEWelcome to Options Explained Simply - The Fundamental Principles Course.My objective is to explain Futures and Options simply enough to enablea wide audience to understand them easily.Balbinder ChaggerJuly 2021ix

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INTRODUCTIONAn Option is a Derivative, which is a contract whose value depends on(i.e., is derived from) the value of an Underlying asset. For example, aMicrosoft Stock is an asset and a Microsoft Option is a contract whosevalue depends on the market price of the Microsoft Stock. Options canbe based on any underlying asset, not only on shares.Options Explained Simply - The Fundamental Principles Course will give you anintuitive and sound understanding of what Futures and Options are,how they are valued, and how they behave in changing marketconditions. It will empower you to analyse Futures and Optionsintelligently.To be able to understand Options, you need to understand Futures andForwards. To be able to understand these, you need to understand Spottransactions and some fundamental concepts, namely: Arbitrage;Expected Value; Risk; and the Time Value of Money. It is with thesefundamental topics that the course begins.No prior specialised financial knowledge is required to be able to followthis course. Furthermore, nor is required any advanced mathematicalability. The level of mathematics usually associated with finance isadvanced and sophisticated; it is beyond the level most people pursue aneducation in mathematics to. A layer of advanced mathematicsintimidates most people and makes financial instruments appear beyondtheir abilities to comprehend. But for the advanced mathematics,understanding Futures and Options is within the capability of a wide

audience. To facilitate learning and understanding, this course usessimple mathematics; all that is required is confidence with arithmetic,basic algebra, calculating averages, simple interest, and reading tables andgraphs.The following steps are also taken to promote learning andunderstanding:xii The subject matter is often taught with reference to familiar,real-life scenarios. The amount of detail is simplified to keep the subject matterclear and unclouded by unnecessary layers of complexity. Visualisation, an important and powerful means for learning formost people, is utilised extensively.Often, the writtenexplanations given are complemented with graphical illustrationsto clarify the subject matter more than words alone do. Thecalculations presented are visually transparent with every keystep in them shown clearly. Colour is used to emphasise andclarify key points, as exemplified in this introduction.

CONTENTSABOUT THE AUTHOR . viiPREFACE .ixINTRODUCTION .xiPART 1 FUNDAMENTALS .3Lesson 1 SPOT .51.1 Spot Trades . 5Lesson 2 POSITION TYPES .92.1 Expressing Ownership of Assets . 92.2 Short Position Types . 12Lesson 3 SPOTS RISK. 173.1 Risk Source . 173.2 Delta: Spot Price Risk Measure . 183.3 Delta of a Long Spot Position . 213.4 Delta of a Short Spot Position . 25Lesson 4 ARBITRAGE . 294.1 Deterministic Arbitrage . 294.2 Statistical Arbitrage . 32

Lesson 5 RATIONALITY . 37xiv

Balbinder Chagger

PART 1FUNDAMENTALSIn this part, we learn about Spot, Position Types, Risks, Arbitrage, and the TimeValue of Money.

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Balbinder ChaggerLesson 1SPOTIn this lesson, we learn what Spot trades are.1.1Spot TradesSay we want a muffin. We walk into a cake shop. We see a muffin welike. Its price is 3. We pay the shop 3. It gives us the muffin. Weleave. What just occurred here is a Spot transaction. It is depicted inFig 1.1.In a Spot transaction, the following things happen simultaneously in thepresent: The trading Agreement is made (i.e., who will buy, who will sell,what will be traded, and the trade price). The trade is Performed (i.e., delivery and payment are made inaccordance with the agreement).The trading parties (i.e., the Buyer and the Seller) initiate and completethe transaction in the present. The transaction does not create anyfuture commitments between them. Both parties move on free of eachother.5

FREE SAMPLE Options Explained Simply - The Fundamental Principles CourseFig 1.1Spot TransactionIn the financial investment world, the thing that is traded is called theSpot. Its price is referred to as the Spot Price.Anything that can be bought and sold can be Spot-traded. This includesphysical products, like a muffin, and intangible services, like a footmassage.Depending on what the Spot is, there may be some customary time gapbetween the trade being agreed and its performance, to allow forpracticalities. For example, a meal in a restaurant might take around 20minutes to prepare and deliver after it has been ordered (i.e., theagreement made), and it is customary to pay for it later, after it has beenconsumed. For other kinds of Spots, the time gap may be longer,perhaps even a few days. But essentially, the trade is agreed andperformed in the present.6

Balbinder ChaggerYou may be familiar with some things that are traded in the financialinvestment world, such as Stocks (Company Shares), Foreign Currencies(Cash), Bonds (Loans), Commodities (e.g., Corn), and Metals (e.g.,Gold). These are all Spots and can be Spot-traded.For example, say we want to buy 100 shares in Apple. We call ourstockbroker for a Spot Price quote. Say the quote is 120 per share. Ifwe are happy with the quote, then we can proceed and buy the shares.Our bank account is debited 12,000, and we become the owners of 100shares in Apple.7

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Balbinder ChaggerLesson 2POSITION TYPESIn this lesson, we learn what the terms Long, Flat, and Short mean.In the financial investment world, the terms Long, Flat, and Short areused to express positions types. They are used in the following twoways:1. To express ownership of assets.2. To express risk exposures.Their use to express risk exposures is explained in the next lesson. Inthis lesson, we learn how they are used to express ownership of assets.2.1Expressing Ownership of AssetsWe use the term Long to express that we own an asset. For example, ifwe say we are Long 3 Houses, this means we own 3 Houses. The signis commonly used to denote Long positions (e.g., 3 Houses). Usuallythough, the sign is omitted (e.g., 3 Houses).9

FREE SAMPLE Options Explained Simply - The Fundamental Principles CourseWe use the term Short to express that we owe an asset. For example, ifwe say we are Short 1,000, this means we owe 1,000. The β sign iscommonly used to denote Short (e.g., - 1,000).We use the term Flat to express that we have no position in an asset, i.e.,we neither own nor owe it. For example, if we say we are Flat Gold, thismeans we neither own nor owe Gold.The use of the and β signs is useful because it enables us to sum upthe individual positions in a particular asset mathematically to an overalltotal. For example, if we are 2,000 in our Savings account and are- 1,200 in our Current account, then we can sum the two positions upand say we are 800 overall.Long and Short positions often bring about costs and benefits upontheir holders. For example, a Long Property position might benefit theowner with rental income, but also entail repair and maintenance costs.Similarly, a Long Cash position (e.g., a bank deposit) might earn interestincome, while a Short Cash position (e.g., a bank loan) might incurinterest charges.To exemplify their use, let us apply these terms to the example of theSpot transaction we looked at in Lesson 1 concerning a muffin.In this example, say when we walk into the shop we have 3. We do nothave a muffin at the time though. We are Long Cash 3 and Flatmuffins. We use the 3 to pay for the muffin. This makes us Flat Cashand Long 1 muffin (i.e., we own a muffin).Now, suppose we walked into the shop being Flat Cash (i.e., we do nothave any money to our name). Can we still pay for the muffin? Yes wecan, if we can firstly borrow 3. A common way to borrow money isthrough a credit card loan. We can pay for the muffin with a credit card.We end up being Short Cash 3 (i.e., we owe 3 to the credit cardcompany) and Long 1 muffin. At some future date, we have to pay 3back to the credit card company to flatten out our Short Cash position.We might also have to pay some credit charges too. This example isdepicted in Fig 2.1.10

Balbinder ChaggerFig 2.1Spot Transaction with Borrowed FundsNow, suppose we walked into the shop and the shop is Flat muffins(i.e., it has no muffins). Can it still sell and deliver a muffin to us? Yes itcan, if it can borrow one first from somewhere, say from a neighbouringcake shop. This results in it being Short 1 muffin (i.e., it owes a muffinto the lender). Eventually, it will have to return a muffin to the lender,and, perhaps, pay some borrowing charges too. In reality though, it isunlikely the shop would borrow a muffin in this manner becausemuffins just are not lent and borrowed in the world like cash is. Butother assets are, like, Stocks. There are lots of large pension companiesout there sitting on huge Long Stock positions. They are only too happyto earn some extra income on their positions by lending them out inreturn for some fees from the borrowers.11

FREE SAMPLE Options Explained Simply - The Fundamental Principles Course2.2Short Position TypesAppreciate that we can sell and deliver an asset without owning it first.The asset must firstly be borrowed from a lender, and then it can bedelivered to the buyer. Thus, we end up with a Short position in theasset, which we must settle up later on.Fig 2.2Covered Short SaleThere are two types of Short positions, as follows:12 Covered Short Uncovered Short

Balbinder ChaggerA Covered Short sale entails selling an asset Short in the certainknowledge that we will receive a supply of the asset at a later date and ata known cost. A Covered Short sale is depicted in Fig 2.2, in 4 steps.The supply received is applied to settle up and close out the Shortposition. A Covered Short sale is a riskless strategy, meaning the endprofit is determinable from the outset, at the time of the sale. The profitis based essentially on the following facts, which are known withcertainty at the time of the sale: The Spot Price of the sale. The cost of the anticipated supply.To determine the complete profit, there will be other details to take intoaccount too, like: The cost of borrowing the asset. The interest income that can be earned on the sale proceedsreceived.These details too can be known with certainty at the time of the sale andfactored into the profit calculation.To exemplify a Covered Short sale, say an Apple company employee isinformed today that in a month from now she will be awarded a bonusin the form of 100 Apple company shares. Even though she will notlegally own the shares until a month from now, her financial interest inthem begins today. Today, she knows what the Spot Price of the shareson the Stock market is. Say it is 120 per share. It could go up or downover the next month. She has no guarantee what the shares will beworth on the day she becomes their legal owner. Her risk is they mightbe worth less than they are today. If she is happy with their 120 marketvalue today and does not want to take the risk of them being worth less,then she can eliminate the risk by selling Short 100 shares today. Thesale is a Covered Short sale because it is done in the certain knowledgethat 100 shares will be received in a monthβs time at zero cost.13

FREE SAMPLE Options Explained Simply - The Fundamental Principles CourseThe Short sale gives her a Long Cash position of 12,000 (100 120)and a Short Stock position of 100 Apple shares. She can determine herend profit right from the outset, at the time of the sale, to be 12,000(12,000 0), plus any interest she can earn on the 12,000 saleproceeds, and less any charges payable on borrowing the shares for theShort sale.Fig 2.3Uncovered Short SaleIn contrast, an Uncovered Short sale entails selling an asset without ananticipated future supply of it at a known cost. At some point in thefuture, the Short position will have to be closed out. This will have tobe done by buying the asset on the open market at the prevailing SpotPrice, which is an unknown figure when the Short sale is made. TheUncovered Short sale is depicted in Fig 2.3, in 4 steps.14

Balbinder ChaggerAn Uncovered Short sale is a risky, speculative strategy, meaning the endprofit is undeterminable at the time of the sale because the cost ofacquiring the asset is unknown. The sale is usually based on thespeculative view that the Spot Price will drop and the asset can bebought cheaper than it was sold for. But, there is the chance the SpotPrice increases. If it does, then the asset will have to be purchased at ahigher Spot Price than it was sold for, and the strategy will result in afinancial loss. The actual result cannot be known at the time of the sale,and can go either way.15

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Balbinder ChaggerLesson 3SPOTS RISKIn this lesson, we learn about the risk Spots give exposure to.3.1Risk SourceThe financial value of a position in a particular asset depends on thefollowing factors: Number of units (Quantity) Type of position (Long or Short) Market price of a unit (Spot Price)We can express the value mathematically as π’π ππ’πππ‘ππ‘π¦ ππππ‘πππππThe number of units we hold is under our complete control. We canbuy and sell them as we wish, and adjust our position to suit our desire.Therefore, the quantity is not a source of risk. But, we have no controlwhatsoever over the Spot Price; the market determines it. We have to17

FREE SAMPLE Options Explained Simply - The Fundamental Principles Courseaccept the Spot Price, whatever it is, as a matter of fact. It can move upand down. As it fluctuates, the value of our position changesaccordingly. If the Spot Price rises, then the following happens: A Long position earns a profit, because we own a more valuableposition. Note the value of a Long position moves in the samedirection as the Spot Price movement. A Short position incurs a loss, because we owe a more valuableposition. Note the value of a Short position moves in theopposite direction to the Spot Price movement.If the Spot Price falls, then the opposite happens, as follows: A Long position incurs a loss, because we own a less valuableposition. Again, note the value of a Long position moves in thesame direction as the Spot Price movement. A Short position earns a profit, because we owe a less valuableposition. Again, note the value of a Short position moves in theopposite direction to the Spot Price movement.In summary, Long Spot position values react in the same directions asthe movements in the Spot Price, and Short position values react in theopposite directions.3.2Delta: Spot Price Risk MeasureThe Spot Price (i.e., the market given price) is a source of risk to ourSpot position because it affects its value; we have no control over it, andit can move against us. This applies to a position in any Spot asset. Forexample, if we have a position in Gold, then the positionβs valuedepends on Goldβs Spot Price. Similarly, if we have a position in CrudeOil, then the positionβs value depends on Crude Oilβs Spot Price.It is very long-winded to have to say how a positionβs value changes relative toSpot Price movements. So, the financial investment world just says Delta18

Balbinder Chaggerinstead, for short. Delta (the Greek letter, uppercase Ξ, lowercase Ξ΄ orπΏ) is the formal, technical name given to the relationship between theSpot Price and the positionβs value. If someone says he has a Delta inCoffee, then everyone understands that he has a position whose valuereacts to movements in the Spot Price of Coffee. In other words, theperson has a risk exposure to the Spot Price of Coffee.It would be useful to know the following things also about the position: Whether its value reacts in the same or opposite direction to theSpot Price movement. The size of the reaction.The financial investment world has thought about these aspects and hasagreed standard ways to communicate them, as follows: The terms Long/Short are used to communicate that theposition value changes in the same/opposite direction as theSpot Price movement. A number is used to communicate the amount the position valuechanges by. The number communicates the amount by which the positionvalue changes as the Spot Price increases by 1. The number is calculated under the assumption that all otherfactors affecting the positionβs value remain static while only theSpot Price increases. Later, when we look at Forwards andOptions, we will appreciate there are also other factors, besidesSpot Price, that affect some positionsβ values.Appreciate that Delta is a standardised Risk Measure; it communicates ina standardised way how a positionβs value reacts to the Spot Price. It isthe first of several risk measures we will encounter as we progressthrough this course.19

FREE SAMPLE Options Explained Simply - The Fundamental Principles CourseIf someone says she is Long 100 Delta in Corn, then everyoneunderstands she has a risk exposure to Cornβs Spot Price such that if itrises by 1, then she will make a 100 profit. Similarly, if someone sayshe is Short 200 Delta in Microsoft, then everyone understands he has arisk exposure to Microsoftβs Spot Price such that if it rises by 1, then hewill suffer a 200 loss.Delta can be expressed mathematically as follows:π·πππ‘π Όπππππ‘πππππDelta communicates a Rate of Change (i.e., how quickly the PositionValue changes as the Spot Price increases by 1).Fig 3.120Rates of Change

Balbinder ChaggerA Rate of Change communicates how much something changes for agiven increase in some factor. It can be thought of as a gradient,communicating the degree of change. A flat, horizontal gradientcommunicates there is no change. An upward gradient communicatesthe change is in the same direction; a downward gradient communicatesthe change is in the opposite direction. The steeper the gradient is, thelarger is the reaction to an increase in the factor. Furthermore, a Rate ofChange value corresponds to a specific point. At another point, theRate of Change may be a different amount. These aspects are illustratedin Fig 3.1.Inflation is an example of a Rate of Change that we are all familiar with.It exemplifies the above aspects of Rates of Changes. Inflation tells ushow the cost of things reacts to the passing of time (usually 1 year). AnInflation value of, say, 3% tells us things costing 100 today will cost 103 in a year from now. The 3% value corresponds to now. Nextmonth (i.e., at a different point in time), Inflation could be some othervalue, say 2.9%.3.3Delta of a Long Spot PositionUnderstanding financial principles is often made easier by consideringactual things. The explanations in this course are based on Stocksbecause most people are familiar with them, and also because they pay adividend, which serves to illustrate some financial principles.Fig 3.2Long 1 Stock Delta vs Spot Price21

FREE SAMPLE Options Explained Simply - The Fundamental Principles CourseThe value of a Long Stock position is calculated as π’π π ππππ‘πππππThe value of a Long 1-share position at various Spot Prices is shown inFig 3.2. Each of the Spot Price increments is 100. When the SpotPrice is 0, the position value is also 0. As the Spot Price rises, thevalue of the position also rises. This signifies the Delta is positive(Long). We see in Fig 3.2 that the position value rises by a constant 100 for every 100 rise in the Spot Price (i.e., a dollar for dollarreaction). This signifies the Delta is 1 (or 100%) at every Spot Price(100/100). This is corroborated by a graph plot of the position valueagainst the Spot Price (Fig 3.3) showing the position value sits on anupward sloping straight line whose gradient is 1.We can prove mathematically the Delta value is 1 at a particular SpotPrice. A simple way to calculate the Delta at a particular observationpoint is to look at how the position value changes between two nearestavailable equidistant points either side of it; the observation point liesexactly in the middle of the two points. For example, to calculate theDelta at the 500 Spot Price, consider how the positionβs value changesfrom a Spot Price of 400 to 600, the nearest Spot Prices for which wehave values. This simple calculation is valid because the 500 Spot Pricelies exactly in the middle of the 400 to 600 Spot Price range.π·πππ‘π π·πππ‘π πππππππ’π π ππππ·πππ‘π 600 400 200 1.0600 400 200The Delta at the other Spot Prices in Fig 3.2 can be calculated in thisway too.Fig 3.4 shows the Delta of the Spot plotted against the Spot Price. It is 1 at every Spot Price.22

Balbinder ChaggerFig 3.3Long Stock Value vs Spot PriceWhen the relationship between two things (in this case, between a SpotPrice and a Position Value) remains the same over a range of values,then the relationship is said to be linear over the range. So, the Delta ofa Long 1-share position is linear and is 1. This applies to all Spottypes, not only to Stocks. Hence, the Delta of a Long 1 unit of a Spot islinear and 1.It follows the Delta of a Long 2-unit Spot position is 2 (or 200%),and so on for larger numbers of units. If someone says her holding in aStock gives her a 300 Delta exposure, then we can say the following: She is Long 300 shares (because the Delta of a Long 1 shareposition is 1).23

FREE SAMPLE Options Explained Simply - The Fundamental Principles Course If the Spot Price rises by 1, then she will earn a profit of 300.Fig 3.4Long Stock Delta vs Spot PriceWe can also say how her position value will react to any amount ofchange in the Spot Price of the Stock, not only to a rise of 1. Forexample, we can say the following: If the Spot Price falls by 1, then she will suffer a loss of 300. If the Spot Price rises by 20.5, then she will profit 6,150(20.5 300).When a positionβs Delta is linear, then the change in the positionβs valuedue to a Spot Price movement is explained completely as π’π π·πππ‘π πππ’π π·πππ‘π π πππ)Later, when we study Futures and Options, we will see Delta can takeon other values besides 1. Furthermore, we will see Delta can also benon-linear, meaning it can be a different value at different Spot Prices.24

Balbinder Chagger3.4Delta of a Short Spot PositionAs the Delta of a Long 1 unit Spot position is linear and 1, then itfollows the Delta of a Short 1 unit Spot position is linear and -1.The value of a Short Stock position is calculated as π’π π ππππ‘πππππThe β sign denotes the position is Short. The value of a Short 1 shareposition at various Spot Prices is shown in Fig 3.5.Fig 3.5Short Stock Delta vs Spot PriceEach of the Spot Price increments is 100. As the Spot Price rises, thevalue of the position falls (i.e., it becomes a larger negative number).Hence, the Delta is negative (Short). The position value falls by aconstant 100 for every 100 rise in the Spot Price (i.e., a dollar fordollar reaction). Therefore, the Delta is -1 at every Spot Price. This iscorroborated by a graph plot of the position value against the Spot Price(Fig 3.6) showing the position value sits on a downward sloping straightline whose gradient is -1. So, the Delta of a Short 1-share position islinear and is -1. Again, this applies to all Spot positions, not only toStocks.Fig 3.7 shows the Delta of the Spot plotted against the Spot Price. TheDelta is -1 at every Spot Price.25

FREE SAMPLE Options Explained Simply - The Fundamental Principles CourseFig 3.6Short Stock Value vs Spot PriceIf someone says his holding in a Stock gives him a -500 Delta exposure,then we can say the following: He is Short 500 shares (because the Delta of 1 Short Stock is-1). If the Spot Price rises by 1, then he will suffer a 500 loss.We can also say how his position value will react to any amount ofchange in the Spot Price of the Stock, not only to a rise of 1. Forexample: 26If the Spot Price falls by 1, then he will profit 500.

Balbinder Chagger If the Spot Price drops by 32.25, then he will profit 16,125( 32.25 500).Fig 3.7Short Stock Delta vs Spot Price27

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Balbinder ChaggerLesson 4ARBITRAGEIn this lesson, we learn what Arbitrage is and why it is important.Arbitrage is the concept of profiting by exploiting price imbalances.There are two types of arbitrages, as follows:1. Deterministic Arbitrage2. Statistical Arbitrage4.1Deterministic ArbitrageAn arbitrage opportunity is Deterministic if the profit from it can bedetermined from the outset with absolute certainty, i.e., there is no riskinvolved.For example, suppose a companyβs shares are trading for 10 on theLondon Stock Exchange and for 13 on the New York Stock Exchangewhile the / currency exchange rate is 1 1.2. As the shares are ofthe one and the same company, then their value ought to be equal,29

FREE SAMPLE Options Explained Simply - The Fundamental Principles Courseregardless of the location and currency. But, as it stands, they areunequal. The London 10 Spot Price implies the New York Spot Priceought to be 12, and the New York 13 Spot Price implies the LondonSpot Price ought to be 10.83. Instead of being equal, the Spot Priceshave spread apart by 1 ( 0.83), for some reason, and are imbalanced, asdepicted in Fig 4.1. The Spot Price in London is cheaper than the onein New York. The price imbalance may be due to some kind of marketinefficiency; perhaps some news has reached one location but not yetthe other. The reason is unimportant. The fact is the Spot Prices areout of line with each other, and the situation presents an opportunity tomake a certain profit of 1 ( 0.83).Fig 4.1Deterministic Arbitrage OpportunityWe can exploit this arbitrage opportunity by executing two Spot tradessimultaneously: one, buying the relatively cheaper London share; and theother, selling the relatively expensive New York share. The London trademakes us Long 1 share, for which we pay out 10 (equivalent to 12),and the New York trade makes us Short 1 share, for which we receive 13 (equivalent to 10.83). The

Jul 02, 2021Β Β· The trading Agreement is made (i.e., who will buy, who will sell, what will be traded, and the trade price). . FREE SAMPLE Options Explained Simply - The Fundamental Principles Course 6 . say we want to buy 100 shares in Apple. We call our stockbroker