Since the city of London and Wall Street became hooked on hiring ‘Rocket Scientists’ in the 1970s, hundreds of different derivatives have been invented. Some are ‘path dependent’, the financial equivalent of betting that Manchester United will be at the top of the league for the entire first half of the season, will then fall back out of the top three and end up finishing second. Don’t be put off by this, or by the various Greek letters uses to describe the way that a derivative responds to changes in eg volatility, interest rates, the underlying security, ‘time decay’, etc. You don’t need to know ‘the Greeks’ or the Black-Scholes option pricing model.

Black-Scholes is great as barrier that separates ‘the professionals’ from the rest of us.  That's how ‘the grown ups’ prefer it: like training for the priesthood, you should spend years at the top of a mountain before being ready for ‘enlightenment’.   But derivatives are not inherently complex.  A child in their school playground talking about sweets or football cards is probably familiar with the main types of financial & derivative transactions:

‘Cash’: You have something (perhaps a stock, or a bond), and I agree to buy it in return for cash that I pay you.  As soon as the agreement is made, payment is due [  This used to take 3 days to process, but with online transactions it may be a bit faster.  Where there is a delay, it will always operate in favour of institutions and against the private investor.  When you are the buyer, you as a private individual will need to have cash on deposit in order to place the order (ie you don’t get 3 days credit), but when an institution buys from you…..].  In the playground, you have a Gary Linekar football card, I agree to buy it for 5p: I hand over 5p and you hand over the card.  Deal done and delivered

Futures / forwards: Binding commitments to buy/sell something on a particular date for a price fixed now.

I want or need something, but not immediately (perhaps because it has not yet been made). I don’t want to wait until when I need it (or it is made), and just buy then at whatever the price may be, because the price may have gone up, so I agree now to buy it at a time in future.  If I am Santa Claus, and I know that I will need a lot of reindeer food in December, then, if I see a ‘Special Offer’ I may want to order all I need, rather than risk paying over the odds.   Booking your holiday air tickets well in advance, to avoid the higher priced usually charged when buying tickets for immediate travel, is an analogy, but not an ideal one as, when buying air tickets early, you have to pay at the time of booking.  The financial and commodity futures markets don’t force buyers to pay until the delivery date.  In the school playground this amounts to ‘When I get my pack of football cards next Wednesday, I will sell them to you for £3.00’

Option: Paying a fee up front for the right to buy/sell something in future for a set price, if you want to, but not being obliged to proceed if you don’t.   If I might want to buy or sell something in the future, I can buy an option that lets me purchase it at a pre-determined price (known as the ‘Strike price’). Lets say that I am Santa, and I have a farm on which I am growing a crop of reindeer food, and that the crop should be enough for my own needs, with a bit left over that I can sell.  But about one year in every seven, my crop fails, so I need to buy in reindeer food to feed Rudolph and the others.  Unfortunately, in years when my crop fails, if it is due to flooding, lots of other farmers’ crops will also have failed, and the price of reindeer food will shoot up.  So, I want to be able to buy reindeer food at the normal (non flood) price, for this insurance policy, I pay a fee to a reindeer food merchant.  Six years out of seven, the merchant pockets my fee, but that’s OK, I can afford the insurance.  And when the flood comes, I can still afford the reindeer food needed to keep the show on the road (or in the air) and get the presents delivered.  The insurance policy is known as a ‘call option’: the right (but unlike the situation with a futures contract, not the obligation) to buy something at a price fixed in advance.  The other type of option is known as a ‘put option’: the right to sell something at a price fixed in advance.

In the playground, only call options are common: I pay you £1.00 now for the right to buy for £3.00 your packet of football cards from you next Wednesday after you have opened them and we know the players (I really need the rare Lionel Messy card, so I want to be able to buy it if you get one, but if you don’t, I am not interested in the others).

Swap: This really is just like a playground deal, an agreement to swap one thing for another.  If I am Santa and I realise that my land is better suited to growing soy beans rather than reindeer food, I might plant soy beans and agree to swap them for reindeer food.  Aside from the value of what is swapped, the main contrast with a child’s exchange of sweets or cards, is that Financial & commodity swaps tend not to be for a single swap.  A swap may involve monthly or quarterly exchanges for one or more years.  In the playground, the agreement may be shorter lasting: My parents always give me a packet of sherbet lemons as my weekly sweet ration, your parents always give you liquorice allsorts, we agree that for the next month, every Friday I will give you a sherbet lemon and you will give me a liquorice allsort (but not the aniseed jelly ones because I don’t like them).

Convertibles: Buy this pack of football cards from me for £3.00 and, if, on opening it you don’t like the cards, I will take them back and give you a pound of Sherbert Lemons instead.  

A swaption is an option to buy/sell a swap. The derivative element of a convertible is actually just an option to do a one-off swap, what makes the convertible more than just a flavour of swaption (for some reason derivatives are often attributed food-like qualities; different types are referred to as ‘flavours’, a simple put or call is called a ‘plain vanilla’ option), is that when you buy a convertible you get both the derivative bit (the option to swap the pack of football cards for a pound if sherbert lemons) and a real thing (the packet of football cards)

Option values

Before casting an eye over the things that drive the value of an option, lets start with some financial history as a cautionary tale.

You don’t need to know about option valuation models in order to make wise investment choices. Unlike macroeconomics, which you can omit because its predictions are seldom better than guesses, option pricing models do produce valuable predictions that are usually right ....... up until the moment they are not (see below)

Rather than put the warnings into the end of the chapter in a ‘How not to lose money on derivatives’ section, or into the chapter on strategy, it is worth looking at warnings from history, before, rather than after, talking about option pricing. Because, the more time you spend learning about pricing & complex formulae, the greater the risk of forgetting that ‘the map is not the territory’ (see surrealist artist Magritte’s ‘This is not a pipe’). For an investor, possessing this knowledge may create the risk of pursuing the financial equivalent of US Secretary of State Madeline Albright’s rhetoric to the US chiefs of staff: “What's the point of having this superb military that you're always talking about if we can't use it?”. Don’t be like the politician who thinks it is a waste to just have an army on standby as a deterrent to enemies who might invade, or to defend the country in the last resort. By all means add to your intellectual defensive forces by learning about option pricing, but keep in mind that those models can break down when they are most needed. In calm markets they can be a great approximation, but when financial waters get stormy the model may tell you to chart a course which will take you to the bottom of the sea.  So don’t think you need to use a model just because it is there & you have learned it.

A little history

Valuing options used to be largely down to guesswork until two mathematicians, Fischer Black and Myron Scholes, came up with a clever model that used calculus to provide a ‘scientific’ valuation.  Black had lost money when he used his theories as a basis for investment in the 1960s, so it was in academia (the University of Chicago) that he and Scholes refined their model. The Black-Scholes option pricing model was published in 1973, and immediately became the industry standard. It was loved by the newly opened Chicago Board of Options Trading (CBOT) as the scientific approach gave respectability to their products, and by Hewlett Packard which made the expensive programmable pocket calculators that could handle the formula. Because the Nobel committee often like ideas to stand the test of time, they waited until 1997 to award Scholes a Nobel prize for economics for the model (Black had died in 1995 and so could not share the honours).

In the twenty four years between 1973 and 1997 Black and Scholes had found they could earn rather more money on Wall Street that at the University of Chicago. When he received the honour in 1997, Scholes was three years in to his role as a founding partner of the hedge fund Long Term Capital Management (LTCM), they had been three years of great returns. The year after the Nobel prize, 1998 saw the Asian financial crisis. Asia has long since bounced back, but Scholes’s reputation and LTCM were not so lucky. Scholes’s model did not allow for such events (which come along with depressing regularity every decade or so: the 1973-4 crash, 1987 Black Monday, the 1998 Asian crisis, the 2000-1 dot com bubble bursting, the 2008-9 credit crunch, etc) were somehow absent from the model, and LTCM suffered multi-billion dollar losses. It was bailed out because its trillion dollar trading position might have undermined the financial system had the business just been allowed to fold.

It is easy to see LTCM’s failure as a modern incarnation of the cycle well known to the ancients: Hubris followed by Nemesis. That is part of the picture, and as is LTCM’s over-leveraging (those trillion dollars of trades were underpinned by under $5 billion in equity), but LTCM’s fatal flaw was that it continued to believe its own models when the real word was screaming at it that the models could not be right. The managers at LTCM were running what they believed was a low-risk arbitrage strategy with minimal chance of losses. When the trading screens started to show large and growing losses, instead of thinking ‘we must have made a mistake, let’s get out while we can’, they probably thought ‘Scholes’s strategy must be right, his model has stood more than 2 decades of use throughout the industry, he won a Nobel prize for it, for goodness sake, if the model says things will soon revert to normal then we just need to hold on for the bumpy ride until it comes back to business as usual’.

Myron Scholes is much much clever than I am, and almost certainly much cleverer than you too. If he can blow up so spectacularly, I am going to tread carefully and embrace my inner coward. When staring reality in the face, rather than stick to my guns, I will conjure up a black and white clip of Bob Hope squaring up to an adversary saying ‘These are my principles, and if you don’t like them...... I have others’

A little knowledge can be a dangerous thing, but in derivative finance, lots and lots of knowledge can also be pretty dangerous. So, as I have failed in my attempts to write a ‘Black Scholes primer for intelligent twelve year olds’, and I don’t work on commission selling HP programmable calculators, I am going to skip the options valuation primer & all attempts at quantative analysis (ie things that will allow you to hang your hat on a particular number) in favour of a qualitative chat about what makes options cheaper and what makes them more expensive.

Back to option values

Strike Price: The biggest determinant of an option’s value is likely to be its ‘strike price’ relative to the prevailing price of the item. If a new Ferrari retails for £95,000, an option to buy one for £100 is going to be a lot more valuable than an option to buy one for £100,000.

While the ability to buy a new Ferrari for £100 has an inherent cash value of the £94,900 discount this represents relative to the list price, the ability to buy it for £100,000 is valuable only insofar as the list price might rise from £95,000 to something above £100,000. This is called the ‘time value’ (or ‘Hope value’). If the option is valid for five or ten years, then that time value may be quite large. Ferrari prices might go up by 10% a year. But if the option is only valid for 3 months, it’s value will be much less: at most it might protect against Ferrari putting up the price once during the period.

Strike Price Terminology

If Reindeer Food is currently £100/tonne then an option to buy (call option) or an option to sell (put option) at £100/tonne is said to be ‘At the money’. If you owned such an option, it would only become valuable if prices changed before the option expired. It’s entire value is ‘Time Value’


Options are known as ‘in the money’ if they let you get a better price than the current market price. Such as being able to buy at £90/tonne or sell at £110/tonne. When an option is ‘in the money’ its price is divided into the ‘cash value’ (in this case the £10/tonne profit that could be made buy dealing at the option strike price rather than the prevailing price) and the ‘time value’ (the value of having time during which to make the choice about buying/selling)


Options are said to be ‘out of the money’ if the price they allow you to get is worse than the prevailing price. Such as being able to buy at £110/tonne or sell at £90/tonne. Although being able to buy at £110/tonne might seem uninteresting when reindeer food is currently £100/tonne, if there is a risk of the price shooting up to £500/tonne, the £110/tonne option can be very useful indeed.

When I was growing up, ‘At The Money’ (ATM) call options went up/down in value by c60% of the change in price of the underlying asset, and Put options by -40% of the change.  But interest rates were higher then.   With interest rates close to zero, the +60%, -40% historic figures do not apply, and we almost see +50%, -50%  (perhaps +50.05 Vs -49.95).  Younger readers, and those expecting continued QE, may want to see +50% (call), -50% (put) as the normal/typical correlations.     The sum of the absolute values (ie ignoring the -ve on the put correlation) should add up to 100%, this applies whether it is +60%, -40% or +50.05%, -49.95%.

But, for the sake of illustration, I will work on the ‘old’ paradigm of ATM call options going up/down in value by c60% of the change in price of the underlying asset. So if a three month call option with a strike price of £100.00 is priced at £5.00 when the underlying price is £100.00, if that underlying price falls to £99.00 the option would be worth £4.40. And if the underlying price rises to £101.00 the option would be worth £5.60. As the underlying price rises, call gets more and more (said to be ‘deeper’) into the money, the correlation between changes in the underlying price and the option value increases until it becomes almost 100%. If the underlying price became £1,000.00 then the option price would probably be something like £901.00 Of this £900.00 is the amount by which it is in the money, the ‘cash value’, and £1.00 is the ‘time value’. As options get deeper into the money their value starts to be ever more responsive to changes in the underlying price. In this case, the change in option value will have become well over 90%, perhaps 99%, of the change in the underlying value. An call option with a strike price that is 10% or less of the prevailing price is like a map whose scale is almost 1:1.

When a put option is ‘at the money’ it used to typically go up/down in value by -40% of the value of any change in the underlying price. So if a three month put option with a strike price of £100.00 is priced at £4.00 when the underlying price is £100.00, if that underlying price falls to £99.00 the option would be worth £4.40. And if the underlying price rises to £101.00 the option would be worth £3.60

Cost of Carry’: if Reindeer food can be stored under a tarpaulin without risk of spoiling, then I will be happy to buy reindeer food in advance if I can get a good deal, as it is cheap to keep until I need it. If Reindeer food must be kept in an atmosphere with under 5% humidity and at a temperature between 2 degrees and 5 degrees centigrade to avoid it spoiling, then I am going to be less keen on buying bails of it before I need them, and so the option to make the purchase just in time is more valuable. Most financial assets don’t have a big cost of carry.

How much prices vary over time. If Reindeer food costs £50/tonne when there has been a bumper harvest but £100/tonne when flood or drought has created a poor harvest, then the potential value of an option (whether it is to buy or to sell) will be lower than would be the case if a poor harvest might see £500/tonne prices. The range over which prices vary (£50 to £100 OR £50 to £500) is called ‘Volatility’, the word comes from The Latin ‘Volo: To fly’ literally the ability of a price to fly away.

The interest rate. Interest rates are important as, if interest rates are high, it may be worth delaying your purchase of the underlying thing (reindeer food) while you use the money to do something else. If it is January and you already have the reindeer food you need for December, and the market price is £50/tonne, but you can get a cheap option to buy it (a call option) in December for £55/tonne, it matters what you could do with the £50 over the year. In the 1970s and early 80s, with interest rates of 15% a year, if you sold the reindeer food in January and put the £50/tonne on deposit, you would earn £7.50 interest by the end of the year, so you could still pay £55/tonne to buy it again in December and make a profit if the option cost you under £2.50/tonne (and if you were definitely needing the reindeer food in December you could offset the cost by selling a put option as well as buying a call. This is a ‘synthetic forward’ (If you sell an at-the-money put option on a tonne of reindeer food, and the price of the reindeer food goes down, then the person who bought the option will want to hold you to the contract and force you to buy the food.  Thus if the price of reindeer food is over £50/tonne you will choose to exercise the call option you have bought, and will buy at £50/tonne from the person who sold you the call, but if the price is under £50/tonne you will be forced to buy at £50/tonne from the person to whom you sold the put).

European Vs American Options

An American option can be exercised at any point during its life.  A European option can only be exercised at the defined expiry time.  As, until the expiry, an option has both a time/hope value as well as an intrinsic value, if you own a American option, and want to exercise it before its expiry, you are probably better off selling the option (you will usually get more than just the intrinsic value).  This means that, most of the time, the distinction between European and American options is academic.  But, as is so often the case, ‘most of the time’ may be fine, but, when it matters, the distinction can be hugely significant.  On 20th April 2020, as the Corona virus panic shut down the world, and people stopped using so much oil for transport, and the factories that used oil-based products showed down/shut, the world had spent some weeks producing more oil than it could use.  Storage facilities were full, people scrabbled to find where to put the oil being produced, so much so that the price of oil turned negative.  People holding futures contracts to buy oil in May were committed to taking delivery on 17th May 2020, and, with nowhere to put it, ended up selling the contracts for a negative amount: in effect paying someone $40 per barrel to take the oil off their hands (each futures contact was for 1,000 barrels, each of 42 Gallons, so rather more than would be practical to load into ones garage and wait for the vius to pass).   These negative prices did not last long, partly because, with a little time, storage could be created/resurrected, old oil tankers were pressed back into service as floating storage, etc.  Futures for delivery on 17 June 2020 never had a negative price, by 28th April 2020 you could buy oil for delivery on 17th June at $12 per barrel.  So, if you had an European-style put option to sell oil, with an expiry of 17 June 2020, it would not have been nearly as useful as an American-style option would have been.  The American option would have allowed you to be paid $40/barrel by someone who couldn't store their 1,000 barrels that arrived on 17th May 2020, but you would have no storage problem, because you could exercise your 17th June 2020 put option a month early.

Cash Settled Vs Physical settlement

In the playground, our options almost always involve physical settlement: there is a handover of football cards, or sweets.  Commodity options to buy oil, wheat, or gold, are also like this.  But there are some options (and futures) that are more like a bet on a sporting event.  I don't go to Ladbrokes and say ‘I will give you £100, when you deliver an Oxford win at the Boat race’, the boat race is an external event that neither I nor Ladbrokes control, we are merely spectators.  It is the same (or should be the same, if there is no corrupt manipulation) with an index option:  If the contract is for £10 per point, the strike value is 5,500, and the index closes at 5,650 when the option expires, then the difference of 150 points means a cash payment of £1,500

More risk (more fun?), or cautious risk management?  

Derivatives are rather Jekyll & Hyde.  Santa can use derivatives to reduce the risk from a bad harvest, or re-balance production if his fields are not suited to reinder food.  Or you / I, who have no need for reindeer food, could use the same derivatives to place bets, with the price of reindeer food serving as an alternative to  the 4.15 at Haydock Park.  

If  Santa loses money on his derivatives, thats no problems.  Its like 'losing money on your car insurance': you didn't have an accident, and are fine with that.

But those of us not in Santa's position, probably use derivatives for speculation, and use Leverage (‘gearing’ as we used to call it in London, until we admitted linguistic defeat and accepted the Wall Street term) to magnify our risk.

Leverage is great when things are going well. If you have £100,000 and expect house prices to go up, rather than just buy a house for £100,000 you could put down £100,000 collateral and agree to buy £1,000,000 of property in 12 months time (a futures contract). If prices go up by 5%, then instead of making £5,000 on your ‘boring’ £100,000 house, you will make £50,000 on your £1,000,000 futures contract. But if prices go down, the leverage works against you. A notional 5% £5,000 loss on the £100,000 house turns into a £50,000 loss on the £1,000,000 futures contract, half your capital is gone. And if prices fall by more than 10% you are not only wiped out, you are in debt. LTCM had derivatives contracts with a face value of $1 trillion ($1,000,000,000,000) underpinned by under $5 billion ($5,000,000,000) in equity. Let’s cancel out nine zeroes and we get $5 of equity with $1,000 of exposure. That’s leverage of 200 to 1. In LTCM’s case it wasn’t quite as bad as that sounds, as some of the positions offset each other: like agreeing to buy ten £100,000 apartments and sell one £1,000.000 mansion: but the point is that leverage reduces your margin for error. It is particularly hazardous when markets are volatile and irrational: you might be absolutely right about multiple small apartments being a sounder investment than one McMansion, but if most apartment buyers need mortgages & the government tells banks to make their lending criteria more restrictive (eg only lend 3 times income when previously they had lent 5 times) the week before you have to sell your apartments, you could come unstuck.