Introduction to Derivatives

After completing this reading, you should be able to:

• Describe the over-the-counter market, distinguish it from trading on an exchange, and evaluate its advantages and disadvantages.
• Differentiate between options, forwards, and futures contracts.
• Identify and calculate option and forward contract payoffs.
• Calculate and compare the payoffs from hedging strategies involving forward contracts and options.
• Calculate and compare the payoffs from speculative strategies involving futures and options.
• Calculate an arbitrage payoff and describe how arbitrage opportunities are temporary.
• Describe some of the risks that can arise from the use of derivatives.
• Differentiate among the broad categories of traders: hedgers, speculators, and arbitrageurs.

The over-the-counter market is a decentralized trading platform, without a central physical location, where market participants use a host of communication channels to trade with one another without a formal set of regulations. The communication channels commonly used include telephone, email, and computers.

In an OTC market, it’s possible for two participants to exchange products/securities privately without others being aware of the terms, including the price. OTC markets are much less transparent than exchange trading.

Stocks traded in an OTC market could belong to a small company that’s yet to satisfy the conditions for listing on the exchange. The OTC market is also popular for large trades.

Advantages of OTC markets over exchanges include:

• There are fewer restrictions and regulations on trades
• The participants have the freedom to negotiate deals
• It’s cost-effective for corporates as service costs lower
• There’s better information flow between a market maker and the customer thanks to one-on-one contact

Disadvantages of OTC markets compared to exchanges include:

• There’s increased credit risk associated with each OTC trade
• Less transparency

Options, Futures, and Forwards

An options contract is an agreement between two parties to transact on an underlying security at a predetermined price called the strike price prior to some date called the expiration date. The option gives the holder a right but not the obligation to buy/sell the underlying at an agreed upon date at the strike price.

A call option gives the holder the right but not the obligation to buy the underlying asset at the strike price prior to the expiration date. A put option, on the other hand, gives the holder the right but not the obligation to sell the underlying asset at the strike price prior to the expiration date.

A forward contract is a non-standardized contract between two parties that specifies the price and the quantity of an asset to be delivered in the future. That it’s non-standardized implies it cannot be traded on an exchange. Instead, they are traded in the OTC market. One party takes the long position and agrees to buy the underlying asset at a specified price on the specified date, while the other party takes the short position and agrees to sell the asset on that same date at that same price.

A futures contract is a standardized, legally-binding agreement between two parties that specifies the price at which to trade a given asset (commodity or financial instrument) at a specified future date. Futures contracts can be traded on an exchange.

Futures contracts differ from forwards in several other aspects:

• Clearinghouse: The clearinghouse is an interposed party between the buyer and the seller which ensures the performance of the contract. In essence, futures contracts have no credit risk.
• Marking to market: Since the clearinghouse must monitor the credit risk between the buyer and the seller, it performs daily marking to market. This is the settlement of the gains and losses on the contract on a daily basis. It avoids the accumulation of large losses over time, something that can lead to a default by one of the parties.
• Margins: Daily settlements may not provide a buffer strong enough to avoid future losses. For this reason, each party is required to post collateral that can be seized in the event of default. The initial margin must be posted when initiating the contract. If the equity in the account falls below the maintenance margin, the relevant party is required to provide additional funds to cover the initial margin.

Calculating and Forward Contract Payoffs

Call Option Payoff

$${ C }_{ T }=max\left( 0,{ S }_{ T }-X \right)$$

Where:

$${ C }_{ T }$$=call option payoff

$${ S }_{ T }$$=stock price at maturity

$$X$$=strike price

To the seller, payoff =$$-{ C }_{ T }$$

The price paid for the call, $${ C }_{ 0 }$$ is also called the call premium.

Thus,

Profit to call option buyer =$${ C }_{ T }-{ C }_{ 0 }$$

Profit to the option seller =$${ C }_{ 0 }-{ C }_{ T }$$

Put Option Payoff

$${ P }_{ T }=max\left( 0,X-{ S }_{ T } \right)$$

Where:

$${ P }_{ T }$$=put option payoff

$${ S }_{ T }$$=stock price at maturity

$$X$$=strike price

To the seller, payoff =$$-{ P }_{ T }$$

The price paid for the put, $${ P }_{ 0 }$$ is also called the put premium.

Thus,

Profit to put option buyer =$${ P }_{ T }-{ P }_{ 0 }$$

Profit to the put option seller =$${ P }_{ 0 }-{ P }_{ T }$$

Forward Contract Payoff

The payoff to the long position is given by:

payoff=$${ S }_{ T }-K$$

Where:

$${ S }_{ T }$$=spot price at maturity

$$K$$=delivery price

The payoff to the short position =$$K-{ S }_{ T }$$

Payoffs from Hedging Strategies Involving Options and Forward Contracts

Hedging is the use derivatives like futures and options to reduce or eliminate financial exposure. Before delving further into hedging, it’s imperative to understand the following points:

• A long position/long exposure in a security, e.g., a stock or bond, means the holder of the position owns the security and will make a profit if the price of the security goes up.
• A long exposure in a futures contract means the holder of the position is obliged to buy the underlying instrument at the contract price at expiry. The holder will make a profit if the price of the instrument goes up.
• A long position in an option implies buying a call option or a put option. A long position in a call option means the holder will make a profit if the price of the underlying soars above the strike price, provided the difference between the price at that time and the strike price is greater than the premium paid. A long position in a put means the holder will make a profit if the price of the underlying falls below the strike price. It helps to lock in the value of an asset whose price the holder believes will decline.
• A short position in a security means the holder of the position borrows the security with the expectation of selling it at a profit and then repurchasing it at a lower price while returning it to the lender. The profit will be made in the face of an interim price decline. Conversely, the holder will make a loss if the price of the shorted security rises prior to repurchase.
• A short exposure in a futures contract means the holder of the position is obliged to sell the underlying instrument at the contract price at expiry. The holder will make a profit if the price of the instrument goes down. Conversely, they will make a loss if the price of the underlying rises dramatically.
• A short position in an option implies selling a call option or a put option. A short position in a call option means the holder makes a profit as long as the price of the underlying stays below the strike price. A short position in a put option means the holder makes a profit as long as the price of the underlying stays above the strike price, in which the put expires worthless, and the seller (writer) get to keep the premium.

How Hedging Works:

An investor with a long position in an asset can hedge the exposure by entering into a short futures contract or by buying a put option. An investor with a short position in an asset can hedge the exposure by entering into a long futures contract or by buying a call option.

A forward contract helps the hedger to lock in the price of the underlying security. Forward contracts do not need any investment at onset. However, the hedger gives up any movement that may have had positive results if they left the position unhedged. Let’s look at an example:

Suppose a U.S. based company is scheduled to receive $$£10 \quad million$$ in six months. The current exchange rate stands at $$1.32/£$$. The management is worried that the pound might depreciate against the dollar. It decides to hedge the exchange risk with a forward contract at $$1.3/£$$.

With the forward, the company will be guaranteed to receive $$13million\left( =£10m×1.3/£ \right)$$. Suppose the company does not hedge the position and the exchange rate in six months turns out to be $$1.25/£$$. The company will receive $$12,500,000$$. Suppose further that the company does hedge the position at $$1.3/£$$, and the rate turns out to be $$1.35/£$$. In this case, the company will still receive $$13 \quad million$$ but will be forced to give up the extra $$500,000$$ it would have received if it didn’t hedge the position in the first place.

Payoffs from Speculative Strategies Involving Futures and Options

Speculative trading refers to the trading of futures contracts without the intention of obtaining the underlying commodity. Speculators basically make bets on the market, unlike hedgers whose priority is to eliminate exposures.

Speculators are motivated by the leverage that comes with futures contracts in which no initial investment is required. All that’s needed is the initial margin required by the clearinghouse/exchange. The margin is no more than a percentage of the notional value of the underlying. The gains or losses associated with futures can be quite large, and payoffs are symmetrical.

Speculators trade in futures with the intention of reselling these contracts before maturity. They expect the futures price to move in their favor and therefore make a profit when selling the contracts. However, there can be no guarantees that the price will move in their favor, and therefore this trading strategy is also laden with risks. If the price moves against a speculator’s position, they could suffer substantial losses.

For options, speculators only need to part with the option’s price at the onset, which is often just a few dollars for 100 shares worth of the underlying. However, options have asymmetrical payoffs. Going long on options can bring in significant gains, but losses are limited to the option’s price paid.

Arbitrage Payoffs

Arbitrage opportunities exist when prices of similar assets are set at different levels. Therefore, an arbitrageur attempts to make a risk-free profit by buying the asset in the cheaper market and simultaneously selling it in the overpriced market.

For example, suppose $$ABC\quad stock$$ is trading at $$200$$ on exchange $$A$$ and $$198$$ on exchange $$B$$. If you buy one $$ABC$$ stock on exchange $$B$$ and simultaneously sell it on exchange $$A$$, you can make a risk-free profit of $$2$$ without any outlay of cash.

However, arbitrage opportunities are normally shortlived. The nature of efficient markets is such that market forces will push up the asset’s price in the underpriced market up while simultaneously pushing down the asset’s price in the overpriced market. At the end of the day, the asset will be priced equally in both markets.

• Market risk: There are no guarantees the market price will move in favor of the derivative trader. For example, an investor who is short a put option has no guarantees the price of the underlying will stay above the strike price, allowing them to keep the premium. The underlying’s price could as well fall below the strike, in which case the option buyer exercises the option, forcing the seller to buy a stock at a price that’s higher than its market price.
• Counterparty risk: There’s always the risk that the buyer, seller, or dealer will default on the contract. This risk is particularly prevalent in OTC markets where regulations are not as strict as in an exchange.
• Liquidity risk: Closing out a deal prior to maturity, e.g., in an American option which can be exercised before maturity, can at times be difficult. Even more likely, bid-ask spreads could be so large as to represent a substantial cost.
• Operational risk: There’s always the risk that a trader with instructions to use derivatives as a hedging tool will be tempted to take speculative positions, possibly in the hope of making a “kill’. Such a move can be disastrous for the firm.

Exam tips:

• The bid price is the “quoted bid,” or the highest price, which a dealer is willing to pay to purchase a security. The offer price is the price at which the security is offered for sale, also known as the “asking price.” The bid-ask spread represents the difference between the offer price and the bid price.
• All European options can only be exercised at maturity. American options, on the other hand, may be exercised any time between issue date and expiration.

Questions

Question 1

An investor enters into a short position in a $$coffee$$ futures contract at $$520.5$$. Each futures contract controls $$100 \quad bags$$. The initial margin is $$5,200$$, and the maintenance margin is $$4,700$$. At the close of trading on the first day, the futures price drops to $$512$$. Which of the following is the amount of the variation margin at the end of the first day?

1. $850 2.$500
3. $350 4.$0

Note that the question asks for the amount of variation margin from the perspective of the investor. Since the investor is short and the price fell, the first days’ position creates a profit and there is no variation margin. However, for the investor who is long, the loss is $$850\left( =520.5–512\times 100 \right)$$, which would bring the equity to $$4,350\left( =5,200–850 \right)$$ . And because this is well below the maintenance margin of $$4,700$$, an additional payment of $$850$$ must be made, by the party that’s long, to bring back the equity to the initial margin of $$5,200$$.

Question 2

A risk manager is worried that the price of gold will rise. He would like to hedge his position but is stuck between buying a futures contract on an exchange and buying a forward contract directly from a counterparty. The manager finds that the futures price is higher than the forward price. Both types of contracts would have the same maturity and delivery conditions. Assuming there’s no arbitrage, which of the following factors would explain this price difference?

1. The forward contract party is more likely to default
2. The futures contract is more liquid and easier to trade
3. The futures contract has less transaction costs compared to the forward contract
4. All of the above