DERIVATIVE SECURITIES

 

Derivative Securities (or Derivatives) are financial instruments with contractually specified payoffs whose values are uncertain when contracts are initiated and which depend on, or derive from, the values of the underlying assets (stocks, indexes or commodities). There are many types of derivative securities and the most common ones are futures, forwards, options and warrants.

Derivatives are used to hedge risks, to lock in arbitrage profit and to reflect a view on the direction of the market. There are mainly three kinds of participants in the derivative markets, namely the hedgers, the speculators and the arbitrageurs. Hedgers are risk-averse and they use derivatives to avoid uncertainty in price movement. Speculators use derivatives to take advantage of price movement in which they are buying to profit from a price increase and selling to profit from a price drop. Arbitrageurs use derivatives to lock in a riskless profit by simultaneously buying and selling the same, or similar, financial products in different markets.

 

Futures

A futures contract is a legally binding agreement to buy or sell an underlying asset at a pre-determined price (i.e. the futures price) on a specific date (i.e. the settlement date) in the future. It is a standardized contract with specifications in the quality, quantity and delivery date. Futures contracts are traded on organized exchanges and they are usually guaranteed by the clearing house.

Futures contracts are marking-to-market daily at their end-of-date settlement prices. They are often settled by closing out the futures position prior to maturity, rather than requiring physical delivery of the underlying asset or final cash settlement. They can also be terminated by entering into an offsetting position, i.e. an equal and opposite position to the opened position.

Margins are an important aspect of futures markets. Any investor in the futures market is required to keep a margin account, which is adjusted daily to reflect the gains or losses that arises due to marking-to-market. There are two types of margins, namely, initial margin and maintenance margin. Initial margin is the total amount of margin required when a futures position is opened while maintenance margin is the minimum level at which the margin account must be maintained. A margin call will be issued if the margin account falls below the maintenance level because of the adverse price movement and funds must be added to bring the margin account back to the initial margin level.

The most common type of futures in Hong Kong is theHang Seng Index Futures(HSI Futures). Its contract months are the spot plus the next month, then the next two quarterly months. For example, if the current month is December 2000, the contract months of the HSI Futures will be January 2001, April 2001 and July 2001. The contract size of HSI Futures is the Hang Seng Index (HSI) times HK$50. The last trading date of HSI Futures is the next day to last business day of the contract month while the settlement date is the first business day following the last trading date. The settlement price of HSI Futures is the arithmetic average of 5-minute HSI on the last trading date, and the contract can only be settled by cash.

 

 

Forwards

A forward contract is a private agreement (i.e. not a standardized contract) between two counterparties to buy or sell an underlying asset at a pre-determined price (i.e. the forward price) on a specific date (i.e. the settlement date) in the future. Forward contracts are traded over-the-counter and they are not guaranteed by the clearing house.

Forward contracts are settled at the end of the contracts, rather than marking-to-market daily. They are usually settled in cash or by physical delivery of underlying assets, whereas futures contracts are usually settled by closing out the position.

 

 

Options

A option is a contract that gives the holder the right, but not an obligation, to buy or sell a fixed quantity of an underlying asset at a predetermined price (i.e. the exercise price or the strike price) on or before a given date (i.e. the expiry date).

 

Call Option - a contract that give the holder the right, but not an obligation, to buy the underlying asset at the strike price on or before the expiry date

Put Option - a contract that give the holder the right, but not an obligation, to sell the underlying asset at the strike price on or before the expiry date

American Option - a contract that give the holder the right to buy or sell the underlying asset on or before the expiry date

European Option - a contract that give the holder the right to buy or sell the underlying asset on the expiry date only

 

 

Some Basic Terms about Options

 

Option Premium - the price that the buyer needs to pay to acquire the right of an option in which the price is determined by the supply and demand of the option, i.e. the purchase price of an option

Intrinsic Value - a measure of the value of an option if immediately exercised

Time Premium - the amount by which the option price exceeds its intrinsic value

At-the-money - a term used to describe an option in which its exercise price is equal to the current trading price of the underlying asset

In-the-money - a term used to describe an option that has a positive value if immediately exercised

Out-of-the-money - a term used to describe an option that has no intrinsic value

Volatility - a measure of the variability of future stock prices

 

 

Some Basic Concepts about Options

 

 

Option Premium = Intrinsic Value + Time Premium

Intrinsic Value of a call option = Max [0, S - X]

Intrinsic Value of a put option = Max [0, X - S]

Time Premium for a call option = Call Premium - Intrinsic Value of a call option

= C - Max [0, S - X]

Time Premium for a put option = Put Premium - Intrinsic Value of a put option

= P - Max [0, X - S]

where S = the current price of the underlying asset

C = the current price of an associated call

P = the current price of an associated put

 

 

Factors Affecting Option Prices

 

There are mainly six factors affecting the price of an option: (i) the current stock price, (ii) the exercise price, (iii) the time to expiration, (iv) the volatility of the stock price, (v) the risk-free interest rate and (vi) the dividends expected during the life of the option.

(Note: The following factors are specified for those whopurchasethe options.)

 

Current Stock Price (S)

The higher the current stock price, the higher the value of the call options and the lower the value of the put options

 

Exercise Price (X)

The higher the exercise price, the lower the value of the call options and the higher the value of the put options

 

Time to Expiration (T)

The longer the time to expiration, the higher the value of both American call and put options as the options has a greater chance to move "in-the-money", whereas the value of both European call and put options does not necessarily increase with the time to expiration

 

Volatility of Stock Price (σ)

The higher the volatility of the stock price, the higher the value of both call and put options as increased volatility increases the chance of upside gaining whereas the downside loss is limited to the option premium paid

 

Risk-free Interest Rate (r)

For call options, the higher the risk-free interest rate, the lower the present value of the exercise price to be paid out when exercised, and thus the higher the value of the options.

For put options, the higher the risk-free interest rate, the lower the present value of the exercise price to be received when exercised and thus the lower the value of the options

 

Dividends (D)

The higher the present value of expected cash dividends from the underlying stocks, the lower the future stock price, and thus the lower the value of the call options and the higher the value of the put options

 

The most common type of options in Hong Kong is theHang Seng Index Options(HSI Options), which is traded in the Hong Kong Futures Exchange. Its quantity is 50 times of Hang Seng Index (HSI) and its expiry date is the second day to the last business day of the contract month. The settlement price of the HSI Options is the average of 5-minute HSI prices on the last trading date and the contract can only be settled by cash.

 

 

Warrants

A warrant is an option entitling the holder the right, but not obligation, to buy or sell an underlying asset (stock, index or commodity) at a pre-determined price (i.e. the exercise price) on or before an expiry date. The major difference between warrants and options is that warrants are issued by the company itself or financial institutions (e.g. investment banks) while options are traded by the market makers, which are appointed by the exchanges and they act as the intermediates between the buyers and sellers. Moreover, the expiry date of a warrant is usually longer than that of an option. A warrant may have a maturity of several years while an option may only have a maturity of several months.

 

Equity Warrants (or Company Warrants) and Covered Warrants are the two major types of warrants. There are also other types of warrants, e.g. Index Warrants and Basket Warrants.

 

Equity Warrants - warrants issued by the company that permits the holder to buy its common stocks

Covered Warrants - listed securities issued by investment banks, to provide an efficient tool to for the holder to manage his investment portfolio

Index Warrants - warrants on stock indexes, issued by either corporate or sovereign entities and guaranteed by an option clearing corporation

Basket Warrants - warrants on a group of stocks that is formed with the intention of either being bought or sold all at once to diversify the risk

 

Warrants are in two different forms: Call Warrant and Put Warrant. These two forms of warrants are also classified into two different styles: American Warrant and European Warrant.

 

American Call - give the holder the right to buy the underlying asset at the exercise price at any time up to the expiry date

American Put - give the holder the right to sell the underlying asset at the exercise price at any time up to the expiry date

European Call - give the holder the right to buy the underlying asset at the exercise price at the expiry date only

European Put - give the holder the right to sell the underlying asset at the exercise price at the expiry date only

 

 

Some Basic Terms about Warrants

 

Amount Outstanding - the total amount of warrants that have been issued

Conversion Ratio - the number of warrants required to exchange for one share of the underlying asset

Expiry Date - the date on which the warrant will expire

Gearing - the scale of exposure to the underlying asset

Implied Volatility - the volatility implied by the warrant price observed in the market

Last Traded Price - the latest price on which a warrant is traded

Parity Ratio - the ratio of the spot price of the underlying asset to the exercise price of the warrant

 

Premium - the percentage by which the stock price needs to move before reaching the break-even price of the warrant at the expiry date

 

 

 

(Note: Negative premium means that the warrant has a discount)

 

 

Warrant Valuation

Black-Scholes Pricing Model

 

Black-Scholes Pricing Model is used to calculated the theoretical prices of European call and put options. The theoretical price is the "fair" value of an option and it may be different from the market price of that option.

 

 

 


C = call price

P = put price

N(d) = the cumulative probability density of a standardized normal variable

S = stock price of current day

X = exercise price of the specific linked warrant

r = annualized risk-free interest rate

T = time to expiration

s = volatility of stock price

 

 

Delta

 

Delta is the change in the warrant price that results from one dollar change in the underlying asset price.

 

 

In other words, delta is the slope of the curve that relates the warrant price to the underlying asset price. For example, if the delta of a call warrant on a stock is 0.6, when the stock price changes by a certain amount (e.g. $10), the warrant price will change by about 60% of that amount (i.e.$6).

 

The delta of a call warrant is positive, implying that an increase in the underlying asset price would result in an increase in the call price. On the contrary, the delta of a put warrant is negative, implying that an increase in the underlying asset price would result in a decrease in the put price. The followings are the formulae to calculate the delta of a call warrant and a put warrant:

 

Delta of a call warrant = N(d1)

Delta of a put warrant = N(d1) - 1