Product Pricing

Derivative warrants have a “theoretical value” that may be very different from their traded (nominal) price. The theoretical value is the price of the derivative warrant calculated by reference to the issuer’s pricing model, taking into account all relevant market factors. 

The price of a derivative warrant (i.e. put/call warrant) generally depends on the price of the underlying asset. However, throughout the term of a derivative warrant, its price will be influenced by a number of other factors, including:

(a)  the exercise price of the derivative warrant;

(b)  the value and volatility of the price of the underlying asset (being a measure of the issuer’s expectation on the fluctuation in the price of the underlying asset over time);

(c)  the time remaining to expiry: generally, the longer the remaining life of the derivative warrant, the greater its value;

(d)  the interim interest rates and expected dividend payments or other distributions on the underlying asset;

(e)  the liquidity of the underlying asset;

(f)  the availability of, and demand for, the derivative warrant;

(g)  the issuer’s hedging transaction costs;

(h)  the creditworthiness of the issuer and/or its guarantor; and

(i)  in case of index warrants, the price and liquidity of the futures contracts relating to such index

Assuming other factors remain unchanged, the theoretical impact of changes in certain key factors on call and put warrants is illustrated in the table below:

* Please note that the table above only shows the theoretical relationship with the key pricing parameters. In reality, there are other factors affecting the price of a derivative warrant.

(a)  The price of a derivative warrant is not only affected by the price of the underlying asset but a range of other factors. This means that movements in the price of a  derivative warrant may not be proportionate, or may even be opposite, to the price movement of the underlying asset. For example, for a call warrant, if the price of the underlying asset increases, but the implied volatility of the price of the underlying asset decreases, the price of the call warrant may decrease as the drop in its implied volatility may offset an increase in the price of the underlying asset;

(b)  if a derivative warrant is deep “out-of-the-money” (e.g. when its theoretical value is substantially less than HK$0.01), the price of the  derivative warrant may be insensitive to any increase (in respect of a call warrant) or decrease (in respect of a put warrant) in the price of the underlying asset;

(c)  if the outstanding volume of a series of derivative warrants in the market is high, the supply and demand of the warrant may have a greater impact on the warrant price than the price of the underlying asset;

(d)  in respect of a call warrant, a decrease in time value may offset any increase in the price of the underlying asset, especially when the call warrant is close to its expiry where the time value usually decreases more rapidly; and

(e)  in respect of a put warrant, a decrease in time value may offset any decrease in the price of the underlying asset, especially when the put warrant is close to its expiry where the time value usually decreases more rapidly.

Time value is the value of a derivative warrant arising from the time left to maturity and is equal to the difference between the current derivative warrant price and its intrinsic value. The time value can be considered as the cost paid in return for the gearing effect. In general, the longer the time to expiry, the higher the probability that the underlying price will move in favour of the derivative warrant holder and hence a higher derivative warrant price. However, the time value of a derivative warrant will become zero when the derivative warrant has reached maturity. This is often referred to as the time decay of a derivative warrant.

“Outstanding quantity” means the quantity held by investors and is generally shown as a percentage. It is calculated by dividing the number of derivative warrants held by the market on a particular day (after closing) by the total number of derivative warrants issued. For example, if the number of certain derivative warrants held after closing on a particular day is 90 million and the number of those derivative warrants that had been issued is 100 million, then the outstanding quantity is 90%.

A product with a high outstanding quantity may be more vulnerable to the influence of the forces of market supply and demand. For example, when there is a selling pressure on a product, the price of that product may be squeezed (that is, brought down) by prevailing market forces. The price of the product may also be volatile due to short supply. As a result, its price may not follow the price of the underlying asset very closely.

Issuers are entitled to increase market supply of a derivative warrant where the outstanding quantity exceeds 50%, to prevent price fluctuations caused by short supply. The way this takes place is that the issuer applies to the Exchange for a further issuance of the product.

Further issuance has the potential to bring greater stability to the product price and minimise the chance of price fluctuations caused by the disequilibrium between supply and demand.

The entitlement ratio for a product is the number of such products required to be converted into a unit of the underlying asset at the strike price on the expiry date. Assuming all other factors affecting two different products are the same (underlying asset, strike price, expiry date, volatility etc.), their respective entitlement ratios would directly affect their respective values per unit. Generally, a product with a higher entitlement ratio would have a relatively small value per unit. However, in theory, the entitlement ratio would not affect the performance of a particular product, as it has been calculated into the effective gearing.

The premium reflects the degree by which the price of the underlying asset needs to move before reaching the break-even price of a product at expiry.

For example, if the premium of a call warrant is 10%, the underlying price should rise by 10% at expiry, in order to reach the break-even price.

You can calculate the premium based on the formula below (based on the payout formula at expiry):

These formulae can therefore be used as a reference to calculate the percentage by which the price of the underlying asset needs to move before reaching the break-even price of a derivative warrant at expiry.

This seems unreasonable as the call warrant price should at least be equal to its intrinsic value, i.e. the excess of the prevailing market price of the underlying stock over the exercise price of the call warrant.

While in most cases a call warrant does trade above its intrinsic value, this does not mean that the intrinsic value must be the minimum value of a call warrant. As explained below, it is possible for a call warrant to trade below its intrinsic value.

Holding a call warrant differs from holding the underlying stock, especially since the holders of the call warrant are not entitled to receive any dividends that might be declared by the underlying stock. In this particular case, the underlying stock was due to announce its annual results in late March. Based on practices in previous years, the underlying stock is likely to go ex-dividend in mid-April. With an expiry date for the call warrant in late April, the market price of the underlying stock would be the ex-dividend price in determining the payout of the call warrant on that expiry date. This would result in a lower payout to call warrant holders than it otherwise should. Although the final dividend that the underlying stock would declare was still unknown in mid-March, it was widely anticipated that the dividend would be no less than $1.5. It was not unreasonable for potential investors and the liquidity provider to deduct the dividend element when pricing the call warrant. 

Delta is the ratio of the change in the derivative warrant price (after adjusted by the entitlement ratio) to the change in the underlying asset’s price.

Delta normally ranges between 0 and 1 for call warrants and 0 and -1 for put warrants (the negative sign shows the opposite directional movement to the underlying). In general, at-the-money call and put warrants have a delta of approximately 0.5 and -0.5 respectively. In-the-money derivative warrants will generally have a higher delta than out-of-the-money derivative warrants with the same underlying asset and maturity. For example, a call warrant with a delta of 0.1 is generally a deep out-of-the money derivative warrant, whereas a call warrant with a delta of 0.9 is generally a deep in-the-money derivative warrant. Vice versa, a put warrant with a delta of -0.1 is generally a deep out-of-the-money derivative warrant, whereas a put warrant with a delta of -0.9 is generally a deep in-the-money derivative warrant.

“Gearing” means the relationship that the cost of the underlying asset bears to the cost of a  derivative warrant. For example, if the gearing for a particular derivative warrant is 10 times, then the investment cost of that derivative warrant is 1/10 of the underlying asset.

However, in the case of a derivative warrant this only relates to the initial cost of the underlying asset and the initial cost of the derivative warrant. It cannot be used later to reflect the dynamic relationship between the price of the underlying asset and the price of the derivative warrant over time. “Effective gearing” of a derivative warrant is calculated by multiplying the gearing and the delta of the derivative warrant (adjusted with entitlement ratio).

Effective gearing is a better measure of the percentage change of a derivative warrant with a 1% change of underlying asset. For example, if the effective gearing is 10 times for a call warrant (and we assume other factors remain unchanged), when the price of the underlying asset rises by 1%, the theoretical price of the call warrant price should rise by 10%. Similarly, when the underlying asset falls by 1%, the theoretical price of the call warrant price should fall by 10%.

However, effective gearing should only be used as a reference as it will change over time given other factors, such as the underlying price, delta, gearing, time decay and implied volatility, also change.

A number of other factors affecting the price of the derivative warrant may also change over time and, therefore, a mere rise in the underlying asset’s price may not necessarily lead to a corresponding increase to the extent of the effective gearing, or to any increase at all in the derivative warrant’s price.

Implied volatility represents the anticipated level of volatility of underlying assets over the remaining life of a derivative warrant, as reflected in the price of the derivative warrant.

Implied volatility is one of the factors influencing the price of a derivative warrant. For example, assuming other factors remain constant, when implied volatility of a derivative Warrant decreases, its price should theoretically also go down, and vice versa. The movement of implied volatility will always cause a same directional movement in the price of a derivative warrant, and implied volatility is commonly used as a measurement to compare the expensiveness of a derivative warrant with products of similar terms.

Implied volatility is a key parameter in the issuer’s pricing formulae that cannot be observed directly. However, issuers can estimate the implied volatility based on:

(a)  the historical volatility of the underlying asset;

(b)  the implied volatility of the listed and OTC options based on market data; and

(c)  the issuer’s market expectation and cost of issuing the derivative warrant.

Implied volatility level of derivative warrants varies between issuers because each issuer may hold a different market expectation on a particular underlying asset from other issuers and has different issuing cost. 

Volatility is determined by annualised statistics measuring changes in price of its underlying asset: the greater the fluctuations, the higher the volatility.

“Historical volatility” is a measure of underlying price fluctuations over a certain period in the past. You may obtain information on historical volatility of the underlying asset by subscribing to the data provision service of a market data information provider.

Implied volatility of a derivative warrant has a close relationship with the implied volatility generated by OTC and listed options.

After an issuer sells a derivative warrant, it generally needs to hedge against the risks arising from that issuance through different channels: two of those channels are OTC options and listed options. OTC options are options that are traded on a bilateral basis outside of the trading facilities provided by any exchange. Usually, the counterparties are institutional professional investors, such as investment banks. Listed options are those traded on a trading facility such as the Exchange.

If the implied volatility of an OTC option or a listed option is moving downward, the implied volatility of a related derivative warrant may also move downward. On the contrary, if the implied volatility of an OTC option or a listed option is going upward, the implied volatility of the related derivative warrant may also go upward. Therefore, variations in the implied volatility of an OTC option or a listed option may indicate a trend in the implied volatility of related derivative warrant. 

OTC options are bilateral contracts traded privately between two participants, off-exchange. As a result, there is no public information available for the implied volatility of an OTC option.

You may obtain information on the implied volatility of a listed option by subscribing to the data provision service of a market data information provider.

When a listed company announces its financial results, it will also generally announce whether dividends will be paid.

Whether or not this affects the price of a related derivative warrant depends on whether or not dividends were expected and, if so, at what level and on what date. This is because the issuer considers past records of dividend distribution and the dividends expected by the market, when calculating the derivative warrant price.

If the dividend distribution and ex-dividend date are as expected and other factors remain constant, theoretically, the dividends should not affect the price of the derivative warrant.

Under normal circumstances, a derivative warrant linked to shares of a company will be adjusted if there is a capital adjustment of those underlying stocks (such as bonus issue, rights issue and restructuring event or spin-off / merger / consolidation). Specifically, an adjustment will be made to the entitlement ratio according to terms specified in the relevant listing documents.

In the case of a merger/consolidation, an adjustment will be made to the entitlement ratio of the derivative warrant of the company being merged or consolidated with. If the merger/consolidation results in an extinguishment of the current underlying, such underlying of the derivative warrant will change from the original underlying to a surviving/new underlying. Where there is a surviving company, no adjustment will be made to the derivative warrant of the surviving company.

Where the effective date of the adjustment occurs after the ex-entitlement date of the underlying stocks (such as in the case of spin-off), no adjustment will be made to those derivative warrants that expire in the interim period.

It is possible that trading of shares of the entities undergoing a merger may be suspended for a period of time. The Listing Rules require suspension of derivative warrants where the underlying stock is suspended. When this happens, the value of derivative warrants may be adversely affected due to time decay during the suspension period.

Under normal circumstances and for the purpose of calculating the value of the rights attached to the spin-off company, issuers will use volume-weighted average price (VWAP) of those auto-matched trades of that company on its first day of listing as the basis of adjustment. The adjustment will take effect from the day following the listing date. Investors should note that no adjustment will be made to those derivative warrants that expire before the effective date of the adjustment.

A call warrant is a short-term trading instrument with a gearing effect, it could magnify your loss relative to the underlying performance.

In addition to the underlying price, the liquidity provider’s quote also depends on a number of other factors.  Assuming all other factors remain constant, although the underlying price went back to HK$50 from HK$48, it is likely that the increase in the underlying price was offset or even outweighed by the decrease in the implied volatility of the call warrant, hence lowered the call warrant price.

The issue price of a call warrant is determined based on the market factors prevailing on the launch date of a warrant.  On the first trading day of the call warrant (being 3 trading days after the launch date), it is possible that substantial changes have occurred in respect of the market factors affecting the price of that call warrant.  

In addition to the terms of the call warrant (i.e. underlying, expiry date and strike price), its price also depends on a number of other factors which are based on different pricing assumptions adopted by individual issuers (e.g. different implied volatilities, interest rate, expected dividends, etc.).   Moreover, even with identical terms, different call warrants may have a different level of market participation and outstanding amount, which may affect the warrant price to a different extent.  Accordingly, the prices of call warrants with identical terms issued by different issuers may vary.

It is likely that the HK$0.01 last traded (nominal) price could have been brought down a while ago and does not reflect its prevailing theoretical value before the rally of the HSI, hence it is not the best reference to gauge the actual performance of the call warrant. 

It is particularly the case for a short term and deep out-of-the-money call warrant. Despite the HSI rallied more than 3%, the warrant is still out-of-the-money with short time to expiry, hence its prevailing theoretical value after the rally of the HSI is still below HK$0.01. 

The liquidity provider is not required to provide quote when the theoretical value of the warrant is less than HK$0.01.

HSI call warrants are not solely priced based on HSI index. They are mainly priced based on HSI index, interest rate and expected dividend. Since HSI futures contract reflects the value of HSI index, interest rate and expected dividend, the pricing of the HSI call warrants is generally priced based on HSI futures contracts.

Liquidity providers can provide bid and ask quotes at the pricing level they deem fair by reference to the theoretical price of the call warrant provided that they comply with the maximum spread requirements. The bid and ask spread may change from the time to time according to the prevailing market conditions affecting the underlying asset such as hedging costs and liquidity, spread and volatility of the relevant hedging vehicles.  Therefore it is possible that their quotes will not match your expected price levels due to the widening of the bid and ask spread.

The closing price of the call warrant and the underlying was as below.

This could happen because:

(a)  some other pricing factors affected the call warrant price (e.g. volatility, expected dividend, time decay, etc.);

(b)  the market closing time of the call warrant and the underlying security was different. Being an eligible security under the closing auction session, it continued to trade in the closing auction session which ended at 4:10 p.m. while the trading in the call warrant ceased at 4:00 p.m. In this case, due to the 10 minutes closing time gap, direct comparison of closing price of the call warrant and the underlying security might not be appropriate and meaningful, or

(c)  the closing price of the call warrant might not reflect the quote price of the liquidity provider. In this case, quotes of the liquidity provider might have moved in line with the underlying but were not reflected in the closing price of the call warrant.The closing price could be (1) calculated based on other exchange participants’ trades and quotes; or (2) carried forward from previous days.

The entitlement and exercise price of the call warrant will be adjusted according to the following formula:

Adjusted entitlement = Adjustment factor * E

Adjusted exercise price = X / Adjustment factor

Where

• Adjustment factor = 1 + N
• E:  Existing entitlement immediately prior to the bonus issue
• X:  Existing exercise price immediately prior to the bonus issue
• N:  Number of additional shares received by a holder of existing shares for each share held prior to the bonus issue

In this case,

• Adjustment factor = 1+ 1/10 = 1.1
• Adjusted entitlement = 1 * 1.1 = 1.1 shares
• Adjusted exercise price = HK$12.28/1.1 = HK$11.164 (rounded to the nearest HK$0.001)

The purpose of the adjustment is to ensure that as far as possible, the theoretical price of the call warrant remains unchanged immediately before and immediately after the adjustment. Assuming all factors being equal, the theoretical price of the call warrant will remain unchanged.