Pricing Parameters and Ratios

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.