Friday, 29 February 2008

Analysis of Warrant Data (Part 8)

Today is the 29th of February 2008. I suppose you know this day only comes once every four years. This year is a leap year. I am not too sure if you know there is also something known as the leap century which occurs once every four hundred years. Something interesting about the leap century is that the 1st of January of a leap century always falls on a Saturday. You can easily verify this with a perpetual calendar if you are interested. The last leap year was 2004 and the last leap century was 2000. We have to wait for another four years till 2012 for another leap year and 2400 for another leap century. I do not think I will see that year coming.


In warrant, there is the effect of time as well and you do not have the luxury of another four years. The Greek used to measure time is known as theta. Theta, also called time decay, measures the rate of change in the price of a warrant as its maturity is running short while all other things being equal. It can be expressed as an absolute value or a percentage relative to the warrant price (theta / warrant price). Unless in some special circumstances, the value of theta is usually negative, reflecting the declining value of a warrant as time passes. The time decay has its greatest effect when the warrant is near to its maturity. Time decay accelerates as time passes.

In percentage terms, time value has the biggest impact on out-of-the-money (OTM) warrants. The value of a warrant consists of intrinsic value and time value. They vary in absolute and relative terms for warrants with different strike prices and maturity dates. In the case of OTM warrants, their intrinsic values are negligible or zero. In other words, time value makes up most of their values. Hence, they are more sensitive to the passage of time. As for the in-the-money (ITM) warrants, given that a large part of their value is made up of intrinsic value, they are less sensitive to the passage of time, and such sensitivity decreases as the maturity date gets nearer.

Investors should find out more about the theta of a warrant as a percentage relative to its price, that is, relative theta. The latter is a better indicator to the sensitivity of a warrant to the passage of time, and will give you a better idea about the effect of time value on the gain or loss on warrants you are holding.


Vega measures the rate of change in the warrant price for each point of movement of its implied volatility. No matter it is a call warrant or a put warrant, Vega is always positive, indicating that the warrant price and its implied volatility always move in the same direction. Vega can be an absolute value or a percentage relative to the warrant price.

In terms of the percentage change in price, changes in implied volatility have the biggest impact on OTM warrants. Besides, the closer they get to the maturity, the bigger the impact. Next come at-the-money (ATM) warrants, and then ITM warrants. For the latter, the closer they get to maturity, the smaller the impact. Hence, in picking warrant, investors should check out its Vega as a percentage relative to change in warrant price, in order to assess the impact of implied volatility on the warrant.


Gamma measures the sensitivity of the delta of a warrant to the price movements of its underlying. The higher the gamma, the bigger the change in delta will be in reaction to a movement in the underlying price.

Gamma = rate of change of delta / rate of change of underlying price

No matter it is a call warrant or put warrant, gamma is always positive. When the underlying goes up, in the case of a call warrant, its delta will go up as it is more likely to be ITM; in the case of a put warrant, the same will happen too as it is more likely to be OTM and its delta will get closer to zero.

ATM warrants (for those with maturity of less than a year) have the highest gamma. This means that they have the highest rate of change of delta.


Rho measures the sensitivity of warrant price to changes in the market interest rate. Call warrants have a positive rho, meaning that the price of a call warrant moves in the same direction as the market interest rate. In contrast, put warrants have a negative rho, and this shows that the price of a put warrant moves in the opposite direction to the market interest rate. Given that changes in interest rates tend to be limited in the short term, their effect on warrant prices is minimal.

This is my last post on analysis of warrant data. What I have discussed above is known as the Greeks of warrant. They look quite similar to those of option. The Greeks are important in trading both warrants and options. Unfortunately, the information for the Greeks for warrants are not easily available as compared with options.

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