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# Valuation of stock warrant

## 1. Stock warrant theoretical value = intrinsic value + time value

Before we look at intrinsic value, we must understand an important concept "equivalent ratio". "Equivalent ratio" is the most basic index to measure the value of stock warrants, which reflects three value states of warrants: in-the-money out-of-the-money and at-the-money.

Equivalent ratio= Underlying assets/ The strike price of the underlying assets represented by the stock warrants

For warrants, if the equivalent ratio is greater than 1, the warrant is "in-the-money"; If the equivalent ratio is less than 1, the warrant is "out-of-the-money". The opposite is true for a put warrant. If it is equal to 1, both a put warrant and a call warrant are equivalent.

Only when a stock warrant is in-the-money could it have "intrinsic value", intrinsic value is a value greater than or equal to 0, even if a warrant is "out-of-the-money", its intrinsic value can not be negative. Therefore, when the intrinsic value of the stock warrant is zero, its value will only remain the time value. Therefore, we can understand why the price of the warrant which is about to expire and is at-the-money or out-of-the-money will be very low.

## 2. Factors affecting the price of warrants

● Changes in underlying asset

If the price of the underlying asset shows an upward trend, the price of the call warrant will also rise, and vice versa; The price of the underlying asset tends to go up, the price of the put warrant will go down, and vice versa.

●  Remaining time

As we mentioned above, the longer the remaining time of warrant, the bigger the time value, that is to say, the price of warrant is higher, it is the same for both call warrants and put warrants. But this is only in theory, we mainly introduce the European stock warrants, because they can be implemented only on the expiry date, the underlying asset price at that time can be high or low, this is also a risk factor, we must pay attention to this.

● The amplitude of underlying asset

Volatility is a standard way of measuring the risk of underlying assets. The greater the volatility, the greater the risk of the underlying assets, so the higher the warrant price will be.

● The risk-free rate of interest

The risk-free rate of interest is generally refered to as HIBOR (Interbank Offered Rate) which is the opportunity cost borne by investors.

The effect of the risk-free rate on warrants is two-sided.

When the risk-free rate rises, the price of the underlying asset theoretically tends to fall, so that the price of the call warrant falls and the price of the put warrant rises.

But from another point of view, due to the investment on stock warrant is a kind of leveraged investment, as interest rates rise, the opportunity cost of purchasing underlying assets will increase, causing some of the sound investors will put more money to charge interest, they will spend a small amount of money to buy call warrants, to strengthen the buyer's power of the call warrants , and the price of call warrants will rise; The price of a put warrant falls as the risk-free rate rises.

When issuing warrants, the issuer may mobilize funds to purchase underlying assets. If the borrowing costs (i.e., the interest rate) increase, the cost will be reflected in the higher warrant price. Likewise, as interest rate rise, the price of a put warrant will fall.

So in general, as the risk-free rate goes up, the price of call warrants goes up and the price of put warrants goes down.

● Cash dividend income during the validity period of the warrant

Since the holder of a warrant generally cannot receive a cash dividend as the holder of the underlying asset can, theoretically speaking, the higher the cash dividend is, the more disadvantageous it is to the price of the call warrant, while the opposite is true for the put warrant. However, since the price of the warrant issued by the issuer has already taken into account the possible dividends during the underlying asset period, if the dividend is in line with expectations, it should have little impact on the price of the warrant.

From the perspective of the actual operation of the market, if the dividend is higher than expected, the price of the underlying asset may rise more than its excessive cash dividend because the investors of the underlying asset are more optimistic about its future prospects. Therefore, it will benefit the price of the call warrant, while that of the put warrant is opposite. If the cash dividend is smaller than expected, while theoretically beneficial to the call warrant, investors in the underlying asset may be bearish on its future prospects and the underlying asset may fall more than the part of the less, thus benefiting the put warrant while the call warrant is in the opposite direction. In summary, we believe the dividend impact is two-sided.