This article will introduce us to the pricing and risk of structured warrants. It will show how the price of a warrant relates to the underlying share and identify significant features that contribute to the valuation of a warrant. It will also stress some important risk aspects that investors must be aware of.

**How the price of a warrant relates to the underlying share?**

Generally, a warrant’s price is closely connected to the behaviour of the underlying share. By behaviour, we mean bow volatile the underlying share is and whether it is moving in a favourable direction for the warrant holder.

However, we must appreciate that the way the underlying share affects the price of the warrant is not consistent. Warrants are not priced as a result of a simple balance between supply and demand (like ordinary shares). They are priced according to a formula – often some variant of the Black Scholes method. The critical inputs for the formula are:

- Whether the warrant is in, out or at the money (determined by the underlying share price and the strike price)
- How long the warrant has until maturity and
- How volatile the underlying shares is expected to be.

Other less important parameters of the formula are interest and dividend rates. With so, many influences on a warrant’s price, it is easy to get lost. But if we master the above in simple terms, we can trade confidently.

### What a warrant is worth?

A warrant can be in the money, out of the money or at the money. An example of a warrant that is in the money is China Construction Bank’s structured call warrant which expires on Nov 26,2010.

It has a strike price of RM2.268 but the underlying share was already trading at RM2.912 as at Sept 18, 2009. We would expect these kinds of warrants to be more expensive. Toyota Motor Cop-C3, an out of the money call warrant that expires on Nov 26,2010, has a strike price of RM135.38 when the underlying share is only trading at RM100.54. These types of warrants are likely to be trading quite cheaply. An at the money warrant will have a strike price that is very close to the underlying share price.

### Time until maturity – how this affects the price of a warrant?

The right to buy or sell at the strike price, but not the obligation, is always worth something even if the warrant is not currently in the money. For example, the Toyota Motor Corp-C3 warrant mentioned above is clearly out of money but it is priced at 27.5 sen on Sept 18, 2009, because no one knows what the underlying share price will be at expiry. This can be construed as the time value of the warrant.

Nevertheless, as we get closer to expiry, the uncertainty falls and the time value decays. Technically, this is referred to as the “theta”, the rate at which a warrant loses value as time passes.

Time decay is not constant and speeds up towards the end of the warrant’s life. For this reason, one must be wary of trading an out of the money warrant that is approaching its expiry. One can lose money because of time decay just by holding onto the warrant a few more days.

### Volatility- how it affects the price of the warrant?

Think of share price volatility as the degree of uncertainty surrounding a share’s returns. A young biotech company’s shares can easily rise or fall by 30% to 50% in a week. In contrast, we don’t expect a stable utility company to behave in this fashion. Say, we hold call warrants on both these two companies, with strike prices 30% above the current share price. The higher volatility of the biotech company means there is a better chance of its share price moving in large magnitudes, leading to a higher possibility of the warrant being in the money. That is why you will find that the warrant with a higher volatility in the underlying share costs more.

### Important risk factors

Besides the rapid time decay or theta mentioned above, other important aspects are the delta, gearing and elasticity.

**1. Delta**

The delta implies how sensitive the warrant price is to the movement in the underlying share price. It is measured by the change in the warrant price divided by the change in the underlying share price. However, remember that the delta says nothing about the percentage change in the warrant versus the share price. The percentage change in the warrant price is normally larger than the share price.

Delta = change in option price/change in underlying share price

You will observe that a warrant that is deep in the money, with a few weeks from expiry, really functions as the underlying share itself and will normally have a delta of 1.0. For example, if the underlying share rises 10 points, we can expect the warrant to rise 10 points as well.

For an at the money warrant, the delta is usually around 0.5. When the underling share price changes 10 points, the warrant changes only five points. For an out of the money warrant, the delta is even smaller. Any change in the underlying share price has very little effect on the warrant’s price.

**2. Gearing**

We’ve just seen that the delta does not tell you the percentage rise in the warrant that you should, expect from a 1 % rise in the underlying share. To work this out, you need to know the warrant’s effective gearing or elasticity. All warrants are geared – owning a warrant gives you the same exposure as owning more than one share in the underlying equity, typically between 5 and 15 shares. You can calculate the gearing by simply dividing the price of the underlying share by the price of the warrant.

**3. Elasticity**

If your warrant has a gearing of eight and a delta of 0.5, then the effective gearing or elasticity is gearing x delta: 8 x 0.5 = 4. Using this example, if the underlying share goes up 1 %, the warrant will rise 4%.

Does elasticity stay the same over the life of the warrant? Of course not, because the delta will change and so will the gearing. So, it will be good to monitor the elasticity of the warrant. As the elasticity gets higher, we’d like to be more careful and closely monitor the warrant as it is extremely sensitive. Intuitively, a deep in the money warrant is usually more elastic than the others.

### Conclusion

This series of articles attempted to illustrate the concept of the structured warrant, how it behaves, significant factors that affect its price and the risk it bears. We’ve also observed how the product can be enhanced for the retailer, with a tighter bid-offer spread and model-based pricing. If the savvy investor comprehends the pricing and risk aspects of this product, it’s a very thrilling experience when he is able to make out why the price of his warrant moves in a specific manner.

*Written by Jasvin Josen, a specialist in developing methodologies for the valuation of various credit products.*

*Source : The Edge*