KYNEX Bulletin
March 2011
Warrants
Calculator Enhancements
Over
the past eighteen months, we have seen warrants being issued with new
features. The most notable feature is protection
from increases in future dividends on the underlying common stock (Dividend
Protection). We have also seen warrants
that can be terminated if the underlying common stock exceeds a pre-set trigger
(Provisionally Callable). We have
enhanced our warrants calculator to accommodate these features. You can also maintain custom volatility
surfaces for stocks to be applied in valuing warrants. The following is a
more detailed explanation regarding the features now supported by our warrants
pricing model:
- Dividend Protection: Our
warrants calculator projects future expected shares per warrant when the
actual dividend on the common stock and/or your future expected dividends
increase beyond a pre-set threshold (which we refer to as the anchor
dividend) in the warrant contract. Therefore, the valuation of the
warrants and the calculation of risk measures are accurate allowing you to
setup trades to capture your dividend expectations in an effective manner. It should be noted that if the actual dividend
on the common stock and/or your future expected dividends are equal to or
less than the anchor, no adjustments are made to the shares per
warrant. Our implementation of
dividend protection for warrants is based on our well-established feature
for convertible bonds. For more
detail, please see our March 2006 Bulletin
which explains how dividend protection is implemented for
convertibles. The impact of
dividend protection on the valuation is driven largely by actual increases
in dividends by the issuer as well as your dividend expectations. You are able to specify your
expectations of future dividends for each underlying
stock. Click here
for instructions on how to specify your dividend assumptions.
- Provisional Calls: Some warrants have a conditional call
feature with a trigger level. We incorporate the probability of early
termination in our valuation based on your volatility assumptions and
stock price level. In the
event of a call, the issuer delivers a fractional number of shares (S – K) / S in return for early
termination. Hence, the dollar value delivered is max(S – K,0), but the investor receives fractional shares and
does not pay the strike price. We also look back at the stock price history and
take into account the number of days the stock price has exceeded the
trigger. Hence, the valuation of
warrants and especially the Delta is very precise allowing you to hedge your
warrants appropriately. Our
implementation of the stock history relating to provisional calls is based
on our implementation for convertibles which is outlined in our October 2009
Bulletin.
- Volatility Surface: You can
value a warrant based on a surface of volatilities specified by you as
opposed to a single flat volatility.
The specification of the volatility surface can be along expiration
as well as along strike (money-ness).
The ability to precisely value warrants, especially long dated ones
based on your volatility expectations allows you to come up with effective
trading strategies. Click here
for instructions on how to create a volatility surface.
Our warrants pricing model
employs standard geometric Brownian motion techniques in an implicit finite
difference grid. The valuation returns the theoretical Fair Value and the
standard sensitivities (Greeks): Delta, Gamma, Vega,
An illustration of the enhanced
warrants calculator details is shown in Fig 1 below, for
the
Below is a brief description of
outputs specific to warrants:
Gearing ~ Ratio of the stock price to warrant price
Break-Even ~ Rate at which the stock must compound over the life of the warrant in order to breakeven on the expense paid (warrant price plus exercise price)
Effective Gearing ~ Ratio of a percentage change in the underlying stock and the resulting percentage change in the warrant price
Elasticity ~ Ratio of a
percentage change in the underlying stock and the resulting percentage change
in the Fair Value
