# Pricing Warrants

How do you adjust the calculated price of a warrant from Black Scholes when the exchange ratio is more than one warrant for a share…for example, say its 1.5 warrants for a share. Thank you.

divide whatever it tells you the warrant is worth on a per share basis by 1.5

Divide by 1.5. Make sure you account for dilution when using BS to value warrants.

What is the best way to account for dilution? I’m researching now but no definitive answer.

Covered in Hull among others. Use B-S but a) Replace S with S + M/N*W where M = # warrants, N= # shares, W = warrant price b) Sigma is the vol of the equity including the warrants not just the stock c) Multiply B-S call price by N*d/(N + M*d) where d= # shares granted per warrant

in a)… how can you have W in the formula…that is what I’m trying to find. Thanks JD

Right - so you have W = g([bunch of stuff], W) so you have to solve for W numerically. It’s like suppose that I said find W where W = sin W + cos W. You would need to get out some numerical solver like Solver in Excel to get the answer (I guess).

seems like a circular error though…not quite following… I am calculating the warrant price as I see it vs want its trading at now whether to determine if its over/undervalued…

Step back for a second. Suppose that I told you to solve W = W^2 - 2. You would subtract W from each side and then use the quadratic formula. If I gave you W = W^7 - 2 there is still a solution but you probably can’t find it using algebra, so you would pull out some software and do Newton-Raphson or something. This is the same thing except that we have W = nasty function(W). Using this, you can start with an equity vol and get a warrant price or vice versa. I’m not sure what you mean by over/under-valued here. The implied vol you calculate on the warrants should be about the same as the implied vol on calls of similar characteristics so you could use this to see if the warrants are fairly priced to the calls. You could also have some model of vol and see if the implied vol is greater or less than your model suggests it ought to be but this is a tough way of making money.

Long ago I found a stock that had \$1 per share in cash and no liabilities, and it was trading at \$1. It had warrants trading at 20 cents. According to BS, the warrants were worth 40 cents. Was I getting \$1 in cash for fifty cents? Was that a value investment?