Kenmare Resources - re-rating due soon?

Blobby

We're solving for C, so it isn't an input assumption.

S = current stock price
t = time until option expiration
r = risk-free interest rate
and
K = option strike price

were set out in my post (i've assumed r is 4.5%, which is slightly high compared to what the 3.5 year swap curve implies).

e = the constant 2.7183..
ln() = natural logarithm of the argument
sqrt() = square root of the argument
^ means exponentiation (i.e., 2 ^ 3 = 8)
and
N = cumulative standard normal distribution

are standard mathematical functions and hence you don't need to make any assumptions for these.

sigma = standard deviation of stock returns (usually written as lower-case 's')
is what I have called volatility in my post. Unlike the other assumptions it's not possible to determine what the relevant volatility assumption should be - hence i've given a selection of assumptions to use. I would guess volatility of 3 year options on the FTSE 100 would be around 15%, but on a share like kenmare, the volatility of return is likely to be higher.
In practice, you could look at the historic volatility of the share price and use this, but this isn't quite the same as is required for the option price calculation (which is all about prospective rather than retrospective volatility). Another way is to work out the market implied volatility eg by backsolving the Black Scholes equation - but I wouldn't do this for KMRW as I don't think the option price is tracking as it should in an efficient market.

If you want to calculate your own option prices check out someone like Ray Steeles web page which has free option pricing software which you can add into miscrosoft excel.