what price will options trade, page-3

Hi Loki,

Applying the Black-Scholes options pricing formula:

C = S Normdist(d1) - Xe^(-rt) Normdist(d2)

Where S is the share price
X is the strike price = 0.025
r is the risk-free rate = 0.07
t is the time to maturity = 3

d1 = 1/(Stdev * Sqrt(t)) * (ln(S/X) + (r+0.5 Stdev^2)t)

Stdev is the annualised standard deviation of returns = 0.25 (calculated using historical data from 6 December 2005)

Hence, d1 = 1/(0.25*Sqrt(3)) * (ln(S/0.025) + (0.07 + 0.5 * 0.25^2) * 3)
= 2.309 * (ln S + 3.992)
= 2.309 ln S + 9.218

d2 = d1 - Stdev * Sqrt (t) = 2.309 ln S + 8.785

Using Excel to calculate C for a range of S's, using the formula =A2*NORMSDIST(2.309*LN(A2) + 9.218)-NORMSDIST(2.309*LN(A2)+8.785)*0.025*EXP(-0.07*3), we have:

Share price (S), Option price (C)
0.01, 0.000131
0.011, 0.000228
0.012, 0.000365
0.013, 0.00055
0.014, 0.000785
0.015, 0.001074
0.016, 0.001418
0.017, 0.001816
0.018, 0.002267
0.019, 0.002769
0.02, 0.00332
0.021, 0.003916
0.022, 0.004554
0.023, 0.00523
0.024, 0.005942
0.025, 0.006685
0.026, 0.007458
0.027, 0.008256
0.028, 0.009078
0.029, 0.00992
0.03, 0.010781
0.031, 0.011658
0.032, 0.012549
0.033, 0.013454
0.034, 0.014369
0.035, 0.015295
0.036, 0.01623
0.037, 0.017172
0.038, 0.018121
0.039, 0.019077
0.04, 0.020037
0.041, 0.021003
0.042, 0.021972
0.043, 0.022945
0.044, 0.023921
0.045, 0.0249
0.046, 0.025881
0.047, 0.026865
0.048, 0.027851
0.049, 0.028838
0.05, 0.029826
0.06, 0.039764
0.07, 0.049745
0.08, 0.059739
0.09, 0.069737
0.1, 0.079736

Although the B-S formula I used above is normally only suitable for European style options, it suffices in this case as we are just looking at very rough estimates. The figures above give you a taste of how the option price might change with increasing share price. As you can see, currently at S = 2c, we have C = 0.003, implying a 0.3c option price.

Let me emphasise again that the figures above are very rough estimates, and depends on a lot of factors, but they do give you a bit of a guide as to how the options may be priced.

As always, please do your own research.

Cheers