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Continuous Time Lognormal model

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asked May 19 in BUS 4028F - Financial Economics by anonymous

Please may someone explain what this statement means:

The Brownian motion model predicts that daily movements of size 10 would occur just as frequently when the process is at a level of 500 as when it is at a level of 5000. 

What would instead be the (opposite of this) characteristic of a good model?

1 Answer

+2 votes
answered May 19 by ErichMaritz (740 points)

Consider two identical gold mining companies. Company A issued 1000 shares, worth R5000 each. Company B issued 10,000 shares, each worth R500. Both companies have market capitalisation of R5m. Suppose the gold price goes up by 10%. The effect should be very similar on the companies' market caps. Suppose the share price of Company A goes up 20% to R6000, i.e. by R1000. We would expect company B's share price to go up by 20% as well, i.e. by R100. So, we think it is better to model the share price change as a proportion of share price, instead of modelling the arithmetic change in value.

 

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