The price of shares in an investment trust company is determined by the supply of and demand for those shares. This is true of any shares.
The price of units (for UTs) and shares (for OEICs) cannot be determined by supply and demand because these are open-ended funds, so if the demand for them increases, then more units/shares will be created, so supply will automatically increase (so supply and demand are a bit meaningless).
So for open-ended funds, the price of units/shares is based on the underlying value of the assets (net asset value).
Since, for an investment trust company, the share price is determined by supply and demand, it is not automatically equal to the net asset value of the underlying assets. When we compare the share price to the net asset value, we often find that the share price is at a discount to net asset value.
Now let's look at the volatility of share/unit prices.
Share/unit prices in open-ended funds will vary if the value of the underlying assets change.
Share prices in closed-ended funds will vary if the value of the underlying assets change AND if the discount varies. This second factor will be affected by market sentiment (of investors) and things like the market's opinion of the fund managers.
So share prices in closed-ended funds (ITCs) depend on more factors, and so are more volatile.