Generally speaking in advanced economies the valuation rests on some estimate of current price, or estimated fair price now, rather than book value i.e. book price (the latter being the acquisition cost of the asset or liability, or the depreciated book value, rather than it's value now).
In the financial industry, valuations are required for all financial assets (liabilities), for various reasons including tax, regulatory and accounting (including reporting to owners and stakeholders). The valuations are as of specified dates e.g. the end of the accounting quarter or year. They may alternatively be mark-to-market (estimates of the current value of assets {liabilities} as of this minute or this day) for the purposes of managing portfolios and associated financial risk (e.g within large financial firms including investment banks and stockbrokers).
Some assets (liabilities) are much easier to value than others. Publicly traded shares and bonds e.g. have prices that are quoted frequently and sometimes minute to minute. Other assets are hard to value e.g. private firms that have no frequently quoted price and financial instruments that have prices that are partly dependent on theoretical constructs of one kind or another. For example, options are generally valued using the Black and Scholes model, whilst the liabilities of life assurance firms are valued using the theory of present value.
It is possible and conventional for financial professionals to make their own estimates of the valuations of assets (liabilities) that they are interested in, and their calculations are of various kinds including analyses of companies that focus on price-to-book, price-to-earnings, price-to-cashflow and present value calculations, and analyses of bonds that focuses on credit ratings (e.g. assessments of default risk), risk premia and levels of real interest rates. All of these approaches may be thought of as creating estimates of value that compete for credibility with the prevailing share or bond prices (where applicable) and may or may not result in buying or selling by market participants.
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