There is a weak relation between a particular measure of order imbalance and subsequent quote revisions, consistent with the predictions of some theoretical models of price formation. We develop routines in Mathematica for pricing various European and American options using the binary option model and Monte Carlo methods. As might be expected, Mathematica permits parsimonious programming of the option pricing expressions. This paper derives closed-form solutions for the investment and market value, under uncertainty, of competitive firms with constant returns to scale production and convex costs of adjustment. Solutions are derived for the case of irreversible investment as well as for reversible investment.
Optimal investment is a non-decreasing function of q, the shadow value of capital.
However, the value of the firm may contain a bubble that does not affect investment behavior. Relative to the case of reversible investment, the introduction of irreversibility does not affect q, but it reduces the fundamental market value of the firm. 13-93 Two hypotheses concerning firms issuing debt for the first time are tested. The second hypothesis is that prior to the establishment of a reputation new firms issuing debt are monitored more intensely. Note holders are then motivated to monitor new banks because the excess discount provides an incentive for notes of new banks to be redeemed.