Intra-country regulation of share markets: does one size fit all?

Abstract

A large body of evidence suggests that financial development is greater in countries that impose stricter regulatory requirements on their major stock exchanges, but this leaves open the question of whether or not such regulation should be uniformly applied to all equity trading platforms within a country. On the one hand, regulatory variation permits a wider choice of investment opportunities for investors, lowers the cost of capital for some firms, and enhances price discovery and efficiency. On the other hand, the presence of lightly regulated exchanges can potentially have adverse spillover implications for a country’s other financial markets.

Appendix: Determining the appropriate test for the imposition of uniform regulation

The value B of the future expected benefits stream is uncertain and evolves according to the geometric Brownian motion process

$$ dB = \mu B\,dt + \sigma B\,d\xi $$

(A1)

where μ and σ are constant parameters and dξ is a Wiener process. To keep things as simple as possible without losing anything essential, we assume the value C of the future expected costs stream is fixed.

The regulator has a perpetual option on the payoff (B−C). Let the value of this option be denoted by F(B; B*), where B* is the optimal stopping value, i.e., the value of B at which uniform regulation is justified. The Bellman optimality principle implies

$$ E[dF] = \rho Fdt $$

(A2)

where ρ is a discount rate. Applying Ito’s Lemma to F and using (A1), Eq. A2 can be written as

$$ \frac{1} {2}\sigma ^{2} B^{2} {F}^{\prime \prime} + (\rho - \delta )V{F}^{\prime} - \rho F = 0 $$

where δ = (μ − ρ). Solving this differential equation yields

$$ F(B;{\text{ }}B^{*}) = (B^{*} - C){\text{ }}{\left( {\frac{B} {{B^{*}}}} \right)}^{\gamma } $$

where

$$ \gamma = {\left( {\frac{1} {2} - \frac{{r - \delta }} {{\sigma ^{2} }}} \right)} + {\sqrt {\frac{{2r}} {{\sigma ^{2} }} + {\left( {\frac{1} {2} - \frac{{r - \delta }} {{\sigma ^{2} }}} \right)}^{2} } } > 1 $$

Maximising F in the usual way then provides the solution for B*:

$$ B^{*} = \lambda C $$

where $\lambda \equiv {\left( {\gamma \mathord{\left/ {\vphantom {\gamma {\gamma - 1}}} \right. \kern-\nulldelimiterspace} {\gamma - 1}} \right)}{\text{ $ > $ 1}}$