**4.3. Descriptive statistics for LCRs of class I and II banks**

In this subsection, we provide 2002 to 2012 LCR descriptive statistics for Class I and II banks.

Table 2 reports the summary statistics of the approximate measures of the LCR for Class I banks, where the mean for the LCR is 74.96 %. In this table, the LCR displays positive skewness. The value of the kurtosis for the LCR in Table 2 is equal to or less than 3, that means that the distribution is flat. The LCR risk measure exhibits normality because the *p*-values are greater than 5 %. Nevertheless, the normality test is very sensitive to the number of observations and may only produce desirable and efficient results if observations are large. From Table 2, it is clear that, in the absence of empirical evidence, it is hard to conclude that the Basel III LCR standard had complied with these standards.


**5. Conclusions and future directions**

**5.1. Conclusions**

numerical results for LCRs.

*5.1.1. Conclusions about the LCR model*

*5.1.2. Conclusions about optimal basel III LCRs*

the cash injection rate, *u*2<sup>∗</sup>

In this section, we draw conclusions about the LCR modeling and optimization and related

In this subsection, we make conclusions about the LCR model, optimal Basel III LCRs and

One of the main contributions of this book chapter is the way the LCR dynamics model is constructed by using stochastic techniques. This model depends on HQLAs, NCOs as well as the liquidity provisioning rate. We believe that this is an addition to pre-existing literature because it captures some of the uncertainty associated with LCR variables. In this regard, we provide a theoretical-quantitative modeling framework for establishing bank LCR reference processes and the making of decisions about liquidity provisioning rates and asset allocation. In Subsecdtion 2.1, we mention the possibility of adjusting the cash injection rate depending on whether the bank is experiencing deficit or surplus liquidity. The latter occurs where cashflows into the banking system persistently exceed withdrawals of liquidity from the market by the central bank. This is reflected in holdings of reserves in excess of the central bank's required reserves. Transitional economies, for example, often attract large capital inflows as the economy opens and undergoes privatization. The effect of these inflows on liquidity is often magnified by central bank intervention in the foreign exchange market when there is upward pressure on the domestic currency. In the wartime economy, consumption is restricted and large amounts of involuntary savings accumulate until goods and services eventually become more widely available. Soviet-style economies have displayed widespread shortages and administered prices. This creates a situation of repressed inflation, whereby prices are too low relative to the money stock, leaving individuals with excess real balances. The importance of surplus liquidity for central banks is threefold and lies in its potential to influence: (1) the transmission mechanism of monetary policy; (2) the conduct of central bank intervention in the money market, and (3) the central bank's balance sheet and income.

We obtained an analytic solution to an optimal bank LCR problem with a quadratic objective function. In principle, this solution can assist in managing LCRs. Here, liquidity provisioning and HQLA allocation are expressed in terms of a reference process. To our knowledge such processes have not been considered for LCRs before. This chapter makes a clear connection

An interpretation of the control laws given by (33) and (34) follows. In times of deficit,

reference process for this ratio, *xr*. The proportionality factor is *qt*/*c*<sup>2</sup> that depends on the relative ratio of the cost function on *<sup>u</sup>*<sup>2</sup> and the deviation from the reference ratio, (*<sup>x</sup>* <sup>−</sup> *<sup>x</sup>r*). The property that the control law is symmetric in *x* with respect to the reference process

, is proportional to the difference between the LCR, *x*, and the

<sup>2</sup> *<sup>c</sup>*3(*<sup>x</sup>* <sup>−</sup> *<sup>x</sup>r*)<sup>2</sup> being symmetric

Optimizing Basel III Liquidity Coverage Ratios

http://dx.doi.org/10.5772/58395

85

between liquidity and financial crises in a numerical-quantitative framework.

*x<sup>r</sup>* is a direct consequence of the cost function *br*(*x*) = <sup>1</sup>

numerical examples. Furthermore, we suggest possible topics for future research.

**Table 1.** 2002 to 2012 LCRs for Class I and II Banks


**Table 2.** Descriptive Statistics of LCR for Class I and II Banks
