• 沒有找到結果。

A REALIZED CAPPED CALL OPTION FRAMEWORK FOR LOAN-RISK SENSITIVE INSURANCE PREMIUM VALUATION

N/A
N/A
Protected

Academic year: 2021

Share "A REALIZED CAPPED CALL OPTION FRAMEWORK FOR LOAN-RISK SENSITIVE INSURANCE PREMIUM VALUATION"

Copied!
10
0
0

加載中.... (立即查看全文)

全文

(1)

Computing, Information and Control ICIC International c 2014 ISSN 1349-4198

Volume 10, Number 1, February 2014 pp. 19–38

A REALIZED CAPPED CALL OPTION FRAMEWORK

FOR LOAN-RISK SENSITIVE INSURANCE PREMIUM VALUATION

Jyh Horng Lin1 and Chuen Ping Chang2,∗

1Department of International Business

Tamkang University

No. 151, Yingzhuan Rd., Tamsui Dist., New Taipei City 25137, Taiwan lin9015@mail.tku.edu.tw

2Department of Wealth and Taxation Management

Kaohsiung University of Applied Sciences

No. 415, Jiangong Rd., Sanmin Dist., Kaohsiung City 807, Taiwan

Corresponding author: cpchang@cc.kuas.edu.tw

Received November 2012; revised March 2013

Abstract. This paper examines the optimal interest margin, the spread between the

loan rate and the deposit rate of a bank, when the risk of corporate borrower default is explicitly capped. Corporate borrower default risk is characterized by a lending function that includes corporate borrower risk and equity default probability. The equity of the bank can be viewed as a realized capped call option on its assets. This approach we will use is to calculate loan-risk sensitive insurance premium. The results show that when the investment value of the corporate borrower is high, market-based estimates of deposit insurance premium which ignore the realized cap are under valued. This type of situation calls for an increase in the deposit insurance premium in lieu with the asset risk of the corporate borrower. An increase in the corporate borrower’s asset risk makes the bank more prone to loan risk-taking at a reduced margin when asset risk itself is low, but makes the bank more prudent to loan risk-taking at an increased margin when asset risk itself is high. Our results demonstrate why realized capped lending considerations may have further applicability to value fair deposit insurance premium in providing more stability in banking system.

Keywords: Corporate borrower default risk, Realized capped call, Deposit insurance premium, Bank interest margin

1. Introduction. Most theoretical work done in the area of deposit insurance tends to confirm that deposit insurance is responsible for the increased risk taking activity in banks arising via moral hazard.1 According to this confirmation, much of the theoretical litera-ture on deposit guarantees has focused on their pricing and the feasibility of risk-adjusted insurance premia.2 Specifically, the Federal Deposit Insurance Corporation (FDIC)

an-nounced an assessment of deposit insurance premium value is based on the total of the risk-related assets.3 Motivated by the previous literature and the FDIC’s announcement,

we assess the extent to which corporate borrower asset risk affects pricing of deposit insurance through bank spread management.

Our paper makes several important contributions to the literature as a result of the following extensions in methodology and scope. First, on the methodological side, we

1About the moral hazard problem that related to deposit insurance, see, for example, Chen et al. [1],

Nier and Baumann [2], Pennacchi [3], and Huizinga and Nicod`eme [4].

2The seminal work by Black and Scholes [5] on the valuation of options has led to an application in

pricing of deposit insurance in the banking literature (for example, [6-9]).

3See http://www.fdic.gov/deposit/insurance/assessments/proposed.htm [10].

(2)

control for the corporate borrower’s levels of investment related to risk by introducing a new framework not previously used in the context of deposit insurance pricing. Based on the standard work of Merton [11], the market-based estimation of deposit insurance premium can be viewed as a put option on the bank’s asset value with a strike price equal to the book value of the bank’s debt.4 The underlying asset value of this standard work, however, does not specify risk characteristics and the necessity to model the equity of the bank as a standard or “naked” call option. This paper highlights the fact that the default risk in the corporate borrower’s equity affects the distribution of bank loan repayments. The market value of the bank’s underlying assets is specified as a realized value of loan repayments reduced by a realized value of a put option given to the corporate borrower who can sell its end-of-period asset at a price of its loan repayments to the bank. The realized loan repayment value is the value with the default-free probability in the corporate borrower’s equity, while the realized put option is the option with the corporate borrower’s default probability. The equity of the bank is viewed as a so-called “realized capped” call option on the bank’s assets. As such, the deposit insurance premium of the FDIC’s claim can be viewed as a realized capped put option that a capped put with the default probability in the bank’s equity return.

Next regarding scope, to the best of our knowledge, we are the first to introduce the bank interest margin, i.e., the spread between the loan rate and the deposit rate, to price deposit insurance premia, explicitly taking into account of corporate borrower default risk. Lending involves acquiring costly information about an opaque corporate borrower. The bank anticipates credit risk compensation from the corporate borrower. The bank interest margin is one of the principal elements of bank net cash flows and after-tax earnings, which is often used in the literature as a proxy for the efficiency of financial intermediation [12,13]. Accordingly, deposit insurance premium evaluated at the optimal bank interest margin should be valued based on an explicit treatment of the risk characteristics of bank loans related to the corporate borrower’s equity return and risk. This paper aims to fill this gap when calculating the loan-risk sensitive insurance premium.

A prime example of this is highlighted in a prior research by Dermine and Lajeri [9] which is modeled explicitly for the risk characteristics of bank assets and calculates loan-risk sensitive insurance premium but failed to consider the impact of a corporate borrower’s investment level related to its invested-fund risk on the bank’s lending strate-gies. Our contribution is to control for corporate borrower’s levels of investment related to default risk, which enables us to better understand bank spread behavior and market-based estimation of deposit insurance premium. Our results indicate that the bank’s equity is higher and the deposit insurance premium is lower when the market-based es-timates of the bank’s equity are based on a naked call than on a realized capped call. When the investment value of the corporate borrower is high, the bank’s interest margin is negatively related to the corporate borrower’s low asset risk, but positively related to the corporate borrower’s high asset risk. Under the circumstances, the deposit insurance premium should be increased when the corporate borrower’s asset risk increases.

One immediate application of the results is to evaluate the plethora of bank equity valuations proposed as alternatives for bank loans and fair deposit insurance premium estimates. Market-based estimates of deposit insurance premium which ignore the realized cap lead to undervaluation of the premium which may prompt the bank’s moral hazard incentive. Our results also suggest that the deposit insurance premium valued at the realized capped call may be more sensible to loan risk-taking exclusively for the corporate

4A closely related group of papers, for example, Merton [6], Ronn and Verma [14], and Episcopos [15],

uses contingent claims in order to price deposit insurance contracts on an actuarially fair basis that the liability to the FDIC is a European put option written on the assets of the bank.

(3)

borrower with high investment at a high risk level, thereby affecting the stability of the banking system. Our findings provide an alternative for affirming market-based estimates of deposit insurance premium for financial stability.

In related work, Delong and Saunders [16] found that banks in general had become a higher risk following the introduction of fixed-rate deposit insurance. Unlike Delong and Saunders [16], we find that the realized capped call estimated deposit insurance premium should be increased when the bank becomes at a higher risk due to its corporate borrower’s investments status and default risk. Analyzing whether explicit deposit insurance actually influences the risk taking of bank is not considered. Rather, this paper explores the determinants of fair deposit insurance premiums based on a simple realized capped call option model under sources of corporate borrower defaults and bank interest margins. We acknowledge that the fairness of the deposit insurance premium is a highly debated issue, but will not be discussed in this paper.

The rest of this paper is organized as follows. Section 2 reviews related literature. Section 3 delineates the firm-theoretical call-option model of a bank capped by corporate borrower asset risk. Section 4 examines the effect of the corporate borrower default risk on the deposit insurance premium through bank interest margin decisions. Section 5 presents a numerical analysis. The final section contains the conclusion.

2. Related Literature. Our theory of credit risk management is related to four strands of the literature. The first is the literature on bank interest margin determination, in which Ho and Saunders [17], Angbazo [18], Maudos and de Guevara [19], and Hawtrey and Liang [20] are major contributors. The prevailing approach to analyzing bank inter-est margin has been the dealership model originated by Ho and Saunders [17]. In this model, banks are viewed as risk-averse dealers in loan and deposit markets where loan requests and deposit funds arrive nonsynchronously at random time intervals. These au-thors analyze the determinants of bank interest margins and find that the margin depends on market competition degree and interest rate risk. This model is further extended to account for default risk [18]. The most recent extension of the Ho and Saunders [17] is studied by Maudos and de Guevara [19], who included operating cost as an explicit com-ponent of bank interest margin and market power measurement. Hawtrey and Liang [20] study the effect of managerial efficiency on bank interest margins, particularly including risk aversion, interest rate volatility, and opportunity cost determinants. While we also explore the determinants of bank interest margin, our focus on the bank interest margin management aspects of the explicit treatment of corporate borrower asset risk takes our analysis in a different direction.

The second strand is the literature on the risk characteristics of bank assets. In a firm-theoretical model where loan losses are the source of uncertainty, changes in capital regulation or deposit insurance premium have direct effects on the bank interest margin [21]. Wong [22] also uses a firm-theoretical approach to explore the determinants of optimal bank interest margins under multiple sources of uncertainty and risk aversion. Dermine and Lajeri [9] adopt an option-based valuation model instead of the commonly used firm-theoretical approach to show that bank lending and credit risk create a specific stochastic process for the asset of a bank. Tsai et al. [12] examine the optimal bank interest margin for a barrier option model, in which a bank provides vendor financing for a borrowing firm in order to unload the distressed loans. The primary difference between our model and these papers is that we propose a model of bank interest margin determination under deposit insurance explicitly creating the need to model bank equity as a realized capped call option. We use the realized capped function to explicitly express the corporate borrower’s asset risk.

(4)

The third strand is the modern deposit insurance literature. Wheelock and Kumbhakar [23] document that deposit insurance subsidizes risk taking; therefore, creating moral hazard in that banks with insured deposits will find it optimal to assume more risks than they would otherwise. Demirguc-Kunt and Detragiache [24] indicate that deposit insurance may increase bank stability by reducing information-driven depositor runs, while deposit insurance may decrease bank stability by encouraging risk-taking on the part of banks. Laeven [25] shows that a relatively high cost of deposit insurance indicates a bank taking excessive risks. Demirguc-Kunt et al. [26] find that deposit insurance may reduce moral hazard if non-deposit creditors are left out. Davis and Obasi [27] suggest that deposit insurance mainly affects bank risk through its relationship with profitability and asset quality. Prior papers largely tend to confirm that deposit insurance is responsible for the increased risk taking activity in banks via moral hazard, but fail to consider the impact of borrower asset quality on deposit insurance premium. This omission is crucial since bank lending and credit risk create a specific stochastic process for the asset of a bank and the leverage relevant for the insurer is the deposits to borrower asset quality. Our main work is to control for the corporate borrower’s investment level, which enables us to better understand the impact of borrower risk on deposit insurance premium.

The fourth strand of the literature to which our work is most directly related on confor-mity, particularly the issue of credit risk and interest margin as in Maudos and de Guevara [19], Williams [28], and Hawtrey and Liang [20], and the issue of credit risk and deposit insurance premium as in Wheelock and Kumbhaker [23], Demirguc-Kunt and Detragiache [24], and Laeven [25]. The fundamental insight shared by these papers is that conformity is generated by a desire to distinguish oneself from the type with which one wishes not to be identified. This insight is an important aspect of pricing deposit insurance premium as well, since bank managers and policy regulators agree with this pricing one to avoid being identified as untalented in estimating bank equity values. What distinguishes our work from this literature is our focus on commingling of the assessment of the corporate borrower’s asset risk with the assessment of deposit insurance premium priced through bank interest margin determination and, in particular, the emphasis we put on the rela-tionship between borrower asset risk and actuarially fair deposit insurance premium in the context of bank interest margin determination.

3. The Model. Consider a one-period (t∈ [0, 1]) contingent-claim framework that com-prises a corporate borrower, a bank with insured deposits, and a deposit insurer: (i) the corporate borrower funds its investment with a bank loan; but (ii) the bank realizes the potential risk of borrower default; so (iii) the bank’s equity is valued with assets and insured liabilities explicitly taking the potential default of the corporate borrower into account; and (iv) the market-based evaluation of deposit insurance premium is priced explicitly with corporate borrower default risk. (i), (iii) and (iv) imply that the frame-work will have to incorporate three distinct but related option-based valuation methods. The advantage of this framework allows us to examine the relationships among potential borrower default risk, bank behavior, and deposit insurance premium.

3.1. Corporate borrower. The equity of the corporate borrower is viewed as a call option on its assets since equity holders are residual claimants on the corporate borrower’s assets after all other obligations have been met [11]. The strike price of the call is the book value of the corporate borrower’s liabilities. We assume that the capital structure of the corporate borrower includes debt and equity. The market value of the corporate borrower’s underlying assets varies continuously over the single-period horizon based on

(5)

the stochastic process of a geometric Brownian motion (GBM) as described below:

dA = µAAdt + σAdWA (1)

where A is the firm’s asset value, µAis the instantaneous expected rate of return on A, σA

is the instantaneous standard deviation of the return, and WA is a Wiener process. We

denote by V the book value of the debt at t = 0, that has maturity at t = 1. The book value of the corporate borrower’s debt payment at t = 1 is specified as V = (1 + RL)L,

where RL is the loan rate set by the bank and L is the loan amount borrowed from the

bank at t = 0. The promised face payment value of V plays the role of the strike price since the market value of equity can be thought of as a call option on A with time to expiration at t = 1. The market value of the corporate borrower’s equity, SA, will then

be given by the Black and Scholes [5] formula for the call option:5

SA= AN (a1)− V e−RLN (a2) (2) where a1 = σ1 A ( lnAV + RL+ σ2 A 2 )

, a2 = a1 − σA, and N (·) = the cumulative density

function of the standard normal distribution.

Default occurs when the corporate borrower cannot fulfill its obligation, repaying bor-rower loan. Given the limited liability of the firm, the value of the loan at t = 1 is the promised payment on the loan reduced by a put option given to the corporate borrower who can sell its asset A at t = 1 at a price V , that the bank (the lender) takes over the corporate borrower’s asset A when it defaults. Similarly, define PA to be the put option

written on A and with an strike price equal to V , that the bank has effectively written to the corporate borrower’s equity holders:

PA= V e−RLN (−a2)− AN(−a1) (3)

The effects of default risk on equity returns may be not readily apparent since equity holders are the residual claimants on the corporate borrower’s cash flows and there is no promised nominal return in equities. The default probability becomes an issue to evaluate the default of the corporate borrower. The default probability is the probability that the corporate borrower’s assets will be less than the book value of the bank’s liabilities. Our approach in calculating the default probability using information about Equation (2) is very similar to the one outlined in Vassalou and Xing [29]. In that case, the theoretical probability of default is given by:

Pdef,A = N (−a3) (4) where a3 = 1 σA ( lnA V + µA− σ2 A 2 )

Default occurs when the ratio of the value of assets to liabilities is less than 1, or its log is negative. The distance to default a3 tells us by how many standard deviations the log

of this ratio needs to deviate from its mean in order for default to occur. Notice that although Equation (2) does not depend on µA, Equation (4) does. This is because a3 in

Equation (4) depends on the future value of asset which is given in Equation (2).

Using information about Equations (2)-(4), we can further define the realized loan payment to the bank from the corporate borrower as:

VA= (1− Pdef,A)(1 + RL)L− Pdef,APA (5)

5In Merton’s [11] model, the equity of a firm is viewed as a call option on the firm’s assets. Recent

related literature includes, for example, dynamic investment strategy in Wang and Wang [30], bank interest margin with vendor financing in Tsai et al. [12], and bank interest margin with structural break barrier in Tsai et al. [13].

(6)

We model Equation (5) such that loan payment includes (1+RL)L with default-free

prob-ability (1−Pdef,A) and PAwith default probability Pdef,A. This setting is understood that

(1 + RL)L is less likely to come into effect and PAis less likely vanish, as Pdef,A increases.

This is because the corporate borrower’s default may or may not occur. Equation (5) will be used in a later subsection when the equity of the bank is analyzed.

3.2. Bank. We consider the bank that has the following balance sheet at t = 0:

L + B = D + K (6)

where B is the amount of liquid assets, D is the quantity of deposits, and K is the stock of equity capital. Loan demand faced by the bank is governed by a downward-sloping demand function, L(RL) and ∂L/∂RL < 0, where RL is chosen by the bank [31]. Liquid

assets in the bank’s earning-asset portfolio earn the security-market interest of R. The total assets financed at t = 0 are partly by deposits. The bank provides depositors with a market rate of return equal to the risk-free rate of RD. The bank’s deposits are insured

by a government-funded deposit insurance scheme. For simplicity, we assume that the bank pays no insurance premium at any time. For capital regulation purposes, we assume that equity capital held by the bank tied by the regulation to be a fixed proposition q of the bank’s deposits, K ≥ qD. The required capital-to-deposits ratio q is assumed to be an increasing function of the loans held by the bank at t = 0, ∂q/∂L > 0. This system of capital standards is designed to force the bank’s capital positions to reflect their asset portfolio risks. When the capital requirement constraint is binding, the balance-sheet constraint of Equation (6) can be restated as L + B = K(1/q + 1).6

The equity of the bank is viewed as a call option on the bank’s risky loans in that loans are explicitly subject to non-performance. We model such underlying assets by VA

in Equation (6). The repayment value as such completely describes the non-performance from the potential risk of borrower default faced by the bank. The market value of the bank’s underlying assets follows a GBM of the form:

dVA= µVAdt + (σ + σA)VAdW (7)

where VA is the value of the bank’s assets, with an instantaneous drift µ, and an

instan-taneous volatility σ + σA where σA is from Equation (1). A standard Wiener process

is W . Equation (7) indicates that the impact on the bank’ underlying assets from the expected performance of the borrowing firm is limited to the instantaneous volatility [32]. This is because µ is unchanged or changed insignificantly but the instantaneous volatility is increased by σA when the asset substitution problem takes place [33]. In the context

of our model, the expression of the bank’s equity is the residual value of the bank after meeting all of the obligations:7

S = VAN (d1)− Ze−δN (d2) (8) where Z = (1 + RD)K q − (1 + R) [ K ( 1 q + 1 ) − L ] , δ = R− RD d1 = 1 σ + σA ( lnVA Z + δ + (σ + σA)2 2 ) , d2 = d1 − (σ + σA)

We label this valuation as realized capped call option since the underlying asset in Equa-tion (8) is defined as the realized value of VA rather than as the value of V in Equation

6The capital requirement constraint will be binding as long as R is sufficiently higher than R D. 7Note that the administrative costs of loans and deposits and the fixed costs are omitted for simplicity,

(7)

(2).8 Similarly, define P to be the put option written on V

A and with a strike price equal

to Z, the liability to the insurer is a put option written on the asset of the bank:

P = Ze−δN (−d2)− VAN (−d1) (9)

Again, we follow Vassalou and Xing [29] to define the default probability in the bank’s equity return as:

Pdef,VA = N (−d3) (10) where d3 = 1 σ + σA ( lnVA Z + µ− (σ + σA)2 2 )

3.3. Insurer. We assume that the insurer examines the bank at t = 1, which coincides with the maturity of current assets. Using information about Equations (9) and (10), we can further define the realized put option of the actuarially fair deposit insurance premium as:

PI = Pdef,VA × P (11)

The insurance liability occurs because the put on the loan repayment of the bank, ex-plicitly associated with the credit risk from the borrowing firm, will be exercised when the bankruptcy prediction of the bank is discounted by its default probability. Again, this discounted factor used in Equation (11) is understood because there is no promised nominal return in the bank’s equities.

4. Solving the Model. With all the assumptions in place, we are ready to solve for the bank’s optimal choice of RL. The first-order condition for the maximization of the market

value of the bank’s equity is:

∂S ∂RL = ∂VA ∂RL N (d1) + VA ∂N (d1) ∂d1 ∂d1 ∂RL ∂Z ∂RL e−δN (d2)− Ze−δ ∂N (d2) ∂d2 ∂d2 ∂RL = 0 (12) where ∂VA ∂RL = (1− Pdef,A) ∂SA ∂RL − Pdef,A ∂PA ∂RL − (SA+ PA) ∂Pdef,A ∂RL < 0 ∂Z ∂RL = [ (R− RD)Kq0 q2 + (1 + R) ] ∂L ∂RL < 0, VA ∂N (d1) ∂d1 ∂d1 ∂RL = Ze−δ∂N (d2) ∂d2 ∂d2 ∂RL

The second-order condition is required to be satisfied, that is, ∂2S/∂R2

L < 0. The first

term on the right-hand side of Equation (12) can be explained as the bank’s risk-adjusted value for its marginal risky-asset repayment of loan rate, while the third term can be explained as the risk-adjusted value for its marginal net-obligation payment. The value of the marginal net-obligation payment is negative in sign, and then the value of the marginal loan repayment is negative based on the first-order condition. The bank determines the optimal loan rate to maximize its market value of the equity when both the marginal values are equal. We further substitute the optimal loan rate to obtain the actuarially fair deposit insurance premium in Equation (11) staying on the optimization.

The optimal bank interest margin is given by the difference between the optimal loan rate and the fixed deposit rate. Since the deposit rate is not a choice variable of the bank, examining the impact of parameter on the optimal bank interest margin is tantamount to examining that on the optimal loan rate. Consider next the impact on the actuarially fair deposit insurance evaluated at the optimal loan rate from changes in the borrower firm’s

8When the underlying asset is defined as V as in Dermine and Lajeri [9], the lending function of the

bank creates the need to model as a capped call option. When the underlying asset is specified as VA in

(8)

asset’s volatility. Differentiation of Equation (11) evaluated at the equilibrium condition of Equation (12) with respect to σA yields:

dPI dσA = ∂PI ∂σA + ∂PI ∂RL ∂RL ∂σA (13) where ∂PI ∂σA = ∂Pdef,VA ∂σA P + Pdef,VA ∂P ∂σA ∂PI ∂RL = ∂Pdef,VA ∂RL P + Pdef,VA ∂P ∂RL , ∂RL ∂σA = 2S ∂RL∂σA / 2S ∂R2 L

The first term on the right-hand side of Equation (13) can be interpreted as the direct effect, while the second term can be interpreted as the indirect effect. The direct effect captures the change in PI due to an increase in σA, holding the loan rate constant. The

indirect effect arises because an increase in σA changes the insurance premium by L(RL)

in every possible state. Both the effects are indeterminate because the added complexity of option valuations does not always lead to clear-cut results. In the next section, we use numerical exercises to explain the reasoning behind the comparative static results of Equation (13).

5. Numerical Exercises. Starting from a set of assumptions on R = 4.00%, RD =

3.00%, K = 20, q = 10.00%, σ = 0.10 and µA= 0.10, we first calculate the market value

of the bank equity S and thus the term ∂RL/∂σAwhich are consistent with Equations (8)

and (13). Let (RL%, L) change from (5.00, 210) to (6.50, 198) due to ∂L/∂RL < 0, and let σA increase from 0.02 to 0.20. RL> R in the numerical exercises indicates fund reserves

as substitution in the earning-asset portfolio [34]. RL> RD implies that the bank interest

margin as a proxy for the efficiency of financial intermediation [35]. The specification of capital adequacy requirements is consistent with the standardized approach of capital regulation, which is set by q = K/D = 10.00% [36].

The relevant distinctions for the argument about Equation (13) are the following three scenarios: (i) the realized loan repayment to the bank from the corporate borrower is capped and specified as Equation (5) with a high level of A = 300, (ii) that as Equation (5) with a low level of A = 250, and (iii) that as Equation (5) equal to (1+RL)L. Scenarios

(i) and (ii) can be motivated based on a realized capped call argument while scenario (iii) can be motivated based on a standard naked call argument. These three scenarios will be compared in the following using the comparative static results of Equation (13). Before proceeding with the analysis of Equation (13), we present the values of VA at the levels

of A = 300 and 250, and VA= (1 + RL)L to explain the need of the three scenarios. The

findings are summarized in Table 1.

In Table 1, we have the results of ∂VA/∂RL< 0 and ∂VA/∂σA< 0 at the level of A = 300

in scenario (i). In scenario (ii), we have the result of ∂VA/∂RL < 0 when σA is low and ∂VA/∂RL > 0 when σA is high, and ∂VA/∂σA < 0 at the level of A = 250. In scenario

(iii), we have the result of ∂VA/∂RL< 0 at the level of VA= (1 + RL)L, which is invariant

to σA. These inconsistent results observed from the three scenarios suggest incentives

to study the effects of corporate borrower default on the deposit insurance premium. As pointed out by Demirguc-Kunt et al. [37], it is a dilemma that has caused deposit insurance to come under public scrutiny and has given rise to widespread discussions of deposit insurance reform. Our work contributes to the existing literature by exploring firm-theoretical aspects of deposit insurance and bank risk relationship.

We use numerical exercises to explain the results of Equation (13) in the first scenario of A = 300. In Table 2, S > 0 consistent with Equation (8) is observed from the first

(9)

option on its assets. This framework develops a model based on bank spread behav-ior that is explicitly capped by corporate borrower default risk. Our model allows the inclusion of more realistic market and credit risk cost conditions along with the more appropriate behavioral mode of loan rate-setting. A failure to recognize this realized cap would lead to undervaluation of the deposit insurance premium and leave the FDIC over-exposed to bank risk-taking at a reduced margin. However, we need to point out one important implication. When the economy recovers from the distress, the corporate borrower investment return is expected to increase. One way the bank may attempt to augment its total returns is by shifting its investments to its loan portfolio and away from the Federal funds market, resulting in increasing the FDIC over-exposed to bank loan risk taking when the realized cap is ignored, thereby adversely affecting the stability of the banking system. It is necessary that the realized cap should be explicitly factored into the specification of risk-based deposit insurance premium.

One caveat that should be stressed is that the deposit insurer cannot opt for bank clo-sure until the expiration of the insurance period in our analysis. This paper does not deal with many other important issues of using path dependent, barrier options in some form to address the problem of early bank closure [39,40]. While they are undoubtedly signifi-cant issues, they can be perhaps best understood only when barriers are economically and statistically significant in a large cross-section of financial firms. Such concerns are be-yond the scope of this paper and therefore are not addressed here. What this paper does demonstrate, however, is the important role played by corporate borrower default risk capped into the call valuation of bank equity in affecting risk-based insurance premium estimates and invariably the stability of banking system.

REFERENCES

[1] A. H. Chen, N. Ju, S. C. Mazumdar and A. Verma, Correlated default risk and bank regulations,

Journal of Money, Credit, and Banking, vol.38, no.2, pp.375-398, 2006.

[2] E. Nier and U. Baumann, Market discipline, disclosure and moral hazard in banking, Journal of

Financial Intermediation, vol.15, no.3, pp.332-361, 2006.

[3] G. Pennacchi, Deposit insurance, bank regulation, and financial system risk, Journal of Monetary

Economics, vol.53, no.8, pp.1-30, 2006.

[4] H. Huizinga and G. Nicod`eme, Deposit insurance and international bank liabilities, Journal of

Bank-ing and Finance, vol.30, no.3, pp.965-987, 2006.

[5] F. Black and M. Scholes, The pricing of options and corporate liabilities, Journal of Political

Econ-omy, vol.81, no.3, pp.637-654, 1973.

[6] R. C. Merton, An analytic derivation of the cost of deposit insurance and loan guarantees, Journal

of Banking and Finance, vol.1, no.1, pp.3-11, 1977.

[7] G. Pennacchi, A reexamination of the over- (or under-) pricing of deposit insurance, Journal of

Money, Credit, and Banking, vol.19, no.3, pp.340-360, 1987.

[8] H. M. Mullins and D. H. Pyle, Liquidation costs and risk-based bank capital, Journal of Banking

and Finance, vol.18, no.1, pp.113-138, 1994.

[9] J. Dermine and F. Lajeri, Credit risk and the deposit insurance premium: A note, Journal of

Economics and Business, vol.53, no.5, pp.497-508, 2001.

[10] Federal Deposit Corporation, http://www.fdic.gov/deposit/insurance/assessments/proposed.htm, 2009.

[11] R. C. Merton, On the pricing of corporate debt: The risk structure of interest rates, Journal of

Finance, vol.29, no.2, pp.449-470, 1974.

[12] J. Y. Tsai, R. Jou and W. M. Hung, A barrier option framework for optimal bank interest margin with vendor financing, ICIC Express Letters, vol.6, no.10, pp.2481-2486, 2012.

[13] J. Y. Tsai, W. M. Hung and R. Jou, A structure-break barrier option model of optimal bank interest margin in a debt crisis, ICIC Express Letters, vol.6, no.9, pp.2289-2293, 2012.

[14] E. Ronn and A. Verma, Pricing risk-adjusted deposit insurance: An option-based model, Journal of

(10)

[15] A. Episcopos, The implied reserves of the bank insurance fund, Journal of Banking and Finance, vol.28, no.7, pp.1617-1635, 2004.

[16] G. Delong and A. Saunders, Did the introduction of fixed-rate federal deposit insurance increase long-term bank risk-taking? Journal of Financial Stability, vol.7, no.1, pp.19-25, 2011.

[17] T. Ho and A. Saunders, The determinants of bank interest margins: Theory and empirical evidence,

Journal of Financial and Quantitative Analyses, vol.16, no.4, pp.581-600, 1981.

[18] L. Angbazo, Commercial bank net interest margins, default risk, interest rate risk and off balance sheet activities, Journal of Banking and Finance, vol.21, no.1, pp.55-87, 1997.

[19] J. Maudos and F. J. de Guevara, Factors explaining the interest margin in the banking sectors of the European Union, Journal of Banking and Finance, vol.28, no.9, pp.2259-2281, 2004.

[20] K. Hawtrey and H. Liang, Bank interest margins in OECD countries, North American Journal of

Economics and Finance, vol.19, no.3, pp.249-260, 2008.

[21] E. Zarruk and J. Madura, Optimal bank interest margin under capital regulation and deposit insur-ance, Journal of Financial and Quantitative Analysis, vol.27, no.1, pp.143-149, 1992.

[22] K. P. Wong, On the determinants of bank interest margins under credit and interest rate risks,

Journal of Banking and Finance, vol.21, no.2, pp.251-271, 1997.

[23] D. C. Wheelock and S. C. Kumbhakar, Which banks choose deposit insurance? Evidence of adverse selection and moral hazard in a voluntary insurance system, Journal of Money, Credit and Banking, vol.27, no.1, pp.186-201, 1995.

[24] A. Demirguc-Kunt and E. Detragiache, Does deposit insurance increase banking system stability?

IMF Working Paper, No.00/3, 2000.

[25] L. Laeven, Bank risk and deposit insurance, World Bank Economic Review, vol.16, no.1, pp.109-137, 2002.

[26] A. Demirguc-Kunt, B. Karacaovali and L. Laeven, Deposit insurance around the world: A compre-hensive database, World Bank Policy Research Working Paper, No.3628, 2005.

[27] E. P. Davis and U. Obasi, Deposit insurance systems and bank risk, Brunel University Working

Paper, No.09-26, 2009.

[28] B. Williams, Factors determining net interest margins in Australia: Domestic and foreign banks,

Financial Markets, Institutions and Instruments, vol.16, no.3, pp.145-165, 2007.

[29] M. Vassalou and Y. Xing, Default risk in equity returns, Journal of Finance, vol.59, no.2, pp.831-868, 2004.

[30] X. Wang and L. Wang, Study on Black-Scholes stock option pricing model based on dynamic in-vestment strategy, International Journal of Innovative Computing, Information and Control, vol.3, no.6(B), pp.1755-1780, 2007.

[31] W. M. Hung and J. H. Lin, Option-based modelling of technology choices and bank performance,

ICIC Express Letters, vol.6, no.8, pp.2019-2024, 2012.

[32] K. Kholodilin and V. W. Yao, Modelling the structural break in volatility, Applied Economic Letters, vol.13, no.7, pp.417-422, 2006.

[33] J. C. Rochet, Rebalancing the three pillars of Basel II, Economic Policy Review, vol.10, no.2, pp.7-21, 2004.

[34] A. K. Kashyap, R. Rajan and J. C. Stein, Banks as liquidity providers: An explanation for the coexistence of lending and deposit-taking, Journal of Finance, vol.57, no.1, pp.33-73, 2002.

[35] A. Saunders and L. Schumacher, The determinants of bank interest rate margins: An international study, Journal of International Money and Finance, vol.19, no.6, pp.813-832, 2000.

[36] D. VanHoose, Theories of bank behavior under capital regulation, Journal of Banking and Finance, vol.31, no.12, pp.3680-3697, 2007.

[37] A. Demirguc-Kunt, E. J. Kane and L. Laeven, Deposit insurance design and implementation: Policy lessons from research and practice, Policy Research Working Paper, No 3969, 2006.

[38] G. Garcia, Deposit insurance: Actual and good practices? Occasional Paper, International Monetary Fund, 2001.

[39] P. Brockman and H. J. Turtle, A barrier option framework for corporate security valuation, Journal

of Financial Economics, vol.67, no.3, pp.511-529, 2003.

[40] A. Episcopos, Bank capital regulation in a barrier option framework, Journal of Banking and

參考文獻

相關文件

• Similar to futures options except that what is delivered is a forward contract with a delivery price equal to the option’s strike price.. – Exercising a call forward option results

• A knock-in option comes into existence if a certain barrier is reached?. • A down-and-in option is a call knock-in option that comes into existence only when the barrier is

• Similar to futures options except that what is delivered is a forward contract with a delivery price equal to the option’s strike price. – Exercising a call forward option results

• A knock-in option comes into existence if a certain barrier is reached.. • A down-and-in option is a call knock-in option that comes into existence only when the barrier is

• Similar to futures options except that what is delivered is a forward contract with a delivery price equal to the option’s strike price. – Exercising a call forward option results

• Similar to futures options except that what is delivered is a forward contract with a delivery price equal to the option’s strike price.. – Exercising a call forward option results

• Similar to futures options except that what is delivered is a forward contract with a delivery price equal to the option’s strike price.. – Exercising a call forward option results

• Similar to futures options except that what is delivered is a forward contract with a delivery price equal to the option’s strike price.. – Exercising a call forward option results