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The purpose of this article is to introduce a model that describes the competition between online lenders who have flexibility in determining the rates charged and covenants imposed. The online lenders lower competition by differentiating themselves with these two choice variables.
The lenders’ profit functions include the severity of loan covenants as an argument, which affects costs.

The borrower’s profit function also includes a measure of the severity of loan covenants.
The resulting model can help practitioners and researchers understand how online lenders who can offer varying terms in the loan contracts will choose the terms based upon the perceived risk of relaxing loan covenants, the number of borrowers, and borrowers’ costs of complying with a given level of severity of loan covenants. The results will help predict future trends in loan covenants and rates in the online lending market based upon the number and characteristics of borrowers.,The Internet provides a means for businesses to connect with customers and do transactions undreamed of a few decades ago.
Buyers and sellers connect on EBay to negotiate prices. Travelers use online sites to find lodging in private homes.

Borrowers can now search for lenders who will offer terms that best fit their needs, and online lenders must compete for that business.
The online lending industry is particularly attractive to households and small businesses with diverse needs and higher risk than established corporate borrowers. Like any industry, businesses will find it beneficial to specialize.

Some lenders will prefer to service more secure borrowers, impose more strict covenants that these borrowers are likely to meet, and charge a lower interest rate.
Another group of lenders will charge higher interest rates to less secure borrowers who cannot meet strict covenants. Our model examines how lenders might differentiate themselves with respect to the interest rates charged and the severity of the loan covenants.

The model contributes to the literature on bank competition that has grown substantially with the trends in deregulation and now the growth of the online lending. Early examples in this line of literature include [1] who model banks’ choices of geographical reach and loan pricing and [2] who examine the competition for deposits.,The model in this paper is an adaptation of a general model developed by [3].
That is now an established model in the industrial organization literature, and it describes a duopoly market where the firms avoid direct competition by offering products with different qualities and prices.

We build upon that model by including three lenders that offer loans with different severity of loan covenants to avoid direct competition. There is one lender who offers only fully secured loans and two online lenders who offer loans with less severe covenants. The online lenders avoid direct competition by differentiating themselves with respect to the severity of the covenants they require and the interest rate they charge borrowers.,The model determines the market share, profits, and equilibrium severity of loan covenant (SLC) levels in terms of exogenous parameters such as the expected loss associated with a given level of SLC, the number of borrowers, the cost of borrowers to comply with the covenants, and macroeconomic risk.
The model demonstrates that when the cost of complying with covenants increases (decreases), the SLCs will decrease (increase) and diverge (converge). When decreasing the severity of loan covenants has a larger (lower) impact on expected losses, however, the SLCs will increase (decrease) and diverge (converge).,The review of the literature in the next section provides the sources of the theories and assumptions used in this model. After that section, we introduce the parameters within the framework of a market where there is one lender who only makes fully secured loans and an online lender who offers loans with less severe covenants at a higher interest rate.

After that, we expand the model to include a second online lender who offers loans with less severe covenants.
Then, there is a section that employs comparative statics to demonstrate the implications of the model, which is followed by summary and discussion.,There is a lengthy literature on the entry of firms into industries where profit opportunities exist. The work in [12] and [13] pioneered the modern sequential-entry models. The work in [14] extended the model to allow for endogenous prices, and this development has characterized later models including the one in this paper. Subsequent work in this area includes [3], [9], [15]-[21].

The model here builds upon the model established in [3]. The model in [3] is a vertical differentiation model with a stable and tractable equilibrium. Furthermore, the consumer utility function of the model in [3] easily adapts to a profit function of a borrowers who pay an interest rate and must incur a cost to comply with loan covenants.,As [11] mentions, there is usually not one “true model” to describe a given market.
Several models may apply. This paper lays a solid foundation for future work in this area by thoroughly investigating the results associated with the modification of an established spatial model in the industrial organizations literature.
In our model, the second-order conditions are satisfied, and the model yields a unique and stable equilibrium.

Having successfully adapted one model from the industrial organizations literature to the market for online loans with lower levels of the severity of loan covenants compared to traditional banks, future research can explore the extent to which other models apply.,This section serves two purposes. It introduces the parameters of the market and the corresponding simplifying assumptions of the model. It also describes the model’s equilibrium with only one online lender offering loans with a low SLC at a higher interest rate. There is also a lender who only makes loans with an SLC sufficiently high so as to make the loans fully secured.second chance payday loans direct lenders
The equilibrium is a standard result, but it sets the stage for examining the results when there are two online lenders competing for loans that are not fully secured.,As mentioned earlier, our model builds upon the model in [3], which only has two firms competing with quality. In our full model, borrowers have three choices.

The first choice is to choose to borrow from a traditional bank. This means the borrowers must meet some high level of SLC, which make the loans fully secured and pay a low interest rate. The other two choices consist of two lenders who offer lower but distinct SLCs and correspondingly higher interest rates.
Before introducing that three-lender market, we first consider a case where there is only one online lender with a low SLC compared to traditional banks.,Y: the level of return expected from investing the proceeds of the loan,,Ri: the interest rate charged on the loan,,Each borrower takes the same size loan and invests the proceeds in an endeavor that will produce a positive return, Y, either in the form of direct profit in the case of a business loan or the elimination of rental payments and capital gains in the case of a home loan. The interest rate consists of two portions: Ri = r0 + ri. The term r0 is the rate charged on a loan where the SLC is high enough to make the loan essentially free of loan specific, i.e., idiosyncratic, risk, therefore, for loans with an SLC = σ0 so there is no idiosyncratic risk R0 = r0.

The term ri is a premium charged by the lender for imposing a lower SLC σi lt, σ0, where σi represents the SLC where idiosyncratic risk is positive. We assume that that R0, the interest rate for loans without idiosyncratic risk, is exogenously determined.,As assumed in the ADT model and many other models of this type, κ is uniformly distributed and identifies each borrower. The lower bound on κ is zero, and there is an upper bound, which we denote K. The value of the density function over zero to K is the number of potential borrowers divided by the upper limit of the covenant cost factor.

Letting N represent the number of borrowers and ϕ’(κ) represent the density function, we can write ϕ’(κ) = N/K when 0 ≤ κ ≤ K, else ϕ’(κ) = 0. At this point we assume that Y is sufficiently high so as to exceed both the interest rate and the costs of adhering to the loan covenants. Future research will examine the implications of the possibility of Y lt, Ri + κσi.,For the lender that makes loans with σ0, the expected loss is negligible.
The low SLC lender will incur higher expected losses by lowering the SLC by the distance given by (σ0 − σ1). There is a scale factor ξ that varies with the state of the economy, and there is an increasing expected loss from each unit increase in (σ0 − σ1). The profit functions are:,The interest rate and SLC and, hence, the profit for the lender making loans with the SLC associated with σ0 are exogenously determined by the economy. Thus, the lender offering loans with the SLC = σ1 makes a choice of the interest rate to charge and the value of σ1.

Substituting κ* into the profit function of that lender and optimizing with respect to the interest rate gives this expression for the optimal rate: R1* = r0 + K(σ0 − σ1)/2.
Using the assumed distribution ofκ gives the following expression: κ* = [K(σ0 − σ1)/2]/(σ0 − σ1) = K/2. This is a standard result in a market where only one firm makes price and quality or quantity decisions. It is immutable with respect to the choices of interest rate and SLC and the lender’s expected loss function2.,Other things equal, a unit increase/decrease in σ0 will increase/decrease σ1 by an equal amount.
The absolute difference in SLCs increases when N or K increases.

Naturally, the online lender finds it profitable to accommodate an increase in the costs of borrowers to meet loan covenants by distinguishing its product more from σ0. Likewise, since dσ1/dξ = 0.125NK/ξ2 gt, 0, the lender will increase SLC when the expected loss parameter ξincreases. Since the low-SLC lender will always lend to K/2 investors, an increase in K motivates the lender to lower the SLC. An increase in N increases the marginal revenue from a given increase in R1, and the lender will lower σ1.,The interest rate is R1 = r0 + 0.0625NK2/ξ.
The profit of the online lender is π1 = 0.015625(NK)2/ξ, and dπ1/dK gt, 0, dπ1/dN gt, 0, dπ1/dξ lt, 0. A higher cost of meeting loan covenants and a larger population of borrowers increase profits.

An increase in the expected loss from a given lowering of the LCS lowers profits.,The results developed in this section are straightforward and conform to intuition. The goal of this section has been to demonstrate the results of the model in the relatively simple case of a single lender that can choose its level of SLC and interest rate competing with a lender who can only make loans free of idiosyncratic risk with an exogenously determined SLC.
The next section investigates the results when a second lower SLC lender enters the market offering borrowers more choices of SLC and interest rate combinations.,The term (N/K)(K − κ2*) indicates the number of online borrowers who take out loans with the lowest SLC from lender 2. The corresponding measure for lender 1 is (N/K)(κ2* − κ1*). Solving for each Ri* as before yields,,The competition forces interest rates on the online loans to decline. The rate R2 in the three lender case is about 14% lower than R1 in the case where there was only the lender who makes fully secured loans and a single low-SLC or online lender. The corresponding SLC declines by about one percent.

These adjustments increase that online lender’s market share from 50% to 52.5%.
Lender 2 serves 26.25% of all potential online borrowers. The remaining 21.25% borrowers choose R0 and σ0.

These market shares are immutable as long as all lenders remain in the market and ξ is the same for both low SLC lenders.,This section examines how changes in exogenous parameters affect the equilibrium derived in the previous section. Comparative statics yield interesting results with respect to how the equilibrium SLC levels, interest rates and profits react to changes in σ0, ξ, N and K. Respectively, these parameters relate to the severity of loan covenants needed to reduce idiosyncratic risk, a scale parameter for the expected losses from lowering the SLC, the number of borrowers, and the costs the borrowers incur from complying with the covenants.,Given a fixed number of potential borrowers, an increase in K implies that the borrowers incur higher costs for complying with the loan covenants.
The equilibrium conditions imply that an increase in K will decrease the SLC, profit and interest rate more for lender 2 than for lender 1. The choice variables for lender 1 are less responsive because lender 0 offers the immutable choice of R0 and σ0. If K falls, the lenders will allow σ2and σ1 to increase, but lender 1 cannot allow σ1 to increase too much because σ0 does not change.
In summary, an increase (decrease) in K decreases (increases) both s1 and s2, the quantity s1-s2 increases (decreases), interest rates diverge (converge) and profits diverge (converge).,This paper demonstrates a methodology for analyzing how online lenders willing to make loans to households and small businesses can compete with different levels of severity of loan covenants (SLCs).

Future research can build on this model, which describes the relationship between a two online lenders, i.e., lenders who offer different levels of lower SLCs. Previous research supports the proposition that a second firm can enter the market if it chooses to produce a product of a different quality, and the existence of a variety of qualities in various financial products, e.g., brokerage services and trading platform accuracy and now online lending, supports this proposition.
Our model demonstrates how the market forces determine interest rates, SLC levels, and profits in a market where there are three lenders of which two choose to offer the lower SLC loans.,These results provide a foundation for both theoretical and empirical research. Future work will relax assumptions concerning the distribution of the covenant cost factor and allow the return, Y, the borrowers plan to earn on their investment to vary across investors and even fall below a range of values Ri + kσi, where k lt, K. Although game-theory models can become very complex, continued work in this field will allow researchers and practitioners to better understand the evolving market for financial services such as the market for loans with different severity of loan covenants.,1The cost function can also be interpreted as being determined by the number of loans made since the distance (σ0 − σ1) also determines the number of loans the low SLC lender makes.

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