Valuation of interest rate ceiling and floor based on the uncertain fractional differential equation in Caputo sense

2020 ◽  
pp. 1-10
Author(s):  
Ting Jin ◽  
Hui Ding ◽  
Bo Li ◽  
Hongxuan Xia ◽  
Chenxi Xue
Keyword(s):  
Interest Rate ◽  
Financial Market ◽  
Supply And Demand ◽  
Dynamic Change ◽  
Asset Price ◽  
Interest Rate Risk ◽  
Proposed Model ◽  
The Interest Rate ◽  
The Right ◽  
Predictor Corrector

As an economic lever in financial market, interest rate option is not only the function of facilitating the bank to adjust the market fund supply and demand relation indirectly, but also provides the guarantee for investors to choose whether to exercise the right at the maturity date, thereby locking in the interest rate risk. This paper mainly studies the price of the interest rate ceiling as well as floor under the uncertain environment. Firstly, from the perspective of expert reliability, rather than relying on a large amount of historical financial data, to consider interest rate trends, and further assume that the dynamic change of the interest rate conforms to the uncertain process. Secondly, since uncertain fractional-order differential equations (UFDEs) have non-locality features to reflect memory and hereditary characteristics for the asset price changes, thus is more suitable to model the real financial market. We construct the mean-reverting interest rate model based on the UFDE in Caputo type. Then, the pricing formula of the interest rate ceiling and floor are provided separately. Finally, corresponding numerical examples and algorithms are given by using the predictor-corrector method, which support the validity of the proposed model.

scholarly journals Lookback Option Pricing Problems of Uncertain Mean-Reverting Stock Model

2021 ◽  
Vol 25 (5) ◽  
pp. 539-545
Author(s):  
Zhaopeng Liu ◽  
Keyword(s):  
Interest Rate ◽  
Option Pricing ◽  
Asset Price ◽  
Option Price ◽  
Cir Model ◽  
Lookback Option ◽  
Proposed Model ◽  
Stock Model ◽  
Path Dependent ◽  
The Interest Rate

A lookback option is a path-dependent option, offering a payoff that depends on the maximum or minimum value of the underlying asset price over the life of the option. This paper presents a new mean-reverting uncertain stock model with a floating interest rate to study the lookback option price, in which the processing of the interest rate is assumed to be the uncertain counterpart of the Cox–Ingersoll–Ross (CIR) model. The CIR model can reflect the fluctuations in the interest rate and ensure that such rate is positive. Subsequently, lookback option pricing formulas are derived through the α-path method and some mathematical properties of the uncertain option pricing formulas are discussed. In addition, several numerical examples are given to illustrate the effectiveness of the proposed model.

scholarly journals Option Pricing Formulas in a New Uncertain Mean-Reverting Stock Model with Floating Interest Rate

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Zhaopeng Liu
Keyword(s):  
Interest Rate ◽  
Option Pricing ◽  
Financial Market ◽  
American Option Pricing ◽  
European Option ◽  
Numerical Examples ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Stock Model ◽  
The Interest Rate

Options play a very important role in the financial market, and option pricing has become one of the focus issues discussed by the scholars. This paper proposes a new uncertain mean-reverting stock model with floating interest rate, where the interest rate is assumed to be the uncertain Cox-Ingersoll-Ross (CIR) model. The European option and American option pricing formulas are derived via the α -path method. In addition, some mathematical properties of the uncertain option pricing formulas are discussed. Subsequently, several numerical examples are given to illustrate the effectiveness of the proposed model.

scholarly journals Risk of Interest Rates at the Level of Commercial Banks in Romania

2017 ◽  
Vol 22 (4) ◽  
pp. 281-288
Author(s):  
Ioana Raluca Sbârcea
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Commercial Banks ◽  
Asset Price ◽  
Banking System ◽  
Interest Rate Risk ◽  
Point Of View ◽  
Risk Indicators ◽  
Rate Risk ◽  
The Interest Rate

Abstract The banking system in Romania is a banking system under development, subject to fluctuations that exist on the market more than on more developed banking systems, fluctuations that can generate losses for banks if they are not properly managed. The losses that may be generated by these fluctuations, known as market risk, refer to the significant fluctuations in three indicators, namely the interest rate, the exchange rate and the asset price. In this article, I will analyse the interest rate risk from a conceptual point of view and the indicators that mitigate this risk. The analysis also contains a study of this risk among commercial banks in the system to highlight the level of risk and possible effects of its manifestation. I calculated and analysed the interest rate risk indicators, individually for the first three banks in the system, but also to comparatively, in order to highlight the existing differences.

scholarly journals Risk Management for Bonds with Embedded Options

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 790
Author(s):  
Antonio Díaz ◽  
Marta Tolentino
Keyword(s):  
Risk Management ◽  
Interest Rate ◽  
Interest Rates ◽  
Interest Rate Risk ◽  
Interest Rate Models ◽  
Management Measures ◽  
Interest Rate Risk Management ◽  
Embedded Options ◽  
The Interest Rate ◽  
Interest Rate Change

This paper examines the behavior of the interest rate risk management measures for bonds with embedded options and studies factors it depends on. The contingent option exercise implies that both the pricing and the risk management of bonds requires modelling future interest rates. We use the Ho and Lee (HL) and Black, Derman, and Toy (BDT) consistent interest rate models. In addition, specific interest rate measures that consider the contingent cash-flow structure of these coupon-bearing bonds must be computed. In our empirical analysis, we obtained evidence that effective duration and effective convexity depend primarily on the level of the forward interest rate and volatility. In addition, the higher the interest rate change and the lower the volatility, the greater the differences in pricing of these bonds when using the HL or BDT models.

Capital Budgeting and business cycles

2021 ◽  
pp. 315-335
Author(s):  
Edward W. Fuller
Keyword(s):  
Interest Rate ◽  
Demand Curve ◽  
Supply And Demand ◽  
Investment Project ◽  
The Other ◽  
Investment Projects ◽  
Scarce Resources ◽  
Other Hand ◽  
The Future ◽  
The Interest Rate

Every investment project is aimed at achieving some future goal. This goal can only be attained by employing scarce resources, like time. Every investment project entails foregoing other investment projects. It is impossible to undertake all investment projects simultaneously because resources are scarce. This means each investment project is subject to cost. The investment project may be unsuccessful in achieving the future goal and the entrepreneur may suffer a loss. On the other hand, investment projects are only undertaken because they are perceived as more valuable than their costs. Every investment project undertaken implies the possibility of earning a profit. Investment projects take time. An investment project can be represented by a time line. Time A represents the beginning of the production process. Time B is the end of the production pro-cess. Line AB is called the period of production. Present goods are scarce resources that can be consumed im-mediately. On the other hand, future goods cannot be consumed immediately. Future goods are only expected to be consumer goods at some point in the future. An investment project entails making an investment at time A and receiving a present good at time B. All else equal, present goods are more valuable than future goods.1 Any good at time A is more valuable than the same good at time B. This is called time preference. Money is the present good par excellence. Therefore, future goods can be called future cash flows. All else equal, present money is more valuable than future money. This is called the time value of money. The interest rate is the price of present goods in terms of future goods. The interest rate is the price which equates the amount of present goods provided by savers with the amount of present goods demanded by investors. Like all prices, the interest rate is determined by supply and demand. Savers are suppliers of present goods. The supply curve (S) is the quantity of present goods supplied at each interest rate. Factor owners (investors) are the demanders, or buyers, of present goods. The demand curve (D) is the quantity of present goods demanded at each interest rate. The intersection of the supply and demand curve determines the interest rate. The interest rate is determined by the supply and demand for present goods:2

scholarly journals Market Structure, Macroeconomic Shocks, and Banking Risk in Kenya

2016 ◽  
Vol 1 (2) ◽  
pp. 81-113
Author(s):  
Nderitu Kingori
Keyword(s):  
Growth Rate ◽  
Interest Rate ◽  
Market Structure ◽  
Interest Rate Risk ◽  
Risk Exposure ◽  
Economic Shocks ◽  
Macroeconomic Shocks ◽  
Net Interest Margin ◽  
The Interest Rate ◽  
Loan Growth

This paper investigates the effect of changing market structure and macroeconomic shocks on the borrowing and lending risk exposure of Kenyan commercial banks using a GMM estimation approach. Borrowing risk exposure was found not to be persistent, being mainly affected by the degree of concentration and external economic shocks. Interestingly, the results also suggest that changes in the short-term interest rate do not affect the net interest margin, which may imply that bank deposit and lending rates are rigid and that the interest rate channel may be ineffective. The lending risk exposure was found to be persistent, and it was affected by the degree of concentration, internal economic shocks, and external economic shocks. The positive relationship between degree of concentration as well as borrowing and lending risk exposure supports the concentration-fragility view, as the declining franchise value did not lower incentives for making good loans during the study period where the degree of concentration was on a downward trend. Further analysis of the factors contributing to the persistence of lending risk exposure using a PVAR model found that the banks' loan growth rate and the market interest rate were key determinants. The effect of the loan growth rate was about double the effect of interest rate risk, implying that risk taking by some of the medium-sized and small banks is the key determinant of the persistence of lending risk exposure.

Evaluating Alternative Explanations

2019 ◽  
pp. 208-229
Author(s):  
Jonas B. Bunte
Keyword(s):  
Developing Countries ◽  
Interest Rate ◽  
Supply And Demand ◽  
Relative Importance ◽  
Demand Side ◽  
Humanitarian Emergencies ◽  
Debt Crises ◽  
The Interest Rate

This chapter evaluates alternative explanations for differences in borrowing portfolios across developing countries. The analysis suggests that borrowing portfolios result from the interaction of supply- and demand-side factors, through their relative importance differs across creditors. Loans from private creditors are more heavily shaped by creditors’ preferences, while recipient preferences strongly affect borrowing from public creditors. The analysis finds no evidence that recognizing Taiwan negatively affects the loan volume obtained from China. Recipient governments do not appear to decide among creditors based on the interest rate of loans offered. Borrowing portfolios do not depend on the use to which the loan is put as differences in borrowing portfolios across coalitions remain irrespective of infrastructure needs, humanitarian emergencies, and debt crises. This suggests that recipients do not use particular creditors for specific projects. Lastly, domestic political considerations appear more important in determining governments’ borrowing decisions than their ideological alignment with creditor governments.

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