ARBITRAGE-FREE VALUATION OF BILATERAL COUNTERPARTY RISK FOR INTEREST-RATE PRODUCTS: IMPACT OF VOLATILITIES AND CORRELATIONS

2011 ◽  
Vol 14 (06) ◽  
pp. 773-802 ◽  
Author(s):  
DAMIANO BRIGO ◽  
ANDREA PALLAVICINI ◽  
VASILEIOS PAPATHEODOROU
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Default Risk ◽  
Net Present Value ◽  
Credit Spread ◽  
Counterparty Risk ◽  
Put Option ◽  
Underlying Risk Factor ◽  
Credit Valuation Adjustment ◽  
Future Work

The purpose of this paper is introducing rigorous methods and formulas for bilateral counterparty risk credit valuation adjustment (CVA) on interest-rate portfolios. In doing so, we summarize the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk, including the default of the investor. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net present value of the contract at the relevant default times. We allow for correlation between the default times of the investor and counterparty, and for correlation of each with the underlying risk factor, namely interest rates. We also analyze the often neglected impact of credit spread volatility. We include close-out netting rules in our examples, although other agreements, such as periodic margining or collateral posting, are left for future work.

PRICING COUNTERPARTY RISK INCLUDING COLLATERALIZATION, NETTING RULES, RE-HYPOTHECATION AND WRONG-WAY RISK

2013 ◽  
Vol 16 (02) ◽  
pp. 1350007 ◽  
Author(s):  
DAMIANO BRIGO ◽  
AGOSTINO CAPPONI ◽  
ANDREA PALLAVICINI ◽  
VASILEIOS PAPATHEODOROU
Keyword(s):  
Interest Rate ◽  
Credit Derivatives ◽  
Credit Default Swaps ◽  
Credit Spread ◽  
Counterparty Risk ◽  
Default Correlation ◽  
Dynamical Models ◽  
Credit Default ◽  
The Impact

This article is concerned with the arbitrage-free valuation of bilateral counterparty risk through stochastic dynamical models when collateral is included, with possible rehypothecation. The payout of claims is modified to account for collateral margining in agreement with International Swap and Derivatives Association (ISDA) documentation. The analysis is specialized to interest-rate and credit derivatives. In particular, credit default swaps are considered to show that a perfect collateralization cannot be achieved under default correlation. Interest rate and credit spread volatilities are fully accounted for, as is the impact of re-hypothecation, collateral margining frequency, and dependencies.

Determinants of Treasury-LIBOR Swap Spreads

2005 ◽  
Vol 08 (04) ◽  
pp. 687-705 ◽  
Author(s):  
D. K. Malhotra ◽  
Vivek Bhargava ◽  
Mukesh Chaudhry
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Default Risk ◽  
Yield Curve ◽  
Short Term ◽  
Long Run ◽  
Interest Rate Volatility ◽  
Short Run ◽  
Using Data ◽  
Swap Spreads

Using data from the Treasury versus London Interbank Offer Swap Rates (LIBOR) for October 1987 to June 1998, this paper examines the determinants of swap spreads in the Treasury-LIBOR interest rate swap market. This study hypothesizes Treasury-LIBOR swap spreads as a function of the Treasury rate of comparable maturity, the slope of the yield curve, the volatility of short-term interest rates, a proxy for default risk, and liquidity in the swap market. The study finds that, in the long-run, swap spreads are negatively related to the yield curve slope and liquidity in the swap market. We also find that swap spreads are positively related to the short-term interest rate volatility. In the short-run, swap market's response to higher default risk seems to be higher spread between the bid and offer rates.

THE IMPACT OF LEARNING ON BUSINESS CYCLE FLUCTUATIONS IN THE CONSUMER UNSECURED CREDIT MARKET

2018 ◽  
Vol 24 (5) ◽  
pp. 1087-1123 ◽  
Author(s):  
Matthew N. Luzzetti ◽  
Seth Neumuller
Keyword(s):  
Business Cycle ◽  
Interest Rates ◽  
Default Risk ◽  
Credit Market ◽  
Credit Spread ◽  
Cross Sectional ◽  
Business Cycle Fluctuations ◽  
Unsecured Debt ◽  
Consumer Default ◽  
The Impact

We document that the credit spread on consumer unsecured debt exhibits a persistent, hump-shaped response to an increase in the charge-off rate. This stylized fact poses a significant challenge for a standard model of consumer default in which lenders have rational expectations and, therefore, the credit spread continuously adjusts to reflect the true default incentives of each borrower. In an effort to explain this feature of the data, we construct a model of consumer default with countercyclical income risk in which lenders learn about default risk over time by observing the history of repayment decisions, as is the case in practice. In addition to matching credit spread dynamics, allowing lenders to learn about default risk substantially improves the model’s ability to generate realistic business cycle fluctuations in the consumer unsecured credit market and match the cross-sectional distribution of unsecured debt and dispersion of interest rates observed in the data.

Economics of harvesting boreal uneven-aged mixed-species forests

2015 ◽  
Vol 45 (8) ◽  
pp. 1102-1112 ◽  
Author(s):  
Janne Rämö ◽  
Olli Tahvonen
Keyword(s):  
Steady State ◽  
Interest Rate ◽  
Interest Rates ◽  
Norway Spruce ◽  
Net Present Value ◽  
Single Species ◽  
Mixed Species ◽  
Volume Yield ◽  
Gradient Based ◽  
The Interest Rate

The subject of this study is the economics of harvesting boreal uneven-aged mixed-species forests consisting of Norway spruce (Picea abies (L.) Karst.), Scots pine (Pinus sylvestris L.), birch (Betula pendula Roth and B. pubescens Ehrh.), and other broadleaves. The analysis is based on an economic description of uneven-aged forestry, applying a size-structured model. The optimization problem is solved in its general dynamic form using gradient-based interior point methods. When volume yield is maximized, the optimal steady state is a nearly pure Norway spruce stand at all site types, producing slightly higher yields than single-species stands. After including sawlog and pulpwood prices, the net present value of stumpage revenues is maximized using 1%, 3%, and 5% interest rates and a 15-year harvesting interval. At less productive sites, the stands are nearly pure Norway spruce stands, regardless of the interest rate. At more productive sites, increasing the interest rate increases the species diversity, with optimal steady states consisting of both Norway spruce and birch. In some cases, rather small changes in relative prices change the optimal steady state into a birch-dominated stand. Optimal solutions converge to the same steady-state solutions, independent of the initial stand state. If other broadleaves without commercial value are not harvested, they will eventually dominate the stand.

scholarly journals Citizen Participation to Finance PV Power Plants Focused on Self-Consumption on Company Roofs—Findings from an Austrian Case Study

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 738
Author(s):  
Matthias Linhart ◽  
Valerie Rodin ◽  
Simon Moser ◽  
Andrea Kollmann
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Citizen Participation ◽  
Power Plants ◽  
Economies Of Scale ◽  
Net Present Value ◽  
Small Scale ◽  
Industrial Parks ◽  
Financial Benefits ◽  
Joint Purchase

Despite large amounts of available roof space, long pay-back periods for investments in photovoltaic (PV) power plants often hinder PV installations in industrial parks. Photovoltaic citizen participation initiatives (PV-CPI) are an alternative way of financing PV power plants that add non-financial benefits to these investments. This paper analyzed the feasibility of the installation of PV power plants focused on high rates of self-consumption financed by citizen participation initiatives on the roofs of five companies located in the Austrian Ennshafen industrial business park based on the net present value and the discounted pay-back period and compared it to a standard financing scheme, assuming a predetermined interest rate for participants as well as economies of scale with respect to the specific installation costs due to a joint purchase of the PV power plants. To calculate the feasibility, site-specific data and literature input have been used. The results show that despite an interest rate above the current interest rates of conservative forms of investments provided to (small-scale) investors, a payback-period of 17–23 years can be reached while the joint purchase can lead to a competitive feasibility of the PV-CPI compared to an individual purchase of PV power plants.

scholarly journals Stochastic Volatility Estimation of Stock Prices using the Ensemble Kalman Filter

2021 ◽  
Vol 3 (2) ◽  
pp. 136-143
Author(s):  
Yudi Mahatma ◽  
Ibnu Hadi
Keyword(s):  
Kalman Filter ◽  
Interest Rate ◽  
Interest Rates ◽  
State Space ◽  
Stochastic Volatility ◽  
Ensemble Kalman Filter ◽  
Price Volatility ◽  
Call Option ◽  
Put Option ◽  
Black Scholes

AbstractVolatility plays important role in options trading.  In their seminal paper published in 1973, Black and Scholes assume that the stock price volatility, which is the underlying security volatility of a call option, is constant.  But thereafter, researchers found that the return volatility was not constant but conditional to the information set available at the computation time.  In this research, we improve a methodology to estimate volatility and interest rate using Ensemble Kalman Filter (EnKF).  The price of call and put option used in the observation and the forecasting step of the EnKF algorithm computed using the solution of Black-Scholes PDE.  The state-space used in this method is the augmented state space, which consists of static variables: volatility and interest rate, and dynamic variables: call and put option price. The numerical experiment shows that the EnKF algorithm is able to estimate accurately the estimated volatility and interest rates with an RMSE value of 0.0506.Keywords: stochastic volatility; call option; put option; Ensemble Kalman Filter. AbstrakVolatilitas adalah faktor penting dalam perdagangan suatu opsi.  Dalam makalahnya yang dipublikasikan tahun 1973, Black dan Scholes mengasumsikan bahwa volatilitas harga saham, yang merupakan volatilitas sekuritas yang mendasari opsi beli, adalah konstan. Akan tetapi, para peneliti menemukan bahwa volatilitas pengembalian tidaklah konstan melainkan tergantung pada kumpulan informasi yang dapat digunakan pada saat perhitungan.  Pada penelitian ini dikembangkan metodologi untuk mengestimasi volatilitas dan suku bunga menggunakan metode Ensembel Kalman Filter (EnKF).  Harga opsi beli dan opsi jual yang digunakan pada observasi dan pada tahap prakiraan pada algoritma EnKF dihitung menggunakan solusi persamaan Black-Scholes.  Ruang keadaan yang digunakan adalah ruang keadaan yang diperluas yang terdiri dari variabel statis yaitu volatilitas dan suku bunga, dan variabel dinamis yaitu harga opsi beli dan harga opsi jual. Eksperimen numerik menunjukkan bahwa algoritma ENKF dapat secara akurat mengestimasi volatiltas dan suku bunga dengan RMSE 0.0506.Kata kunci: volatilitas stokastik; opsi beli; opsi jual; Ensembel Kalman Filter.

Emerging Markets Interest Rates, International Reserves and Net Foreign Assets

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Joseph Bitar ◽  
Martin Boileau
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Risk Premium ◽  
Default Risk ◽  
International Reserves ◽  
Net Foreign Assets ◽  
Portfolio Balance ◽  
The Interest Rate ◽  
Interest Differential ◽  
Foreign Assets

Abstract In the context of a managed float regime, we adopt the portfolio balance view to show the effects of the net foreign assets of an economy and its gross international reserves level on interest rate differentials. We argue that the interest rate differential can be explained by three components, where the components are the expected depreciation of the domestic currency, a default risk premium, and a portfolio balance premium. Our theoretical analysis suggests that the interest differential is a convex function of the level of gross international reserves. In particular, the differential and gross reserves are inversely related at low levels of reserves, but positively at higher levels. We evaluate our framework for the case of Lebanon. We find that the differential is inversely related to both net foreign assets and gross international reserves. These findings are then confirmed with data from Indonesia and Mexico.

scholarly journals Commercial Real Estate at the ZLB

2018 ◽  
Vol 13 (1) ◽  
pp. 32-53
Author(s):  
Bjørnar Karlsen Kivedal ◽  
Trond Arne Borgersen
Keyword(s):  
Interest Rate ◽  
Real Estate ◽  
Interest Rates ◽  
Systemic Risk ◽  
Net Present Value ◽  
Weighted Average ◽  
Commercial Real Estate ◽  
Federal Funds Rate ◽  
Evaluation Models ◽  
The Difference

This paper analyses the implications of a low interest rate environment (the zero lower bound – ZLB) for the demand of commercial real estate. The main intention of the paper is to track any asymmetry between evaluation models at ZLB relative to more “normal” interest rate levels. First we apply a conventional net-present value (NPV) approach, where the weighted average cost of capital (WACC) and the capital asset pricing model (CAPM) are used for evaluation. Considering the invariance level of systemic risk we find WACC to be an alternative to CAPM for offensive and defensive investments when interest rates are “normal”. However, at the ZLB, WACC is an alternative for investments that carry the same risk as the market and beta-values are close to one. Second, we simulate our models using US data to see how the WACC shortcut performs across different interest rate levels, and especially at ZLB, in this economy. We see differences between the period preceding the financial crisis and the period after 2010, even though the Federal Funds rate is close to zero in both periods. We relate this to the difference in systemic risk between the two periods, and show how the result in the latter period is quite equal across evaluation models.

scholarly journals Fund Matching between Fund-Raisers and Investors in Financing Platform with Consideration of Default Risk

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Kenan Li ◽  
Xin Li ◽  
Zhijun Lin ◽  
Jing Lu ◽  
Pak Hou Che
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Default Risk ◽  
Random Variable ◽  
Expected Profit ◽  
General Distribution ◽  
Time Interval ◽  
The Interest Rate ◽  
The Cost ◽  
Fund Raiser

We construct a stochastic model to study the fund matching between fund-raisers and investors in a financing platform. The raising time is assumed to be a random variable. Then, there is a successful transaction probability that the fund matching is realized. Meanwhile, the interest and the commission rate that the platform earns affect the value of the probability. The platform maximizes its revenue by adjusting the commission rate. We find that the optimal commission rate decreases in investment time. However, when the time interval between two adjacent investments obeys the general distribution, the optimal commission rate increases in the annual interest rate. Besides, we extend the model into a duopoly case in which two fund-raisers compete for customers in the same platform by deciding their own interest rate. Due to lacking competition, the optimal interest rate in the monopoly case is lower than that in the duopoly case. Because the interest rate is the cost for the fund-raiser, the expected profit of the fund-raiser in the monopoly is higher than the expected profit of each fund-raiser in the duopoly case but lower than the total expected profit of two fund-raisers. The platform should choose some small loans as far as possible. The loans with smaller amount are easier for the platform to complete fundraising. For those large loans, the platform should try to ask for higher interest rates or more sufficient time to raise funds.

scholarly journals Economic effects of grouse-friendly forest management

Silva Fennica ◽  
2021 ◽  
Vol 55 (3) ◽  
Author(s):  
Arto Haara ◽  
Juho Matala ◽  
Markus Melin ◽  
Janne Miettinen ◽  
Kari Korhonen ◽  
...  
Keyword(s):  
Forest Management ◽  
Interest Rate ◽  
Interest Rates ◽  
Management Practices ◽  
Net Present Value ◽  
Economic Effects ◽  
Negative Effects ◽  
Management Guidelines ◽  
Thinning Intensity ◽  
Management Approaches

Traditional timber production may have negative effects on other ecosystem services. Therefore, new forest management guidelines have been developed in order to enhance a habitat suitable for wildlife. In Finland, a recent example of this is grouse-friendly forest management (GFFM) which emphasises the preservation of grouse species (Tetronidae) habitats. This study aimed to analyse the economic effects of these guidelines. An analysis was made on how the application of GFFM affected the Net Present Value (NPV) in a 30-year simulation of forest management of four large forest holdings located from south to north in Finland. In the simulations, traditional forest management practices were compared to two levels of GFFM. Five levels of interest rate were used, namely 1, 2, 3, 4, and 5%. In most of the simulations, the NPV was reduced by about 1% or less due to the application of GFFM in comparison to the traditional reference forest management. Only in one case with more intensive GFFM, was the reduction of NPV more than 5%. The interest rates had an impact on the differences between the management approaches. For example, a low interest rate resulted in a higher thinning intensity in GFFM in comparison to traditional forest management, which lead to a higher NPV in GFFM. To sum up, it seems that it would be possible to manage forest holdings in a grouse-friendly manner with minor effects on the economics.

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