scholarly journals THE SMALL AND LARGE TIME IMPLIED VOLATILITIES IN THE MINIMAL MARKET MODEL

2012 ◽  
Vol 15 (08) ◽  
pp. 1250057
Author(s):  
ZHI JUN GUO ◽  
ECKHARD PLATEN
Keyword(s):  
Interest Rates ◽  
Implied Volatility ◽  
Large Time ◽  
Time Limit ◽  
Market Model ◽  
Explicit Formulas ◽  
Time Limits ◽  
Long Run ◽  
Minimal Market Model ◽  
Short Time

This paper derives explicit formulas for both the small and the large time limits of the implied volatility in the minimal market model. It is shown that interest rates do impact on the implied volatility in the long run, even though they are negligible in the short time limit.

CURRENCY DERIVATIVES UNDER A MINIMAL MARKET MODEL WITH RANDOM SCALING

2005 ◽  
Vol 08 (08) ◽  
pp. 1157-1177 ◽  
Author(s):  
DAVID HEATH ◽  
ECKHARD PLATEN
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Stochastic Volatility Model ◽  
Market Model ◽  
European Options ◽  
Bessel Processes ◽  
Exchange Rate Dynamics ◽  
Volatility Model ◽  
Minimal Market Model ◽  
Implied Volatility Surfaces

This paper uses an alternative, parsimonious stochastic volatility model to describe the dynamics of a currency market for the pricing and hedging of derivatives. Time transformed squared Bessel processes are the basic driving factors of the minimal market model. The time transformation is characterized by a random scaling, which provides for realistic exchange rate dynamics. The pricing of standard European options is studied. In particular, it is shown that the model produces implied volatility surfaces that are typically observed in real markets.

A Linear Poroelastic Analysis of Time-Dependent Crack-Tip Fields in Polymer Gels

2018 ◽  
Vol 85 (11) ◽  
Author(s):  
Yalin Yu ◽  
Nikolaos Bouklas ◽  
Chad M. Landis ◽  
Rui Huang
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Crack Tip ◽  
Polymer Gels ◽  
Time Limit ◽  
Time Limits ◽  
Long Time ◽  
Short Time ◽  
Over Time

Based on a linear poroelastic formulation, we present an asymptotic analysis of the transient crack-tip fields for stationary cracks in polymer gels under plane-strain conditions. A center crack model is studied in detail, comparing numerical results by a finite element method to the asymptotic analysis. The time evolution of the crack-tip parameters is determined as a result of solvent diffusion coupled with elastic deformation of the gel. The short-time and long-time limits are obtained for the stress intensity factor and the crack-tip energy release rate under different chemo-mechanical boundary conditions (immersed versus not-immersed, displacement versus load controlled). It is found that, under displacement-controlled loading, the crack-tip energy release rate increases monotonically over time for the not-immersed case, but for the immersed case, it increases first and then decreases, with a long-time limit lower than the short-time limit. Under load control, the energy release rate increases over time for both immersed and not-immersed cases, with different short-time limits but the same long-time limit. These results suggest that onset of crack growth may be delayed until the crack-tip energy release rate reaches a critical value if the applied displacement or traction is subcritical but greater than a threshold.

scholarly journals Mobile Money Use: The Impact of Macroeconomic Policy and Regulation

Economies ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 51
Author(s):  
Lorna Katusiime
Keyword(s):  
Exchange Rate ◽  
Interest Rates ◽  
Financial Innovation ◽  
Macroeconomic Policy ◽  
Mobile Money ◽  
Distributed Lag ◽  
Distributed Lag Model ◽  
Long Run ◽  
Short Run ◽  
The Impact

This paper examines the effects of macroeconomic policy and regulatory environment on mobile money usage. Specifically, we develop an autoregressive distributed lag model to investigate the effect of key macroeconomic variables and mobile money tax on mobile money usage in Uganda. Using monthly data spanning the period March 2009 to September 2020, we find that in the short run, mobile money usage is positively affected by inflation while financial innovation, exchange rate, interest rates and mobile money tax negatively affect mobile money usage in Uganda. In the long run, mobile money usage is positively affected by economic activity, inflation and the COVID-19 pandemic crisis while mobile money customer balances, interest rate, exchange rate, financial innovation and mobile money tax negatively affect mobile money usage.

scholarly journals The economic market outcomes and income distribution when capital is not homogeneous

2019 ◽  
Vol 1 (1) ◽  
pp. 38-56
Author(s):  
Ahmet Özçam
Keyword(s):  
Measurement Problem ◽  
Physical Capital ◽  
Threshold Level ◽  
Market Model ◽  
Economic Market ◽  
Constant Elasticity ◽  
Content Type ◽  
Macroeconomic Analysis ◽  
Long Run ◽  
Short Run

Purpose An aggregate production function has been used in macroeconomic analysis for a long time, even though it seems that it is conceptually confusing and problematic. The purpose of this paper is to argue that the measurement problem related to the heterogenous capital input that exists in macroeconomics is also relevant to microeconomic market situations. Design/methodology/approach The author constructed a microeconomic market model to address both the problems of the measurement of the physical capital and of substitutability between labor and capital in the short run using two types of technologies: labor neutral and labor reducing. The author proposed that labor and physical capital inputs are complementary in the short run and can become substitutes only in the long run when the technology advances. Findings The author found that even if the technology improves at a fast rate over time, there are then diminishing returns of profits to technology and an upper limit to profits. Moreover, the author showed that under the labor-reducing technology, labor class earns more initially as technology improves, but their incomes start declining after some threshold level of passage of time. Originality/value The author cautioned the applied researcher that the estimated labor and capital coefficients of generalized Cobb–Douglas and constant elasticity of substitution of types of production functions could not be interpreted as partial elasticities of labor and capital if in reality the data come from fixed-proportions types of processes.

scholarly journals Was the Gibson Paradox for real? A Wicksellian study of the relationship between interest rates and prices

2014 ◽  
Vol 21 (2) ◽  
pp. 139-163 ◽  
Author(s):  
Jagjit S. Chadha ◽  
Morris Perlman
Keyword(s):  
Interest Rates ◽  
Positive Relationship ◽  
Formal Model ◽  
Natural Rate ◽  
Market Rate ◽  
Long Run ◽  
Advanced Economies ◽  
The Uk ◽  
Gibson Paradox ◽  
The Relationship

We examine the relationship between prices and interest rates for seven advanced economies in the period up to 1913, emphasising the UK. There is a significant long-run positive relationship between prices and interest rates for the core commodity standard countries. Keynes ([1930] 1971) labelled this positive relationship the ‘Gibson Paradox’. A number of theories have been put forward as possible explanations of the paradox but they do not fit the long-run pattern of the relationship. We find that a formal model in the spirit of Wicksell (1907) and Keynes ([1930] 1971) offers an explanation for the paradox: where the need to stabilise the banking sector's reserve ratio, in the presence of an uncertain ‘natural’ rate, can lead to persistent deviations of the market rate of interest from its ‘natural’ level and consequently long-run swings in the price level.

scholarly journals EXACT PRICING AND LARGE-TIME ASYMPTOTICS FOR THE MODIFIED SABR MODEL AND THE BROWNIAN EXPONENTIAL FUNCTIONAL

2011 ◽  
Vol 14 (04) ◽  
pp. 559-578 ◽  
Author(s):  
MARTIN FORDE
Keyword(s):  
Stock Price ◽  
Implied Volatility ◽  
Large Time ◽  
Transition Density ◽  
Closed Form Expression ◽  
Modified Model ◽  
Exponential Functional ◽  
Price Distribution ◽  
Zero Correlation ◽  
Sabr Model

We derive a closed-form expression for the stock price density under the modified SABR model [see section 2.4 in Islah (2009)] with zero correlation, for β = 1 and β < 1, using the known density for the Brownian exponential functional for μ = 0 given in Matsumoto and Yor (2005), and then reversing the order of integration using Fubini's theorem. We then derive a large-time asymptotic expansion for the Brownian exponential functional for μ = 0, and we use this to characterize the large-time behaviour of the stock price distribution for the modified SABR model; the asymptotic stock price "density" is just the transition density p(t, S0, S) for the CEV process, integrated over the large-time asymptotic "density" [Formula: see text] associated with the Brownian exponential functional (re-scaled), as we might expect. We also compute the large-time asymptotic behaviour for the price of a call option, and we show precisely how the implied volatility tends to zero as the maturity tends to infinity, for β = 1 and β < 1. These results are shown to be consistent with the general large-time asymptotic estimate for implied variance given in Tehranchi (2009). The modified SABR model is significantly more tractable than the standard SABR model. Moreover, the integrated variance for the modified model is infinite a.s. as t → ∞, in contrast to the standard SABR model, so in this sense the modified model is also more realistic.

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.

A numerical method to price European derivatives based on the one factor LIBOR Market Model of interest rates

2008 ◽  
Vol 2 (2) ◽  
pp. 568-589 ◽  
Author(s):  
Luca Vincenzo Ballestra ◽  
Graziella Pacelli ◽  
Francesco Zirilli
Keyword(s):  
Interest Rates ◽  
Numerical Method ◽  
Market Model ◽  
Libor Market Model ◽  
The One

Relationship between Budget Deficit and Economic Growth: Evidence from Ethiopia

2021 ◽  
Vol 2 (2) ◽  
pp. 10-15
Author(s):  
Desalegn Emana
Keyword(s):  
Economic Growth ◽  
Interest Rates ◽  
Budget Deficit ◽  
Time Series Data ◽  
Negative Impact ◽  
Positive Impact ◽  
Negative Relationship ◽  
Nominal Exchange Rate ◽  
Series Data ◽  
Long Run

This study examined the relationship between budget deficit and economic growth in Ethiopia using time series data for the period 1991 to 2019 by applying the ARDL bounds testing approach. The empirical results indicate that budget deficit and economic growth in Ethiopia have a negative relationship in the long run, and have a weak positive association in the short run. In line with this, in the long run, a one percent increase in the budget deficit causes a 1.43 percent decline in the economic growth of the country. This result is consistent with the neoclassical view which says budget deficits are bad for economic growth during stimulating periods. Moreover, in the long run, the variables trade openness and inflation have a positive impact on Ethiopian economic growth, and on the other hand, the economic growth of Ethiopia is negatively affected by the nominal exchange rate in the long run. Apart from this, in the long run, gross capital formation and lending interest rates have no significant impact on the economic growth of the country. Therefore, the study recommends the government should manage its expenditure and mobilize the resources to generate more revenue to address the negative impact of the budget deficit on economic growth.

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