A FORWARD EQUATION FOR COMPUTING DERIVATIVES EXPOSURE

2019 ◽  
Vol 22 (03) ◽  
pp. 1950015
Author(s):  
BERNARD LAPEYRE ◽  
MAROUAN IBEN TAARIT
Keyword(s):  
Term Structure ◽  
Intrinsic Value ◽  
Small Dimension ◽  
Financial Derivatives ◽  
Local Times ◽  
Higher Dimension ◽  
Area Formula ◽  
Forward Equation ◽  
Time Value ◽  
Dimension One

We derive a forward equation for computing the expected exposure of financial derivatives. Under general assumptions about the underlying diffusion process, we give an explicit decomposition of the exposure into an intrinsic value which can be directly deduced from the term structure of the forward mark-to-market, and a time value which expresses the variability of the future mark-to-market. Our approach is inspired by Dupire’s equation for local volatility and leads to an ordinary differential equation qualifying the evolution of the expected exposure with respect to the observation dates. We show how this approach can be linked with local times theory in dimension one and to the co-area formula in a higher dimension. As for numerical considerations, we show how this approach leads to an efficient numerical method in the case of one or two risk factors. The accuracy and time-efficiency of this forward representation in small dimension are of special interest in benchmarking XVA valuation adjustments at trade level.

Joint asymptotic behavior of local and occupation times of random walk in higher dimension

2007 ◽  
Vol 44 (4) ◽  
pp. 535-563 ◽  
Author(s):  
Endre Csáki ◽  
Antónia Földes ◽  
Pál Révész
Keyword(s):  
Asymptotic Behavior ◽  
Random Walk ◽  
Unit Ball ◽  
Local Time ◽  
Occupation Time ◽  
Local Times ◽  
Higher Dimension ◽  
Occupation Times ◽  
Symmetric Random Walk

Considering a simple symmetric random walk in dimension d ≧ 3, we study the almost sure joint asymptotic behavior of two objects: first the local times of a pair of neighboring points, then the local time of a point and the occupation time of the surface of the unit ball around it.

PARTIAL IMMUNIZATION BOUNDS AND NON-PARALLEL TERM STRUCTURE SHIFTS

2013 ◽  
Vol 08 (02) ◽  
pp. 1350006 ◽  
Author(s):  
GEOFFREY POITRAS
Keyword(s):  
Interest Rate ◽  
Term Structure ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Fixed Income ◽  
Time Value ◽  
Fixed Income Portfolio ◽  
Theoretical Results ◽  
Selection Of

A variety of approaches have been proposed to extend classical fixed income portfolio immunization theory to cases where shifts in the term structure are not parallel. Following Reitano (1991a, 1991b, 1992, 1996) and Poitras (2007), this paper uses partial durations and convexities to specify benchmark partial immunization bounds for non-parallel term structure shifts. Theoretical results are obtained by exploiting properties of the multivariate Taylor series expansion of the spot interest rate pricing function. It is demonstrated that the partial immunization bounds can be effectively manipulated by adequate selection of the securities being used to immunize the portfolio. The inclusion of time values permits the results obtained to be related to previous studies by Christensen and Sorensen (1994), Chance and Jordan (1996), Barber and Copper (1997) and Poitras (2005, Ch. 5) on the time value-convexity tradeoff.

scholarly journals Periodic points of post-critically algebraic holomorphic endomorphisms

2021 ◽  
pp. 1-33
Author(s):  
VAN TU LE
Keyword(s):  
Complex Analysis ◽  
Complex Dynamics ◽  
Rational Maps ◽  
Higher Dimension ◽  
Holomorphic Maps ◽  
Rational Map ◽  
Critical Set ◽  
Princeton University ◽  
Dimension One ◽  
Hyperbolicity Assumption

Abstract A holomorphic endomorphism of ${{\mathbb {CP}}}^n$ is post-critically algebraic if its critical hypersurfaces are periodic or preperiodic. This notion generalizes the notion of post-critically finite rational maps in dimension one. We will study the eigenvalues of the differential of such a map along a periodic cycle. When $n=1$ , a well-known fact is that the eigenvalue along a periodic cycle of a post-critically finite rational map is either superattracting or repelling. We prove that, when $n=2$ , the eigenvalues are still either superattracting or repelling. This is an improvement of a result by Mattias Jonsson [Some properties of 2-critically finite holomorphic maps of P2. Ergod. Th. & Dynam. Sys.18(1) (1998), 171–187]. When $n\geq 2$ and the cycle is outside the post-critical set, we prove that the eigenvalues are repelling. This result improves one obtained by Fornæss and Sibony [Complex dynamics in higher dimension. II. Modern Methods in Complex Analysis (Princeton, NJ, 1992) (Annals of Mathematics Studies, 137). Ed. T. Bloom, D. W. Catlin, J. P. D’Angelo and Y.-T. Siu, Princeton University Press, 1995, pp. 135–182] under a hyperbolicity assumption on the complement of the post-critical set.

Study on MCU Based Programmable Frequency Detector

2011 ◽  
Vol 328-330 ◽  
pp. 2036-2039
Author(s):  
Zi Yi Zhang ◽  
Lin Hui Zhao ◽  
Miao Miao Tan ◽  
Hong Hong Guo
Keyword(s):  
Data Transmission ◽  
Hardware Design ◽  
Power Line ◽  
Small Dimension ◽  
Flow Chart ◽  
Band Width ◽  
Flip Flop ◽  
Program Flow ◽  
Dimension One ◽  
Frequency Detector

An MCU based programmable frequency detector was developed and relative tests were carried out. The detector used few elements which are very common and cheap, one MCU which has only 8 pins and with small dimension, one Schimidt trigger, one D type flip-flop and several resistors and capacitors. Cost for the detector is very low. Besides hardware work, software program has played very important role in the detector. By adjusting program parameters, different frequency can be detected and detecting band width can also be adjusted. Program flow chart is given in this thesis. Test shows that the detector is stable and sensitive and is suitable for different applications, e.g. over power line data transmission, etc. This paper introduces theory of the detector, hardware design and the software programming.

The Intrinsic Value of Cooperation

2005 ◽  
Author(s):  
Robert Fisher ◽  
Yany Gregoire ◽  
Kyle B. Murray
Keyword(s):  
Intrinsic Value

The Influence of Lactate and Dipyridamole on Myocardial Fatty Acid Metabolism in Man, Traced with 123l-17-lodo-heptadecanoic Acid

1990 ◽  
Vol 29 (01) ◽  
pp. 28-34 ◽  
Author(s):  
F. C. Visser ◽  
M. J. van Eenige ◽  
G. Westera ◽  
J. P. Roos ◽  
C. M. B. Duwel
Keyword(s):  
Fatty Acid ◽  
Fatty Acid Metabolism ◽  
Acid Metabolism ◽  
Time Activity ◽  
Time Value ◽  
Myocardial Fatty Acid Metabolism ◽  
Coronary Vasodilatation ◽  
Activity Curve ◽  
Normal Human ◽  
Plasma Lactate Level

Changes in myocardial metabolism can be detected externally by registration of time-activity curves after administration of radioiodinated fatty acids. In this scintigraphic study the influence of lactate on fatty acid metabolism was investigated in the normal human myocardium, traced with 123l-17-iodoheptadecanoic acid (123l-17-HDA). In patients (paired, n = 7) lactate loading decreased the uptake of 123l-17-HDA significantly from 27 (control: 22-36) to 20 counts/min/pixel (16-31; p <0.05 Wilcoxon). The half-time value increased to more than 60 rriin (n = 5), oxidation decreased from 61 to 42%. Coronary vasodilatation, a well-known side effect of lactate loading, was studied separately in a dipyridamole study (paired, n = 6). Coronary vasodilatation did not influence the parameters of the time-activity curve. These results suggest that changes in plasma lactate level as occurring, among other effects, during exercise will influence the parameters of dynamic 123l-17-HDA scintigraphy of the heart.

Analysis of Myocardial Time-Activity Curves of 123l-Heptadecanoic Acid II. The Acquisition Time

1987 ◽  
Vol 26 (06) ◽  
pp. 248-252 ◽  
Author(s):  
M. J. van Eenige ◽  
F. C. Visser ◽  
A. J. P. Karreman ◽  
C. M. B. Duwel ◽  
G. Westera ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Acquisition Time ◽  
Half Time ◽  
Constant Ratio ◽  
Time Activity ◽  
Time Activity Curve ◽  
Time Value ◽  
Activity Curve ◽  
Low Amplitude ◽  
Parameter Values

Optimal fitting of a myocardial time-activity curve is accomplished with a monoexponential plus a constant, resulting in three parameters: amplitude and half-time of the monoexponential and the constant. The aim of this study was to estimate the precision of the calculated parameters. The variability of the parameter values as a function of the acquisition time was studied in 11 patients with cardiac complaints. Of the three parameters the half-time value varied most strongly with the acquisition time. An acquisition time of 80 min was needed to keep the standard deviation of the half-time value within ±10%. To estimate the standard deviation of the half-time value as a function of the parameter values, of the noise content of the time-activity curve and of the acquisition time, a model experiment was used. In most cases the SD decreased by 50% if the acquisition time was increased from 60 to 90 min. A low amplitude/constant ratio and a high half-time value result in a high SD of the half-time value. Tables are presented to estimate the SD in a particular case.

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