Not-so-complex Logarithms in the Heston Model
|
|
- Randall Hines
- 8 years ago
- Views:
Transcription
1 Not-so-complex Logarithms in the Heston Model Christian Kahl * Department of Mathematics, University of Wppertal, Gaßstraße, Wppertal, D-49, Germany, and Qantitative Analytics Grop, ABN AMRO, 5 Bishopsgate, London ECM 4AA, UK Peter Jäckel Head of credit, hybrid, commodity, and inflation derivative analytics, ABN AMRO, 5 Bishopsgate, London ECM 4AA,UK Abstract: In Heston s stochastic volatility framework [Heston 993], semi-analytical formlæ for plain vanilla option prices can be derived. Unfortnately, these formlæ reqire the evalation of logarithms with complex argments dring the involved inverse Forier integration step. This gives rise to an inherent nmerical instability as a conseqence of which most implementations of Heston s formlæ are not robst for moderate to long dated matrities or strong mean reversion. In this article, we propose a new approach to solve this problem which enables the se of Heston s analytics for practically all levels of parameters and even matrities of many decades. Introdction The Heston stochastic volatility model is given by the system of stochastic differential eqations ds t = µs t dt + V t S t dw S (t), () dv t = κ(θ V t )dt + ω V t dw V (t) () with correlated Brownian motions dw S (t)dw V (t) = ρdt. [Heston 993] fond a semi-analytical soltion for pricing Eropean calls and pts sing Forier inversion techniqes. The price for a Eropean Call with strike K and time to matrity τ can be expressed very similarly to the Black-Scholes one, namely C(S, K, V,τ)= P(τ ) [ (F K) + π ] (F f K f ) d (3) where f and f are ( ) ( ) e i ln K ϕ( i) e i ln K ϕ() f := Re and f := Re, (4) if i with F = Se µτ, and P(τ ) is the discont factor to the option expiry date. The fnction ϕ( ) is defined as the log-characteristic fnction of the nderlying asset vale S τ at expiry: Note that by virte of definition (5) we have ϕ() := E[e i ln Sτ ]. (5) ϕ() = and ϕ( i) = F. (6) Eqation (3) for the price of a call option given the log-characteristic fnction of the nderlying asset at expiry is generic and applies to any model, stochastic volatility or otherwise. It can be derived directly by the 94 Wilmott magazine
2 TECHNICAL ARTICLE 6 aid of the general reslt from fnctional analysis that the Forier transform of the Heaviside fnction is given by a Dirac and a hyperbolic component: e π ix h(x) dx = δ() + πi. (7) Specifically for the Heston model, we have ϕ() = e C(τ,)+D(τ,)V +i ln F. (8) The coefficients C and D are soltions of a two-dimensional system of ordinary differential eqation of Riccati-type. They are C(τ, ) = κθ ( ( )) c()e d()τ (κ ρωi + d()) τ ln, (9) ω c() κ ρωi + d() D(τ, ) = ω with the axiliary fnctions ( e d()τ ) c()e d()τ κ ρωi + d() c() = κ ρωi d(), d() = (ρωi κ) + iω + ω. () What remains to be done for the valation of plain vanilla options is the nmerical comptation of the integral in eqation (3). This calclation is made somewhat complicated by the fact that the integrands f j are typically of oscillatory natre. Still, the integration can be done in a reasonably simple fashion by the aid of Gass-Lobatto qadratre [Gander and Gaschi ]. The real problem, however, starts when the fnctions f j are evalated as part of the qadratre scheme since the calclation of the embedded complex logarithm on the right hand side of eqation (9) is not as straightforward as it may look at first sight. Two Types of Complex Discontinity The first obvios problem with the inverse Forier transformation (3) is the choice of branch of the mltivaled complex logarithm embedded in C in eqation (9). This is a generic problem with option pricing calclations based on the inverse Forier transformation (3) of an expression derived from the log-characteristic fnction. One sggestion in the literatre to remedy this is to careflly keep track of the branch [Schöbel and Zh 999, Lee 5] along a discretised path integral of f j () as goes from to. Let s recall that the logarithm of a complex variable z = a + ib = re i(t+π n) with t [ π, π), n Z, and r R + can be written as () ln z = ln r + i(t + πn). () If we restrict or choice to the principal branch, the fnctions f j as defined in eqation (4) incr discontinities as is shown in figre for f. Integrating this fnction with an adaptive qadratre scheme will not only reslt in the wrong nmber (becase the area nder the discontinos crve shown in figre is not the same as the area nder the continity-corrected crve), it will also take nnecessarily long de to the fact f () Figre : The fnction f defined in (4). Underlying: ds t = µs t dt + V t S t dw S (t) with S = and µ =. Variance: dv t = κ(θ V t ) dt + ω V t dw V (t) with V =., κ =, θ =., ω =.5 and ρ =.3, time to matrity: τ = 3, strike: K =, red crve: implementation sing only the principal branche, green dashed crve: adjsted crve sing formla (3). that the adaptive rotine refines the nmber of sampling points excessively near the discontinity. In order to nderstand the mechanisms that gives rise to the discontinity, we now examine more closely the component C defined in eqation (9). To simplify the notation frther on, we divide this term as follows: C(τ, ) = R(τ, ) α ln G(τ, ) (3) R(τ, ) := α(κ ρωi + d)τ (4) α := κθ ω (5) G(τ, ) := cedτ (6) c Looking at the whole fnction ϕ() in (8), one cold arge that it is not necessary to evalate a complex logarithm at all since ϕ() = G(τ, ) α e R(τ,)+D(τ,)V +i ln F. (7) This is tre, thogh, we jst shifted the problem from the logarithm to the evaltation of G() α as this is exactly the part of the fnction where the jmp arises. Indeed, if we try this formla in or implementation, the discontinities do not go away (yet). The branch switching of the complex logarithm is in fact not the main problem that gives rise to the jmps of f (). A second effect is at work here and we will have to investigate frther. ^ Wilmott magazine 95
3 In the following, we make repeated se of the fact that, for any complex variable, we can choose either a real/imaginary part or a radis/ phase representation: z = a z + ib z = r z e itz, t z [ π, π). (8) The fact that we restrict the phase t z [ π, π) means that we ct the complex plane along the negative real axis. Taking z to the power α gives z α = r α z eiαtz. (9) Whenever G() crosses the negative real axis along its path (as varies) the sign of the phase of G() changes from π to π and therefore the phase of G() α changes from πα to πα. This leads to a jmp since { e iπ = e iπ e iαπ = e iαπ if α/ Z () e iαπ = e iαπ else In other words, what appeared earlier as a problem with the branch choice of the mltivaled complex logarithm in the evalation of f given by eqation (4) is in fact a problem with the branch switching of the complex power fnction which is related, thogh slightly different. To demonstrate this frther, consider the case when, by coincidence, the parameter setting leads to α Z. In this scenario, there is no jmp at all as we can see in figre. In general, thogh, we have α / Z. This woldn t be a problem if G() didn t cross the negative real axis. However, as it trns ot, the trajectory of G() in the complex plane as is varied from to, tends to start initially with a rapidly otwards f () Figre : The fnction f defined in (4) in the case that α Z. Underlying: ds t = µs t dt + V t S t dw S (t) with S = and µ =. Variance: dv t = κ(θ V t ) dt + ω V t dw V (t) with V =.5, κ =, θ =.5, ω =.5 and ρ =.3, exponent: α =, time to matrity: τ = 3, strike: K =. moving spiral, prior to entering an asymptotic escaping behavior. This is displayed in figre 3 for G(). Note that the shown trajectory is that of ln ln G() γ() := G(), i.e. we have rescaled the coordinate system doblelogarithmically in radis to compensate for the rapid otward move- G() ment of the spiralling trajectory of G(). The he h [, ) of the crve is given by h = log ( + ) mod which means that segments of slowly varying color represent rapid movement of G() as a fnction of. Another aspect why the correct treatment of the phase jmps of G() is so important is the fact that it does not reqire nsal or particlarly large parameters for the nmerically indced discontinity to occr. We show in figre 4 how the discontinities in the complex phase of G() arise simply as time to matrity is increased. What we can learn from all of the above is that the only way to avoid the discontinity of the integrands f j () altogether is to ensre that the phase of G() is continos. Varios athors [Schöbel and Zh 999, Lee 5, Sepp 3] propose the idea to keep track of the nmber of jmps by comparing G( k ) and G( k+ ) where k and k+ are adjacent points in their respective nmerical integration scheme. This is an involved technical procedre leading to the need for a particlarly complicated algorithm if we want to se an adaptive qadratre method. Frthermore, we have to make sre that we accont for all jmps which means that, for this to work reliably, we oght to have an estimate for the total nmber of discontinities. Fortnately, however, there is a mch simpler procedre to garantee the continity of G() which we present in the following. 96 Wilmott magazine Im[γ()] 4 ln ln G() γ() := G() G() he: log ( + )mod Re[γ()] Figre 3: Part of the trajectory of the fnction G() in the complex plane has the strctral shape of a spiral which gives rise to repeated crossing of the negative real axis. Here: ρ =.8, κ =, ω =, time to matrity τ =.
4 TECHNICAL ARTICLE 6 First, we introdce the notation c =: r c e itc, () d =: a d + ib d. () The next step is to have a closer look at the denominator of G which was defined in eqation (6): c = r c e itc (3) =: r e iχ +π m where [ ] tc + π m := int (4) π χ := arg(c ) (5) r := c (6) and with int[ ] denoting Gass s integer brackets. Note that we have assmed arg(z) [ π, π) z. The key observation is that the sbtraction of the nmber from the complex variable c is simply a shift parallel to the real axis and therefore the phase of (c ) [ π, π) if t c [ π, π), or in general, both χ and t c can be assmed to be on the same phase interval. In other words, taking a complex nmber of arbitrary phase, and adding the real nmber, cannot possibly give rise to this operation moving the complex nmber across the negative real axis since this wold reqire the addition of an imaginary component. We now do the same calclation with the nmerator of G ln G() = ln( r / r ) + i [χ χ + π(n m)]. (33) In figre (5), we show the rotation cont corrected angle arg (G()) compared with the reslt by sing jst the principal branch of G(). We see that, withot the correction, de to the sheer nmber of discontinities, it can be very difficlt indeed to keep track of the jmps by simply comparing neighboring integration points. Note that it does not reqire the choice of nsal parameters: the discontinities arise qite natrally for practically all choices of stochastic volatility configrations simply as time to matrity is increased, as was shown in figre 4. The procedre for the discontinity-corrected evalation of fnction f is smmarized in algorithm. The evalation of f () is to be done by the same procedre with replaced by ( i) in all bt the last step of algorithm, with a sbseqent division by the forward as one wold expect from eqation (4). Remark. Whilst algorithm is mathematically correct, it cannot actally be implemented directly in its presented form. For long times to matrity τ, the nmerator term G N can become very large which leads to nmerical overflow. In order to avoid this, we can monitor the expression Re(d) τ : when this term becomes greater than ln(dbl EPSILON) we can neglect 3 the sbtraction of in steps 6 and 9 and the whole procedre of estimating the term ln(g()) shold be done in logarithmic coordinates. Defining ce dτ = r c e itc e (ad +ibd )τ = r c e ad τ e i(tc+bd τ) [ ] (tc + b d τ + π) n := int π (7) (8) χ := arg ( ce dτ ) (9) r := ce dτ, (3) we have ce dτ = r e i(χ +π n). (3) Again, we sed the fact that the sbtraction of does not affect the rotation cont of the phase of a complex variable. Combining these reslts we obtain G() = cedτ c = r r ei[χ χ +π(n m)] (3) wherein the innocos bt crcial rotation cont nmbers m and n are given by eqations (4) and (8). We are now in the position to compte the logarithm of G() qite simply as Figre 4: Withot special handling, the phase of G() incrs more and more jmps as time to matrity is increased. Here: ρ =.8, κ =, ω =, time to matrity τ [, ]. ^ Wilmott magazine 97
5 Algorithm Evalate f () Reqire: F, K,κ,θ,ω,τ >,V and ρ (, ) : C d := (ρωi κ) + ω (i + ) : C c := κ ρωi+d κ ρωi d 3: R t c := arg(c) 4: C G D := c {Denominator of G()} 5: Z m := int [ ] tc+π π 6: C G N := ce dτ [ ] {Nmerator of G()} 7: Z n := int (tc+im(d)τ +π) π 8: C lng := ln(abs(g N )/abs(g D )) + i (arg(g N ) {see (33)} arg(g D ) + π(n m)) ) 9: C D := κ ρωi+d e dτ ω ( ce dτ : C C := κθ [(κ ρωi + d)τ lng] {see (3)} ω : C ϕ := exp(c + D V + i ln(f)) [ ] : R f := Re exp( i ln(k))ϕ 3 Integration scheme i The choice of the right integration scheme is another crcial point for a robst implementation of the semi-analytical Heston soltion. De to the fact that the integrand can vary in its shape from almost simply exponentially decaying to highly oscillatory depending on the choice of parameters, most simple qadratre or nmerical integration schemes are bond to fail significantly for some relevant scenarios. More advanced schemes sch as the adaptive Gass-Lobatto algorithm [Gander and Gatschi ], however, are capable of handling the wide range of fnctional forms attainable by the integrand defined in (4). Since the Gass-Lobatto algorithm is designed to operate on a closed interval [a, b], we show below how one can transform the original integral bondaries [, ) to the finite interval [, ], taking into accont or knowledge of the analytical strctre of the integrand for large. Adapting the transformation to the asymptotic strctre for not only aids the stability of the adaptive qadratre scheme, it also makes the integration scheme significantly more efficient in the sense that far fewer evalation points are needed. Preposition 3. Assming that κ, θ, ω, τ > and ρ (, ) we obtain the following asymptotics: d() lim = ω ρ =: d (34) lim c() = + ρ + iρ ρ = D() ρ + iρ lim = ω ( i ρ + ρ) (35) (36) C() lim = iαωρτ αd τ (37) arg (G()) arg (G()) (a) (b) Figre 5: The phase of G() as defined in eqation (6) with (dashed) and withot (solid) rotation cont correction given by eqation (33), for κ = and τ = 3. (a) ρ =.8, ω =.5. (b) ρ =.95, ω = Wilmott magazine
6 TECHNICAL ARTICLE 6 This leads to ( ) e it lim f j() f j () e C Re = f j () e C sin(t ) (38) i with ( ) ρ ρ C = αd τ + V = (V + κθτ) (39) ω ω as well as t = αωρτ ρv + ln(f/k). (4) ω The initial vales f j () are given in propositions 3. and 3.3. Proof: The proof can be fond in appendix A. Eqation (38) shows that the asymptotic decay of the integrand is at least exponential. In particlar, C > garantees the existence of the integral. A simple and reliable transformation is to translate the integration according to with f j () d = f j ((x)) x C dx (4) (x) = ln x. (4) C The transformation is only possible when C >. Fortnately, this is given as long as ρ =. One last step is needed before we can proceed with the implementation. Looking at the fnctions f j in (4), we can see that f j () is, strictly speaking, not defined at =. The continity of the fnction at zero in figres and gives s hope, thogh, that we can find the vale analytically by the aid of l Hospital s rle. Preposition 3. The fnction ( ) e i ln K ϕ( i) f () = Re if has the following property at zero: lim f () = ln(f/k) + Im ( C ( i) ) + Im ( D ( i) ) V (44) with (43) Im ( C ( i) ) = e(ρ ω κ)τ θκ + θκ((κ ρω)τ ) (κ ρω) (45) Im ( D ( i) ) ρω)τ e (κ = (κ ρω), (46) provided that (κ ρω) =. When (κ ρω) =, we obtain Im ( C ( i) ) = κθτ 4 (47) Proof: The proof can be fond in Appendix A. Preposition 3.3 The fnction ( ) e i ln K ϕ() f () = Re i has the following property at zero: with Im ( D ( i) ) = τ. (48) (49) lim f () = ln(f/k) + Im ( C () ) + Im ( D () ) V (5) Im ( C () ) = e κτ θκ + θκ(κτ ) κ (5) Im(D ()) = e. (5) κ Proof: The proof can also be fond in Appendix A. The above analysis enables s to implement the reqired Forier inversion as a Gass-Lobatto integration over the interval [, ] sing the transformation given by (4), (4), and (39). Since Gass-Lobatto qadratre evalates its integrand at the bondary vales, we need to se the analytical limit vales (44) and (5) for the evalation of f j ((x)) x=. The limit vales at x = seem at first sight to be more complicated. However, it is straightforward to see from eqation (38) that those limit vales are zero as long as C > which in trn is given as long as ρ <. In practice, we combine all calclations in (3) into the single nmerical integration for the ndisconted call option price with C(S, K, V,τ)/P(τ ) = κτ y(x) dx (53) y(x) := (F K) + F f ( ln x ) K f C ( ln x ) C (54) x π C and F = S e µτ, as before. The limits of y(x) at the bondaries of the integral are lim y(x) = (F K) (55) x and lim y(x) = x (F K) + F lim f () K lim f () (56) π C with lim f () and lim f () given by (44) and (5), respectively. An example for the set of sampling points chosen by the adaptive Gass- Lobatto scheme for a target accracy of 6 is shown in figre 6. ^ Wilmott magazine 99
7 ..8 y(x) Gass-Lobatto sampling (accracy =.E-6) Figre 6: The sampling points selected by the adaptive Gass-Lobatto scheme for the integration of eqation (53). S = F =, µ =, V = θ, θ=.6, κ =, ω =, ρ =.8, τ =, K =. The total nmber of evalation points was 98, and the reslting integral vale was 4.95%. 7% 6% 5% 4% 3% % % K/F τ Figre 7: Black implied volatilities from the Heston model. Underlying: ds t = µs t dt + V t S t dw S (t) with S = F = and µ =. Variance: dv t = κ(θ V t ) dt + ω V t dw V (t) with V = θ =.6, κ =, ω =, ρ =.8, τ [/4, 5], and K [/, 4]. Wilmott magazine
8 TECHNICAL ARTICLE 6 The stability of Gass-Lobatto integration over the interval x [, ] of the transformed integrand f j ((x)) / (x C ) as described is sch that even extremely far ot-of-the-money option prices can be compted, as well as very long dated matrities. We demonstrate this in figre 7, where implied Black volatilities are displayed for the same parameters as previosly sed in figre 4. 4 Conclsion The problem we addressed was that Forier inversion integrals of the form (3) sed for the calclation of option prices based on analytical knowledge of the log-characteristic fnction of the nderlying stochastic process are particlarly prone to nmerical instabilities de to their involved complex logarithms and complex power expressions. We fond that the difficlty is ltimately not, as was previosly reported, cased by the mltivaled natre of the complex logarithm, bt instead by the mltivaled natre of the complex power fnction. We analysed this isse for the Heston stochastic volatility model, thogh, the key insight is readily transferable to the calclation of option prices in other models that are amenable to the Forier inversion integral approach [Carr 999, Carr and Madan 999] based on a log-characteristic fnction. We also presented a detailed analysis how the Forier integral itself can be compted reliably by the aid of adaptive Gass- Lobatto qadratre, sing asymptotic analytical methods to identify the most sitable transformation from the half-open integration domain [, ) to the interval [, ]. These reslts, too, are not only sefl for the prpose of compting option prices for the Heston model, bt also to illstrate how similar methods can be devised for other models that are to be evalated with Forier integration techniqes. A Proofs In this section we present the missing proofs of section 3. Proof:[Prop.3.] The proof of eqation (34) is basic analysis: d() lim = lim ω ( ρ ) iω (ρκ )/ ω + κ / (57) Note that lim c() =. In order to show eqation (36), we need the calclation [ ] [ ( e d()τ lim = lim + c() )] c()e d()τ c() c()e d()τ = lim c() c() = lim c() (59) = + ρ iρ ρ. (6) D() lim = ω ( + ρ iρ ρ )( ρωi + ω ρ ) = iρ ρ. (6) ω Finally, we prove (37) lim ln [ c()e d()τ c() From here, we obtain ]/ [ ]/ = lim ln e d()τ c() c() (6) ( = lim ln [ e ] [ ]) / c() d()τ + ln c() (63) = lim d()τ/ = d τ. (64) C() lim = ατ (d + iωρ). (65) Combination of the limit reslts for D() and C() makes it straightforward to arrive at the statements (38) and (39) for f j (). Proof:[Prop.3.] Considering the fnction f as given in (4) we see that ], i)+d(τ, i) V +ln(f) i ln(f/k) ec(τ lim f () = lim Im [e. (66) F = ω ρ Using this reslt, we are able to confirm eqation (35) ρωi + ω ρ lim c() = ρωi ω ρ = (ω ρ ρωi) ω ( ρ ) + ρ ω = ω ( ρ ) iω ρ ρ ρ ω ω = + ρ + iρ ρ = ( i ρ + ρ). (58) The expressions that need attention for the evalation of this limit are lim C(τ, i) as well as lim D(τ, i). We start with lim d( i) = κ ρω. (67) The limit lim c( i) depends on the sign of κ ρω. We first consider the case where κ ρω <. We obtain κ iρω( i) + d( i) lim c( i) = lim =. (68) κ iρω( i) d( i) This allows s to dedce lim D( i) =, lim C( i) =. (69) ^ Wilmott magazine
9 The case κ ρω > is a little bit more complicated. First we see that κ iρω( i) + d( i) lim c( i) =lim = (7) κ iρω( i) d( i) as the denominator goes to zero. Using this we can see that ( ) κ iρω( i) + d( i) e d( i)τ lim D( i) = lim ω c( i)e d( i)τ Frthermore, we have (7) =. (7) lim C( i) = lim α ((κ iρω( i) + d( i))τ [ ]) ln e d( i)τ + ed( i)τ c( i) (73) =. (74) Last we have to check the case κ ρω =. First we have to notice that d( i) lim = lim ω ( ρ ) iω = iω. (75) We have to mention that this limit is not zero as ω = if κ ρω = and κ>. Using this we obtain lim c( i) = + lim = + lim Again we get lim D( i) = and ρωi ρωi d( i) (76) ρωi ρωi + =. iω (77) lim C( i) = α lim ((κ ρω + d( i))τ [ ]) c( i)e d( i)τ (78) ln c( i) [ ] = α ln = (79) Hence in all different cases lim e i ln(f/k)+c( i)+d( i)v =. (8) Now we decompose the exponent into a real and imaginary part i ln(f/k) + C(τ, i) + D(τ, i) V =: H() + ij() (8) with fnctions H, J : R R. De to (), we also know that lim H() =, lim J() =. (8) Now we can calclate [ ] e H()+iJ() f () = lim Im [ ] H() cos(j()) + i sin(j()) = lim Im e H() sin(j()) = lim e = lim e H() lim sin(j()) (83) (84) (85) (86) = lim J () cos(j()) = lim J (), (87) where we applied the rle of l Hospital in the last step. Ths, f () = lim J () = J () = ln(f/k) + Im ( C ( i) ) + Im ( D ( i) ) V. (88) The comptation of C and D is tedios bt straightforward. We obtain Im ( C ( i) ) = e(ρ ω κ)τ θκ + θκ((κ ρω)τ ) (κ ρω), (89) Im ( D ( i) ) ρω)τ e (κ = (κ ρω), (9) if (κ ρω) =, and otherwise which completes the proof. Im ( C ( i) ) = κθτ 4, (9) Im ( D ( i) ) = τ, (9) Proof:[Prop.3.3] The proof of the limit lim f () can be done in complete analogy to the proof of lim f (). FOOTNOTE & REFERENCES. Note that the phase, as we refer to it here, is also known as the argment and some mathematical software packages se the expression arg for the calclation of the phase of a complex nmber.. The he is a nmber in the range [, ) which varies the color from red at throgh the entire rainbow spectrm to prple (arond.8), and then reconnecting to red at. 3. The C header <float.h> provides the macro DBL_EPSILON which is defined as the smallest floating point nmber that, when added to the nmber, still reslts in a nmber that is distinct from in the compter s floating point nmber representation. P. Carr. Option Pricing sing Integral Transforms, 3. carrp/papers/pdf/integtransform.pdf. P. Carr and D.B. Madan. Option valation sing the fast Forier transform. The Jornal of Comptational Finance, :6 73, 999. Wilmott magazine
10 TECHNICAL ARTICLE 6 W. Gander and W. Gatschi. Adaptive Gass-Lobatto Qadratre. S. L. Heston. A closed-form soltion for options with stochastic volatility with applications to bond and crrency options. The Review of Financial Stdies, 6:37 343, 993. R. Lee. Option Pricing by Transform Methods: Extensions, Unification, and Error Control. Jornal of Comptational Finance, 7(3):5 86, 5. S. Mikhailov and U. Nögel. Heston s Stochastic Volatility Model Implementation Calibration and Some Extensions. Wilmott magazine, 3. A. Sepp. Pricing Eropean-Style Options nder Jmp Diffsion Processes with Stochastic Volatility: Application of Forier Transform. Working paper, Institte of Mathematical Statistics, Faclty of Mathematics and Compter Science, University of Tart, J. Liivi, 549 Tart, Estonia, September 3. R. Schöbel and J. Zh. Stochastic Volatility With an Ornstein Uhlenbeck Process: An Extension. Eropean Finance Review, 3:3 46, 999. W Wilmott magazine 3
WHITE PAPER. Filter Bandwidth Definition of the WaveShaper S-series Programmable Optical Processor
WHITE PAPER Filter andwidth Definition of the WaveShaper S-series 1 Introdction The WaveShaper family of s allow creation of ser-cstomized filter profiles over the C- or L- band, providing a flexible tool
More informationUsing GPU to Compute Options and Derivatives
Introdction Algorithmic Trading has created an increasing demand for high performance compting soltions within financial organizations. The actors of portfolio management and ris assessment have the obligation
More informationModeling Roughness Effects in Open Channel Flows D.T. Souders and C.W. Hirt Flow Science, Inc.
FSI-2-TN6 Modeling Roghness Effects in Open Channel Flows D.T. Soders and C.W. Hirt Flow Science, Inc. Overview Flows along rivers, throgh pipes and irrigation channels enconter resistance that is proportional
More informationEvery manufacturer is confronted with the problem
HOW MANY PARTS TO MAKE AT ONCE FORD W. HARRIS Prodction Engineer Reprinted from Factory, The Magazine of Management, Volme 10, Nmber 2, Febrary 1913, pp. 135-136, 152 Interest on capital tied p in wages,
More informationOn the urbanization of poverty
On the rbanization of poverty Martin Ravallion 1 Development Research Grop, World Bank 1818 H Street NW, Washington DC, USA Febrary 001; revised Jly 001 Abstract: Conditions are identified nder which the
More informationCorporate performance: What do investors want to know? Innovate your way to clearer financial reporting
www.pwc.com Corporate performance: What do investors want to know? Innovate yor way to clearer financial reporting October 2014 PwC I Innovate yor way to clearer financial reporting t 1 Contents Introdction
More informationSpectrum Balancing for DSL with Restrictions on Maximum Transmit PSD
Spectrm Balancing for DSL with Restrictions on Maximm Transmit PSD Driton Statovci, Tomas Nordström, and Rickard Nilsson Telecommnications Research Center Vienna (ftw.), Dona-City-Straße 1, A-1220 Vienna,
More informationCandidate: Suzanne Maxwell. Date: 09/19/2012
Medical Coder / Billing Clerk Assessment Report Szanne Maxwell 09/19/2012 www.resorceassociates.com Szanne Maxwell 09/19/2012 Prepared For: NAME Prepared by: John Lonsbry, Ph.D. & Lcy Gibson, Ph.D., Licensed
More informationIntroduction to HBase Schema Design
Introdction to HBase Schema Design Amandeep Khrana Amandeep Khrana is a Soltions Architect at Clodera and works on bilding soltions sing the Hadoop stack. He is also a co-athor of HBase in Action. Prior
More informationOptimal Trust Network Analysis with Subjective Logic
The Second International Conference on Emerging Secrity Information, Systems and Technologies Optimal Trst Network Analysis with Sbjective Logic Adn Jøsang UNIK Gradate Center, University of Oslo Norway
More informationASAND: Asynchronous Slot Assignment and Neighbor Discovery Protocol for Wireless Networks
ASAND: Asynchronos Slot Assignment and Neighbor Discovery Protocol for Wireless Networks Fikret Sivrikaya, Costas Bsch, Malik Magdon-Ismail, Bülent Yener Compter Science Department, Rensselaer Polytechnic
More informationPrimary Analysis of Effective Permeability of the Flame in Burning Natural Gas
Jornal of etals, aterials and inerals. Vol.7 No. pp.63-66. rimary Analysis of Effective ermeability of the Flame in Brning Natral Gas Rakoš JAROSAV * and Repasova AGDAENA * Department of Thermal Technology,
More informationA Spare Part Inventory Management Model for Better Maintenance of Intelligent Transportation Systems
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 A Spare Part Inventory Management Model for Better Maintenance of Intelligent
More informationBonds with Embedded Options and Options on Bonds
FIXED-INCOME SECURITIES Chapter 14 Bonds with Embedded Options and Options on Bonds Callable and Ptable Bonds Instittional Aspects Valation Convertible Bonds Instittional Aspects Valation Options on Bonds
More information9 Setting a Course: Goals for the Help Desk
IT Help Desk in Higher Edcation ECAR Research Stdy 8, 2007 9 Setting a Corse: Goals for the Help Desk First say to yorself what yo wold be; and then do what yo have to do. Epictets Key Findings Majorities
More informationGUIDELINE. Guideline for the Selection of Engineering Services
GUIDELINE Gideline for the Selection of Engineering Services 1998 Mission Statement: To govern the engineering profession while enhancing engineering practice and enhancing engineering cltre Pblished by
More informationCloser Look at ACOs. Making the Most of Accountable Care Organizations (ACOs): What Advocates Need to Know
Closer Look at ACOs A series of briefs designed to help advocates nderstand the basics of Accontable Care Organizations (ACOs) and their potential for improving patient care. From Families USA Updated
More informationDIRECT TAX LAWS Taxability of Capital Gains on By-back of Shares - Debate ignites after AAR s rling in RST s case BACKGROUND 1. Recently, the Athority for Advance Rlings ( AAR ) in the case of RST, In
More informationDesigning and Deploying File Servers
C H A P T E R 2 Designing and Deploying File Servers File servers rnning the Microsoft Windows Server 2003 operating system are ideal for providing access to files for sers in medim and large organizations.
More informationCloser Look at ACOs. Designing Consumer-Friendly Beneficiary Assignment and Notification Processes for Accountable Care Organizations
Closer Look at ACOs A series of briefs designed to help advocates nderstand the basics of Accontable Care Organizations (ACOs) and their potential for improving patient care. From Families USA Janary 2012
More informationEffect of Angular Velocity of Inner Cylinder on Laminar Flow through Eccentric Annular Cross Section Pipe
Asian Transactions on Engineering (ATE ISSN: -467) Volme 3 Isse Effect of Anglar Velocity of Inner Cylinder on Laminar Flow throgh Eccentric Annlar Cross Section Pipe Ressan Faris Hamd * Department of
More informationOptimal Personalized Filtering Against Spear-Phishing Attacks
Optimal Personalized Filtering Against Spear-Phishing Attacks Aron Laszka and Yevgeniy Vorobeychik and Xenofon Kotsokos Institte for Software Integrated Systems Department of Electrical Engineering and
More informationOPTIMAL TRADE CREDIT REINSURANCE PROGRAMS WITH SOLVENCY REQUIREMENTS
OPTIMAL TRADE CREDIT REINSURANCE PROGRAMS WITH SOLVENCY REQUIREMENTS Lca Passalacqa Dipartimento di Scienze Attariali e Finanziarie La Sapienza, Università di Roma Viale Regina Elena, 295 00161 Roma, Italy
More information10 Evaluating the Help Desk
10 Evalating the Help Desk The tre measre of any society is not what it knows bt what it does with what it knows. Warren Bennis Key Findings Help desk metrics having to do with demand and with problem
More informationAnalytical Calculation of Risk Measures for Variable Annuity Guaranteed Benefits
Analytical Calclation of Risk Measres for Variable Annity Garanteed Benefits Rnhan Feng Department of Mathematical Sciences University of Wisconsin - Milwakee fengr@wm.ed Hans W. Volkmer Department of
More informationOn a Generalized Graph Coloring/Batch Scheduling Problem
Reglar Papers On a Generalized Graph Coloring/Batch Schedling Problem Giorgio Lcarelli 1, Ioannis Milis Dept. of Informatics, Athens University of Economics and Bsiness, 104 34, Athens, Greece, {glc, milis}@aeb.gr
More informationHorses and Rabbits? Optimal Dynamic Capital Structure from Shareholder and Manager Perspectives
Horses and Rabbits? Optimal Dynamic Capital trctre from hareholder and Manager Perspectives Nengji J University of Maryland Robert Parrino University of exas at Astin Allen M. Poteshman University of Illinois
More informationStock Market Liquidity and Macro-Liquidity Shocks: Evidence from the 2007-2009 Financial Crisis
Stock Market Liqidity and Macro-Liqidity Shocks: Evidence from the 2007-2009 Financial Crisis Chris Florackis *, Alexandros Kontonikas and Alexandros Kostakis Abstract We develop an empirical framework
More informationAn unbiased crawling strategy for directed social networks
Abstract An nbiased crawling strategy for directed social networks Xeha Yang 1,2, HongbinLi 2* 1 School of Software, Shenyang Normal University, Shenyang 110034, Liaoning, China 2 Shenyang Institte of
More information8 Service Level Agreements
8 Service Level Agreements Every organization of men, be it social or political, ltimately relies on man s capacity for making promises and keeping them. Hannah Arendt Key Findings Only abot 20 percent
More informationLIMITS IN CATEGORY THEORY
LIMITS IN CATEGORY THEORY SCOTT MESSICK Abstract. I will start assming no knowledge o category theory and introdce all concepts necessary to embark on a discssion o limits. I will conclde with two big
More informationCandidate: Kyle Jarnigan. Date: 04/02/2012
Cstomer Service Manager Assessment Report 04/02/2012 www.resorceassociates.com To Improve Prodctivity Throgh People. Cstomer Service Manager Assessment Report 04/02/2012 Prepared For: NAME Prepared by:
More informationConfiguration Management for Software Product Lines
onfigration Management for Software Prodct Lines Roland Laqa and Peter Knaber Franhofer Institte for Experimental Software Engineering (IESE) Saerwiesen 6 D-67661 Kaiserslatern, Germany +49 6301 707 161
More informationResearch on Pricing Policy of E-business Supply Chain Based on Bertrand and Stackelberg Game
International Jornal of Grid and Distribted Compting Vol. 9, No. 5 (06), pp.-0 http://dx.doi.org/0.457/ijgdc.06.9.5.8 Research on Pricing Policy of E-bsiness Spply Chain Based on Bertrand and Stackelberg
More information11 Success of the Help Desk: Assessing Outcomes
11 Sccess of the Help Desk: Assessing Otcomes I dread sccess... I like a state of continal becoming, with a goal in front and not behind. George Bernard Shaw Key Findings Respondents help desks tend to
More informationTrustSVD: Collaborative Filtering with Both the Explicit and Implicit Influence of User Trust and of Item Ratings
TrstSVD: Collaborative Filtering with Both the Explicit and Implicit Inflence of User Trst and of Item Ratings Gibing Go Jie Zhang Neil Yorke-Smith School of Compter Engineering Nanyang Technological University
More informationOptimal control and piecewise parametric programming
Proceedings of the Eropean Control Conference 2007 Kos, Greece, Jly 2-5, 2007 WeA07.1 Optimal control and piecewise parametric programming D. Q. Mayne, S. V. Raković and E. C. Kerrigan Abstract This paper
More informationSample Pages. Edgar Dietrich, Alfred Schulze. Measurement Process Qualification
Sample Pages Edgar Dietrich, Alfred Schlze Measrement Process Qalification Gage Acceptance and Measrement Uncertainty According to Crrent Standards ISBN: 978-3-446-4407-4 For frther information and order
More informationCandidate: Charles Parker. Date: 01/29/2015
Software Developer / Programmer Assessment Report 01/29/2015 www.resorceassociates.com To Improve Prodctivity Throgh People. Janary 29, 2015 01/29/2015 The following pages represent a report based on the
More informationMarket Impact and Optimal Equity Trade Scheduling
Market Impact and Optimal Eqity Trade Schedling Dan dibartolomeo Northfield Information Services, Inc. Colmbia University Math Finance Seminar September 2007 Presentation Otline Brief review of the optimal
More informationHerzfeld s Outlook: Seasonal Factors Provide Opportunities in Closed-End Funds
VIRTUS HERZFELD FUND Herzfeld s Otlook: Seasonal Factors Provide Opportnities in Closed-End Fnds When it comes to investing in closed-end fnds, a comprehensive nderstanding of the inefficiencies of the
More informationCandidate: Shawn Mullane. Date: 04/02/2012
Shipping and Receiving Specialist / Inventory Control Assessment Report Shawn Mllane 04/02/2012 www.resorceassociates.com To Improve Prodctivity Throgh People. Shawn Mllane 04/02/2012 Prepared For: NAME
More information3. Fluid Dynamics. 3.1 Uniform Flow, Steady Flow
3. Flid Dynamics Objectives Introdce concepts necessary to analyse flids in motion Identify differences between Steady/nsteady niform/non-niform compressible/incompressible flow Demonstrate streamlines
More informationPhone Banking Terms Corporate Accounts
Phone Banking Terms Corporate Acconts If there is any inconsistency between the terms and conditions applying to an Accont and these Phone Banking Terms, these Phone Banking Terms prevail in respect of
More informationHSBC Internet Banking. Combined Product Disclosure Statement and Supplementary Product Disclosure Statement
HSBC Internet Banking Combined Prodct Disclosre Statement and Spplementary Prodct Disclosre Statement AN IMPORTANT MESSAGE FOR HSBC CUSTOMERS NOTICE OF CHANGE For HSBC Internet Banking Combined Prodct
More informationStock Market Liquidity and Macro-Liquidity Shocks: Evidence from the 2007-2009 Financial Crisis
Stock Market Liqidity and Macro-Liqidity Shocks: Evidence from the 2007-2009 Financial Crisis Chris Florackis *, Alexandros Kontonikas and Alexandros Kostakis Abstract We develop an empirical framework
More informationCompensation Approaches for Far-field Speaker Identification
Compensation Approaches for Far-field Speaer Identification Qin Jin, Kshitiz Kmar, Tanja Schltz, and Richard Stern Carnegie Mellon University, USA {qjin,shitiz,tanja,rms}@cs.cm.ed Abstract While speaer
More informationDeploying Network Load Balancing
C H A P T E R 9 Deploying Network Load Balancing After completing the design for the applications and services in yor Network Load Balancing clster, yo are ready to deploy the clster rnning the Microsoft
More informationPractical Tips for Teaching Large Classes
Embracing Diversity: Toolkit for Creating Inclsive, Learning-Friendly Environments Specialized Booklet 2 Practical Tips for Teaching Large Classes A Teacher s Gide Practical Tips for Teaching Large Classes:
More informationSIMPLE DESIGN METHOD FOR OPENING WALL WITH VARIOUS SUPPORT CONDITIONS
SIMPLE DESIGN METHOD FOR OPENING WALL WITH VARIOUS SUPPORT CONDITIONS Jeng-Han Doh 1, Nhat Minh Ho 1, Griffith School of Engineering, Griffith University-Gold Coast Camps, Qeensland, Astralia ABSTRACT
More informationCHAPTER ONE VECTOR GEOMETRY
CHAPTER ONE VECTOR GEOMETRY. INTRODUCTION In this chapter ectors are first introdced as geometric objects, namely as directed line segments, or arrows. The operations of addition, sbtraction, and mltiplication
More informationEnabling Advanced Windows Server 2003 Active Directory Features
C H A P T E R 5 Enabling Advanced Windows Server 2003 Active Directory Featres The Microsoft Windows Server 2003 Active Directory directory service enables yo to introdce advanced featres into yor environment
More informationEffect of flow field on open channel flow properties using numerical investigation and experimental comparison
INTERNATIONAL JOURNAL OF ENERGY AND ENVIRONMENT Volme 3, Isse 4, 2012 pp.617-628 Jornal homepage: www.ijee.ieefondation.org Effect of flow field on open channel flow properties sing nmerical investigation
More informationHigh Availability for Internet Information Server Using Double-Take 4.x
High Availability for Internet Information Server Using Doble-Take 4.x High Availability for Internet Information Server Using Doble-Take 4.x pblished April 2000 NSI and Doble-Take are registered trademarks
More informationA Novel QR Code and mobile phone based Authentication protocol via Bluetooth Sha Liu *1, Shuhua Zhu 2
International Conference on Materials Engineering and Information Technology Applications (MEITA 2015) A Novel QR Code and mobile phone based Athentication protocol via Bletooth Sha Li *1, Shha Zh 2 *1
More informationHigh Availability for Microsoft SQL Server Using Double-Take 4.x
High Availability for Microsoft SQL Server Using Doble-Take 4.x High Availability for Microsoft SQL Server Using Doble-Take 4.x pblished April 2000 NSI and Doble-Take are registered trademarks of Network
More informationResource Pricing and Provisioning Strategies in Cloud Systems: A Stackelberg Game Approach
Resorce Pricing and Provisioning Strategies in Clod Systems: A Stackelberg Game Approach Valeria Cardellini, Valerio di Valerio and Francesco Lo Presti Talk Otline Backgrond and Motivation Provisioning
More informationCloser Look at ACOs. Putting the Accountability in Accountable Care Organizations: Payment and Quality Measurements. Introduction
Closer Look at ACOs A series of briefs designed to help advocates nderstand the basics of Accontable Care Organizations (ACOs) and their potential for improving patient care. From Families USA Janary 2012
More informationSickness Absence in the UK: 1984-2002
Sickness Absence in the UK: 1984-2002 Tim Barmby (Universy of Drham) Marco Ecolani (Universy of Birmingham) John Treble (Universy of Wales Swansea) Paper prepared for presentation at The Economic Concil
More informationA Contemporary Approach
BORICP01.doc - 1 Second Edition Edcational Psychology A Contemporary Approach Gary D. Borich The University of Texas at Astin Martin L. Tombari University of Denver (This pblication may be reprodced for
More informationPlanning an Active Directory Deployment Project
C H A P T E R 1 Planning an Active Directory Deployment Project When yo deploy the Microsoft Windows Server 2003 Active Directory directory service in yor environment, yo can take advantage of the centralized,
More informationHOMOTOPY FIBER PRODUCTS OF HOMOTOPY THEORIES
HOMOTOPY FIBER PRODUCTS OF HOMOTOPY THEORIES JULIA E. BERGNER Abstract. Gien an appropriate diagram of left Qillen fnctors between model categories, one can define a notion of homotopy fiber prodct, bt
More informationCandidate: Cassandra Emery. Date: 04/02/2012
Market Analyst Assessment Report 04/02/2012 www.resorceassociates.com To Improve Prodctivity Throgh People. 04/02/2012 Prepared For: Resorce Associates Prepared by: John Lonsbry, Ph.D. & Lcy Gibson, Ph.D.,
More information10.4 Solving Equations in Quadratic Form, Equations Reducible to Quadratics
. Solving Eqations in Qadratic Form, Eqations Redcible to Qadratics Now that we can solve all qadratic eqations we want to solve eqations that are not eactly qadratic bt can either be made to look qadratic
More informationPlanning a Managed Environment
C H A P T E R 1 Planning a Managed Environment Many organizations are moving towards a highly managed compting environment based on a configration management infrastrctre that is designed to redce the
More informationMSc and MA in Finance and Investment online Study an online MSc and MA in Finance and Investment awarded by UNINETTUNO and Geneva Business School
MSc and MA in Finance and Investment online Stdy an online awarded by UNINETTUNO and Geneva Bsiness School Awarded by Geneva Bsiness School Geneva Barcelona Moscow Class profile The connects yo with stdents
More information& Valuation. GHP Horwath, P.C. Member Crowe Horwath International
March/April 2012 & Valation Litigation BRIEFING Owner salaries and how they affect lost profits When divorce enters the pictre A qalified valation expert can make a hge difference Boltar illstrates the
More informationChapter 3. 2. Consider an economy described by the following equations: Y = 5,000 G = 1,000
Chapter C evel Qestions. Imagine that the prodction of fishing lres is governed by the prodction fnction: y.7 where y represents the nmber of lres created per hor and represents the nmber of workers employed
More informationDocument management and records (based in part upon materials by Frank Upward and Robert Hartland)
Today s lectre IMS1603 Lectre 21 What does docment management entail? Docment management and records (based in part pon materials by Frank Upward and Robert Hartland) www.monash.ed. a Thinking more abot
More informationContinuity Analysis of Programs
Continity Analysis of Programs Swarat Chadhri Pennsylvania State University swarat@cse.ps.ed Smit Glwani Microsoft Research smitg@microsoft.com Roberto Lblinerman Pennsylvania State University rlble@ps.ed
More informationRegular Specifications of Resource Requirements for Embedded Control Software
Reglar Specifications of Resorce Reqirements for Embedded Control Software Rajeev Alr and Gera Weiss University of Pennsylvania Abstract For embedded control systems a schedle for the allocation of resorces
More informationPosition paper smart city. economics. a multi-sided approach to financing the smart city. Your business technologists.
Position paper smart city economics a mlti-sided approach to financing the smart city Yor bsiness technologists. Powering progress From idea to reality The hman race is becoming increasingly rbanised so
More informationDesigning a TCP/IP Network
C H A P T E R 1 Designing a TCP/IP Network The TCP/IP protocol site defines indstry standard networking protocols for data networks, inclding the Internet. Determining the best design and implementation
More informationCosmological Origin of Gravitational Constant
Apeiron, Vol. 5, No. 4, October 8 465 Cosmological Origin of Gravitational Constant Maciej Rybicki Sas-Zbrzyckiego 8/7 3-6 Krakow, oland rybicki@skr.pl The base nits contribting to gravitational constant
More informationManipulating Deformable Linear Objects: Characteristic Features for Vision-Based Detection of Contact State Transitions
Maniplating Deformable Linear Objects: Characteristic Featres for Vision-Based Detection of Contact State Transitions Jürgen Acker Dominik Henrich Embedded Systems and Robotics Lab. (RESY) Faclty of Informatics,
More informationCFD Platform for Turbo-machinery Simulation
CFD Platform for Trbo-machinery Simlation Lakhdar Remaki BCAM- Basqe Centre for Applied Mathematics Otline p BCAM-BALTOGAR project p CFD platform design strategy p Some new developments p Some reslts p
More informationKey words. renewal risk models, surplus dependent premiums, boundary value problems, Green s operators, asymptotic expansions,
EXACT AND ASYMPTOTIC RESULTS FOR INSURANCE RISK MODELS WITH SURPLUS-DEPENDENT PREMIUMS HANSJÖRG ALBRECHER, CORINA CONSTANTINESCU, ZBIGNIEW PALMOWSKI, GEORG REGENSBURGER, AND MARKUS ROSENKRANZ Abstract.
More informationDirect Loan Basics & Entrance Counseling Guide. For Graduate and Professional Student Direct PLUS Loan Borrowers
Direct Loan Basics & Entrance Conseling Gide For Gradate and Professional Stdent Direct PLUS Loan Borrowers DIRECT LOAN BASICS & ENTRANCE COUNSELING GUIDE For Gradate and Professional Stdent Direct PLUS
More informationPlanning a Smart Card Deployment
C H A P T E R 1 7 Planning a Smart Card Deployment Smart card spport in Microsoft Windows Server 2003 enables yo to enhance the secrity of many critical fnctions, inclding client athentication, interactive
More informationThe Boutique Premium. Do Boutique Investment Managers Create Value? AMG White Paper June 2015 1
The Botiqe Premim Do Botiqe Investment Managers Create Vale? AMG White Paper Jne 2015 1 Exective Smmary Botiqe active investment managers have otperformed both non-botiqe peers and indices over the last
More informationInter-Dealer Trading in Financial Markets*
S. Viswanathan Dke University James J. D. Wang Hong Kong University of Science and Technology Inter-Dealer Trading in Financial Markets* I. Introdction Trading between dealers who act as market makers
More informationCurriculum development
DES MOINES AREA COMMUNITY COLLEGE Crriclm development Competency-Based Edcation www.dmacc.ed Why does DMACC se competency-based edcation? DMACC tilizes competency-based edcation for a nmber of reasons.
More informationTowers Watson Manager Research
Towers Watson Manager Research How we se fnd performance data Harald Eggerstedt 13. März 212 212 Towers Watson. All rights reserved. Manager selection at Towers Watson The goal is to find managers that
More informationPeriodized Training for the Strength/Power Athlete
Periodized Training for the /Power Athlete Jay R. Hoffman, PhD, FACSM, CSCS *D The se of periodized training has been reported to go back as far as the ancient Olympic games. Its basic premise is that
More informationAISC Live Webinars. AISC Live Webinars. High-Strength Bolts: The Basics. AISC Live Webinars. There s always a solution in steel.
AISC Live Webinars Thank yo for joining or live webinar today. We will begin shortly. Please standby. Thank yo. Need Help? Call ReadyTalk Spport: 800.843.9166 AISC Live Webinars Today s adio will be broadcast
More informationPricing Barrier Options under Local Volatility
Abstract Pricing Barrier Options under Local Volatility Artur Sepp Mail: artursepp@hotmail.com, Web: www.hot.ee/seppar 16 November 2002 We study pricing under the local volatility. Our research is mainly
More informationExecutive Coaching to Activate the Renegade Leader Within. Renegades Do What Others Won t To Get the Results that Others Don t
Exective Coaching to Activate the Renegade Leader Within Renegades Do What Others Won t To Get the Reslts that Others Don t Introdction Renegade Leaders are a niqe breed of leaders. The Renegade Leader
More informationNAZIA KANWAL VECTOR TRACKING LOOP DESIGN FOR DEGRADED SIGNAL ENVIRONMENT. Master of Science Thesis
NAZIA KANWAL VECTOR TRACKING LOOP DESIGN FOR DEGRADED SIGNAL ENVIRONMENT Master of Science Thesis Examiners: Professor Jari Nrmi, Adjnct Professor Simona Lohan and Dr. Heikki Hrskainen Examiner and topic
More informationIn the insurance business risky investments are dangerous
Noname manscript No. (will be inserted by the editor) In the insrance bsiness risy investments are dangeros Anna Frolova 1, Yri Kabanov 2, Sergei Pergamenshchiov 3 1 Alfaban, Moscow, Rssia 2 Laboratoire
More informationEN0175 Advanced Mechanics of Solids
N0175 Advanced Mechanics of Solids Hajian Gao Office: Bars & Holley 610 Phone: 863-66 mail: Hajian_Gao@Brown.ed http://www.engin.brown.ed/corses/en175/ Corse Otline 1. Introdction 1.1 Scope of the corse
More informationCandidate: Kevin Taylor. Date: 04/02/2012
Systems Analyst / Network Administrator Assessment Report 04/02/2012 www.resorceassociates.com To Improve Prodctivity Throgh People. 04/02/2012 Prepared For: Resorce Associates Prepared by: John Lonsbry,
More informationNewton s three laws of motion, the foundation of classical. Applications of Newton s Laws. Chapter 5. 5.1 Equilibrium of a Particle
Chapter 5 Applications of Newton s Laws The soles of hiking shoes are designed to stick, not slip, on rocky srfaces. In this chapter we ll learn abot the interactions that give good traction. By the end
More informationFUNCTIONAL COEFFICIENT MODELS UNDER UNIT ROOT BEHAVIOR. 1. Introduction
FUNCTIONAL COEFFICIENT MODELS UNDER UNIT ROOT BEHAVIOR TED JUHL Abstract. We analyze the statistical properties of nonparametrically estimated fnctions in a fnctional-coefficient model if the data has
More informationHedging Exotic Options
Kai Detlefsen Wolfgang Härdle Center for Applied Statistics and Economics Humboldt-Universität zu Berlin Germany introduction 1-1 Models The Black Scholes model has some shortcomings: - volatility is not
More informationSEGREGATED ACCOUNTS COMPANIES ACE CAPABILITIES: AN OVERVIEW
SEGREGATED ACCOUNTS COMPANIES CAPABILITIES: AN OVERVIEW SIMPLICITY OUT OF COMPLEXITY SEGREGATED ACCOUNTS CAPABILITIES Managing yor own risks jst got simpler. In recent years, increasing reglation has led
More informationA taxonomy of knowledge management software tools: origins and applications
Evalation and Program Planning 25 2002) 183±190 www.elsevier.com/locate/evalprogplan A taxonomy of knowledge management software tools: origins and applications Peter Tyndale* Kingston University Bsiness
More informationFINANCIAL FITNESS SELECTING A CREDIT CARD. Fact Sheet
FINANCIAL FITNESS Fact Sheet Janary 1998 FL/FF-02 SELECTING A CREDIT CARD Liz Gorham, Ph.D., AFC Assistant Professor and Family Resorce Management Specialist, Utah State University Marsha A. Goetting,
More informationResearch on Staff Explicitation in Organizational Knowledge Management Based on Fuzzy Set Similarity to Ideal Solution
Send Orders for Reprints to reprints@benthamscience.ae The Open Cybernetics & Systemics Jornal, 015, 9, 139-144 139 Open Access Research on Staff Explicitation in Organizational Knowledge Management Based
More informationaééäçóáåö=táåççïë= péêîéê=ommp=oéöáçå~ä= açã~áåë
C H A P T E R 7 aééäçóáåö=táåççïë= péêîéê=ommp=oéöáçå~ä= açã~áåë Deploying Microsoft Windows Server 2003 s involves creating new geographically based child domains nder the forest root domain. Deploying
More information