down and out barrier option s pricing kernel

QUANTUM FINANCE Path Integrals and Hamiltonians for Options and Interest Rates doc

Ngày tải lên : 23/03/2014, 12:20

... created; these instruments demand advanced valuation and risk assessment models and systems that quantify the returns and risks for investors and financial institutions [63, 100] The widespread use in ... Bonds and fixed-income securities are briefly discussed Chapter on ‘Derivative securities’ introduces the concept of financial derivatives and discusses the pricing of derivatives The classic analysis ... chapters Systems with finite number of degrees of freedom In this part Hamiltonians and path integrals are applied to the study of stock options and stochastic interest rates models These models are...

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finance - turning finance into science - risk management and the black-scholes options pricing model

Ngày tải lên : 08/04/2014, 12:09

... of Risk Scientific American , pp 91.] 14 However, Scholes says that it was not so much the formula itself that caused these losses, rather its misuse by market traders Every statistician and mathe ... mics (Royal Swedish Academy of Sciences, 1997) Derivatives make the news because, like an airplane crash, their losses can dramatic and chaotic Enormou s losses by Proctor & Gamble and Gibson ... relies on imputs and assu me s a functioning market It is a powerful way to manage risk, but it s not a crystal ball Scholes says this equation should be used as a tool for making decisions, not a...

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POWER SERIES TECHNIQUES FOR A SPECIAL SCHRÖDINGER OPERATOR AND RELATED DIFFERENCE EQUATIONS MORITZ docx

Ngày tải lên : 23/06/2014, 00:20

... made use of the abbreviations A≡ a2 ≥ 0, B≡ (b − 1)2 ≥0 (2.6) for the sake of simplicity In the next section, we are going to solve (2.3) in these three special cases—the same as in Bessel s case ... a one-dimensional subspace of solutions y∗ is obtained—being of type (3.2)—which satisﬁes the integrability condition (4.1) for some γ > On the one hand, if b ≥ −1, this subspace is spanned by ... Power series techniques and Schr¨ dinger operators o (i) x is the dimensionless radial distance (in the plane) (ii) ψ gives information on the probability density for measuring a particle signal...

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Định giá cổ phiếu phát hành lần đầu theo mô hình định giá quyền chọn Black Scholes trên thị trường chứng khoán Việt Nam .

Ngày tải lên : 09/04/2013, 15:03

... nhiên sau : S S dS = dV + dt + ∂V ∂t S σ V ∂V 2 2 dt Giải phương trình ta tìm nghiệm S lim dS dt→0 S = S dV S dV V = ∂V S ∂V V S Website: http://www.docs.vn Email : lienhe@docs.vn Tel ... giá trị s s ch tài s n giá trị s s ch doanh nghiệp.Giá trị s s ch tài s n tức giá trị kế toán tài s n đó,nó chi phí mua s m tài s n trừ phần khấu hao tích lũy tài s n đó.Giá trị s s ch doanh ... động Browns hình học d ( S 0) = µ S 0.dt + σ S 0.d ( B t ) Trong : µ : Lợi suốt kỳ vọng tài s n s σ : Độ giao động tài s n s µ , σ : Không đổi S B t : Tài s n s : Chuyển động Browns b: Giá...

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Markov processes and the Kolmogorov equations

Ngày tải lên : 18/10/2013, 03:20

... h S T F s = v s; S s : This is a special case of Theorem 5.51 Because v t; S t is a martingale, the sum of the formula, dt terms in dv t; S t must be h By Itˆ s o i dv t; S ... processes and the Kolmogorov equations and the boundary condition vt; 0 = 0; 187 t T: An example of such a process is the following from J.C Cox, Notes on options pricing I: Constant elasticity ... variance diffusions, Working Paper, Stanford University, 1975: dS t = rS t dt + S t dBt; where The “volatility” sponding Black-Scholes equation is S ,1t decreases with increasing stock price...

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The Schwarzschild Solution and Black Holes

Ngày tải lên : 23/10/2013, 20:20

... possesses a timelike Killing vector This property is so interesting that it gets its own name: a metric which possesses a timelike Killing vector is called stationary There is also a more restrictive ... massless particles actually move in a straight line, since the Newtonian gravitational force on a massless particle is zero (Of course the standing of massless particles in Newtonian theory is ... dwarfs are found between points A and B, and neutron stars between points C and D Point B is at a height of somewhat less than 1.4 solar masses; the height of D is less certain, but probably less...

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Numerical Solutions of the Black Scholes Equation

Ngày tải lên : 25/10/2013, 19:20

... difference scheme described above 8.2 CONDITIONS FOR SATISFACTORY SOLUTIONS The six schemes set out in the last section all seem quite reasonable; but are there any tests we can carry out ahead ... difference, Crank Nicholson and Douglas methods are always stable r The Richardson method is always unstable r Dufort and Frankel is always stable but as we saw above, it may not be consistent with the ... This is 3% away from the Black Scholes result, which for an absurdly small number of steps is quite surprising The performance of these ﬁnite difference methods as a function of step numbers is...

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The Black Scholes Model

Ngày tải lên : 25/10/2013, 19:20

... interest rates are constant However the result is more general, and holds for variable interest rates also The reason is that a futures contract costs nothing to enter so that arbitrage assures that ... plus stock borrowing cost (iii) Prices, Values and Greeks of Forwards and Futures: Before going on to discuss other markets it is worth brieﬂy recapping on the meanings of the words “price” and ... is a very straightforward cash market, i.e the commodity (stock) is purchased directly with physical delivery as soon as possible after purchase In most established markets there are traded options...

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Phương trình vi phân ngẫu nhiên và vấn đề định giá quyền chọn theo mô hình black scholes khoá luận tốt nghiệp đại học

Ngày tải lên : 19/12/2013, 14:05

... = Yt0 + s b( s )ds + s d (s )dWs t X t = t0 X t0 + s b (s )ds + s 1d ( s )dWs t0 1 t0 t0 t0 t t t t0 = nờn X t = t X t0 + s 1b( s) ds + s 1d ( s) dWs , ú t = exp a ( s) ds Vỡ t0 ... ( s, Ys ( k 1) ) dWs T t E ( s, Ys 2k + (k ) ) ( s, Y ( k 1) s Mt khỏc, ) ds + 2k +2 t E ( s, Y ) ( s, Y (k ) s ( k 1) s ) ữ ữ ds ( ( s, Ys ( k ) ) ( s, Ys ( k 1) ) ( s, Ys ... ( ) t ) ( s, X s ) ds t ( s, Ys ( n) ) ( s, X s ) ds Do ú, t E ( s, Ys (n) t ) ( s, X s ) ds t.E ( s, Ys ( n) ) ( s, X s ) ds 2 Qua gii hn L ( P) (2.8) ta suy Xt tha phng...

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Tài liệu Bài 5: Định giá quyền chọn bằng mô hình Black-Scholes pptx

Ngày tải lên : 25/01/2014, 11:20

... MÔ HÌNH BLACK SCHOLES Giá cổ phiếu biến động ngẫu nhiên phát triển theo phân phối logarit chuẩn Lãi suất phi rủi ro độ bất ổn tỷ suất sinh lợi theo logarit cổ phiếu khơng thay đổi suốt thời gian ... với giá cổ phiếu, xác giá cổ phiếu thay đổi nhỏ CÁC BIẾN S TRONG MÔ HÌNH B -S CÁC BIẾN S TRONG MÔ HÌNH B -S CÁC BIẾN S TRONG MÔ HÌNH B -S Giá cổ phiếu Phòng ngừa delta xây dựng danh mục phòng ... NOBEL C = S N(d ) − Xe − rc T N(d ) Với ln (S0 /X) + (rc + σ /2)T d1 = σ T d2 = d − σ T N(d1), N(d2) = xác suất phân phối chuẩn tích lũy σ = độ bất ổn hàng năm (độ lệch chuẩn) tỷ suất sinh lợi...

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Functional analysis sobolev spaces and partial differential equations

Ngày tải lên : 04/02/2014, 11:10

... lemma has many important applications in analysis It is a basic tool in proving some seemingly innocent existence statements such as “every vector space has a basis” (see Exercise 1.5) and “on ... convex subsets such that A ∩ B = ∅ Assume that A is closed and B is compact Then there exists a closed hyperplane that strictly separates A and B Proof Set C = A − B, so that C is convex, closed (check!), ... Universitext For other titles in this series, go to www.springer.com/series/223 Haim Brezis Functional Analysis, Sobolev Spaces and Partial Differential Equations 1C Haim Brezis Distinguished...

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Tài liệu Boundary Value Problems, Sixth Edition: and Partial Differential Equations pptx

Ngày tải lên : 17/02/2014, 14:20

... c1 cosh(λt) + c2 sinh(λt) as the general solution of Eq (14), where c1 and c2 are arbitrary constants Example: Mass–Spring–Damper System The displacement of a mass in a mass–spring–damper system ... sin(λa) is not 0, the only possibility is that c2 = In this case we ﬁnd that the solution is u(x) ≡ 0, < x < a Physically, this means that the column stands straight and transmits the load to its support, ... mass in a mass–spring–damper system, starting 18 Chapter Ordinary Differential Equations Figure Mass–spring–damper system with an external force from rest, with an external sinusoidal force (see...

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Entropy and partial differential equations evans l c

Ngày tải lên : 17/03/2014, 14:29

... problem a Small noise asymptotics b Perturbations against the ﬂow Appendices: A Units and constants B Physical axioms References INTRODUCTION A Overview This course surveys various uses of “entropy” ... as we consider our processes on “slower and slower time scales” The model without dissipation corresponds simply to setting R1 ≡ 0, R2 ≡ To further develop our model we next assume as an instance ... Although we will for simplicity of exposition mostly discuss simple ﬂuid systems, it is important to understand that many interpretations are possible (See, e.g., Zemansky [Z].) Extensive parameter...

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harmonic analysis and partial differential equations - b. dahlberg, c. kenig

Ngày tải lên : 31/03/2014, 15:16

... compactness arguments) we have used Hence it is not possible to solve the Dirichlet problem for, say Lipschitz-domains by approximating with C domains k , solve some Dirichlet problems for these and ... that these kernels are of CZ -type and adopt the convention that whenever we discuss kernels K , they are assumed to be of CZ -type unless we explicitly state the converse Starting with a kernel ... follows from H lder 's inequality Fact 3: Connection between BMO and Carleson measures Carleson measures originally appeared as answers to the following question Question: Which positive measures...

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math. and phys. data - equations and rules of thumb - s. gibilisco

Ngày tải lên : 31/03/2014, 16:19

... Fields RF Transmission Lines Antennas Bridge Circuits Null Networks Chapter Physical and Chemical Data Units Classical Mechanics Fluidics and Thermodynamics Waves and Optics Relativistic and Atomic ... 551 Suggested Additional References 553 Index 555 Preface This is a comprehensive sourcebook of deﬁnitions, formulas, units, constants, symbols, conversion factors, and miscellaneous data for use ... use by engineers, technicians, hobbyists, and students Some information is provided in the ﬁelds of mathematics, physics, and chemistry Lists of symbols are included Every effort has been made to...

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Báo cáo hóa học: " Local stability of the Pexiderized Cauchy and Jensen’s equations in fuzzy spaces" pptx

Ngày tải lên : 20/06/2014, 22:20

... Fuzzy Sets Syst 159, 730–738 (2008) doi:10.1016/j.fss.2007.07.011 Mirmostafee, AK, Moslehian, MS: Fuzzy versions of Hyers-Ulam-Rassias theorem Fuzzy Sets Syst 159, 720–729 (2008) doi:10.1016/j.fss.2007.09.016 ... Hyers-Ulam-Rassias stability of a Pexiderized quadratic inequality Math Inequal Appl 4, 93–118 (2001) Jung, S- M: Hyers-Ulam-Rassias stability of Jensen s equation and its application Proc Am Math Soc ... Trans Am Math Soc 347, 3111–3119 (1995) doi:10.2307/2154775 Hyers, DH, Isac, G, Rassias, ThM: Stability of Functional Equations in Several Variables Birkhäuser, Basel (1998) Hyers, DH, Isac,...

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Báo cáo hóa học: " Research Article First-Order Singular and Discontinuous Differential Equations" docx

Ngày tải lên : 21/06/2014, 20:20

... Equations with Discontinuous Righthand Sides, vol 18 of Mathematics and Its Applications (Soviet Series), Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988 11 S Heikkil¨ and V Lakshmikantham, ... of the solutions In Section we prove two existence results in case f does not have such a strong bound as in Section singular problems , which requires the addition of some assumptions over the ... continuous cases e Discontinuous Lower and Upper Solutions Another modiﬁcation of the concepts of lower and upper solutions concerns the possibility of allowing jumps in their graphs Since the task...

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Báo cáo hóa học: " Research Article Stability of Mixed Type Cubic and Quartic Functional Equations in Random Normed Spaces" potx

Ngày tải lên : 22/06/2014, 02:20

... 1991, Gajda answered the question for the case p > 1, which was raised by Rassias This new concept is known as Hyers-Ulam-Rassias stability of functional equations see 5–12 Jun and Kim 13 introduced ... Hyers, G Isac, and Th M Rassias, Stability of Functional Equations in Several Variables, vol 34 of Progress in Nonlinear Diﬀerential Equations and Their Applications, Birkh¨ user, Boston, Mass, ... adopt the usual terminology, notations, and conventions of the theory of random normed spaces, as in 19–21 Throughout this paper, Δ is the space of distribution functions that is, the space of...

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Báo cáo hóa học: " Editorial Harnack’s Estimates: Positivity and Local Behavior of Degenerate and Singular Parabolic Equations" pdf

Ngày tải lên : 22/06/2014, 19:20

... half spaces In this case they assume there exists a Lie structure over RN+1 under which L is left invariant Finally, these results are applied to several examples of operators Lewis and Vogel study ... o forms and by potentials in suitable Kato classes Similar results were obtained by Biroli in a previous paper for operators associated to subelliptic p-Laplacians, but the techniques used there ... Problems but comments on the geometric and probabilistic signiﬁcance of Harnack s inequalities as well The attention is mainly on classical results and an extensive and thorough list of references...

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NONSMOOTH AND NONLOCAL DIFFERENTIAL EQUATIONS IN LATTICE-ORDERED BANACH SPACES ¨ SIEGFRIED CARL AND doc

Ngày tải lên : 23/06/2014, 00:20

... f satisﬁes the hypotheses (f0) and (f1) The hypothesis (c) is also valid, whence the asserted results follow from Theorem 3.2 Example 3.4 Consider the following system of IVPs: v (s) ds v (s) ds ... (u,v) = 1+ 1+ v (s) ds v (s) ds v (s) ds v (s) ds v(1) + v(1) ,2 √ , t+2 , 1+ 1+ u (s) ds u (s) ds u (s) ds u (s) ds u(1) + u(1) , | , (4.17) The hypotheses (f0), (f1), (c), and (d) hold, with respect to 1-norm ... hypotheses (g0) and (g1) imply that f satisﬁes the hypotheses (f0) and (f1) The hypotheses (c0) and (d) are also valid, whence the asserted results follow from Theorem 5.2 S Carl and S Heikkil¨...

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