double knock out barrier option s pricing kernel

... 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 finance of stochastic ... profit Thus, eliminating fluctuations also eliminates the possibility of some ‘good’ fluctuations in the process Options, though not costless to enter, often allow investors to manage risks without having ... combinations of knock- in and knock- out options [51] More exotic options such as the look-back option, quanto option, basket option, hybrid option, dual-strike option and so on are designed to serve...

Ngày tải lên: 23/03/2014, 12:20

... investor s from excessive risk by means of pricing options However, this formula containe d financially unrealistic assum p tion s, such as the existence of negative values for stock prices and ... Calculus 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 ... interest rate (Stix, 1998) His paper was shelved and went unnoticed for decades It wasn’t until 1955 that the idea of options pricing resurfaced, when a profess o r at the Massachuset t s Institute...

Ngày tải lên: 08/04/2014, 12:09

... 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 ... There is a quite general power series method for solving second-order differential equations of “Bessel-type” as discussed above; we refer for instance to [1] We give an outline of this technique ... 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...

Ngày tải lên: 23/06/2014, 00:20

... 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...

Ngày tải lên: 09/04/2013, 15:03

... 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 ... 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 ... 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...

Ngày tải lên: 18/10/2013, 03:20

... 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 than solar masses The process of collapse is complicated, ... motion of test particles in the solar system, and hence geodesics of the Schwarzschild metric; this is therefore a good place to pause and consider these tests Einstein suggested three tests: the ... 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...

Ngày tải lên: 23/10/2013, 20:20

... 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 ... 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 ... grid points in the x-direction In this example we use α = and six steps in the x-direction; these values are chosen to make the set-up as close as possible to the binomial example of the last chapter...

Ngày tải lên: 25/10/2013, 19:20

... with physical delivery as soon as possible after purchase In most established markets there are traded options on the most important stocks, although forwards and futures on single stocks have ... hedge options, since they involve no initial cash outlay (iv) Foreign Exchange: These are the largest and most liquid markets considered in this book Most of the Black Scholes assumptions of Section ... meanings of the words “price” and “value” In the cash markets (equities, spot FX, spot commodities) the two mean exactly the same: if a stock price is $50 its value is $50 In the case of options, usage...

Ngày tải lên: 25/10/2013, 19:20

... = 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...

Ngày tải lên: 19/12/2013, 14:05

... 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...

Ngày tải lên: 25/01/2014, 11:20

... components with respect to some basis In some sense, Corollary 2.4 replaces, in infinite-dimensional spaces, the use of components Sometimes, one expresses the conclusion of Corollary 2.4 by saying that ... Zorn s 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 ... 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!),...

Ngày tải lên: 04/02/2014, 11:10

... 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 ... 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 ... 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,...

Ngày tải lên: 17/02/2014, 14:20

... 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 ... process (T (t), V (t)), a ≤ t ≤ This is only possible if R1 ≡ R2 ✷ The foregoing proofs demonstrate that our model with dissipation in some sense “approximates an ideal model without dissipation”...

Ngày tải lên: 17/03/2014, 14:29

... 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 ... the space BMOp to consist of those functions f such that kf kp; < Thus (BMOp; k kp; ) becomes a semi-normed vectorspace with semi-norm vanishing on the constant functions The letters BMO stand...

Ngày tải lên: 31/03/2014, 15:16

... 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 ... represent the variables, and a0 through an represent constants, usually real numbers Existence of solutions Suppose there exists a set of m linear equations in n variables If m Ͻ n, there exists ... Acknowledgments xiii Chapter Algebra, Functions, Graphs, and Vectors Sets Denumerable Number Sets Non-denumerable Number Sets Properties of Operations Miscellaneous Principles Inequalities Simple Equations...

Ngày tải lên: 31/03/2014, 16:19

... 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 ... 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, ... functions in quasiBanach spaces J Math Anal Appl 337, 399–415 (2008) doi:10.1016/j.jmaa.2007.03.104 Najati, A, Park, C: Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras associated...

Ngày tải lên: 20/06/2014, 22:20

... discontinuous nonlinearities,” Dynamics of Continuous, Discrete & Impulsive Systems Series A, vol 10, no 6, pp 931–947, 2003 E R Hassan and W Rzymowski, “Extremal solutions of a discontinuous scalar ... 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 ... have lim sup f t, y ≤ f t, x ≤ lim inf f t, y y → x− y→x 2.1 A similar result was established in 20 assuming moreover that f is superpositionally measurable, and the systems case was considered...

Ngày tải lên: 21/06/2014, 20:20

... unbounded In 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 ... Gifted Students at Semnan University for its financial support References S M Ulam, Problems in Modern Mathematics, chapter 6, John Wiley & Sons, New York, NY, USA, 1940 D H Hyers, “On the stability ... the sequel we 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,...

Ngày tải lên: 22/06/2014, 02:20

... 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 ... also that they yield the solution to certain symmetry problems Despite the sophisticated hard analysis used by the authors, the paper is quite accessible Lieberman considers parabolic equations...

Ngày tải lên: 22/06/2014, 19:20

... (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 hypothesis (c) is also valid, whence the asserted results follow from Theorem 3.2 Example 3.4 Consider the following system ... and that Gu increases if c(u) or f (·,u) increases Thus the assertions follow from Lemmas 3.1 and 2.2 S Carl and S Heikkil¨ 169 a As a special case, we obtain an existence result for the IVP...

Ngày tải lên: 23/06/2014, 00:20