sparse grid method in the libor market model. option valuation and the

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Bibliography L. Andersen. A simple approach to the pricing of bermudan swaptions in the multifactor LIBOR Market Model. Journal of Computational Finance, 3:5–32, 1999. F. Black and M. Scholes. The pricing of options and corporate liabilities. Journal of Political Economy, 81(3):637–659, 1973. J. Blackham. Sparse grid solutions to the LIBOR Market Model. Master’s thesis, Magdalen College, University of Oxford, 2004. Z. Bodie, A. Kane, and A.J. Marcus. Investments. 6th edition edition, 2004. A. Brace, D. Gatarek, and M. Musiela. The market model of interest rate dynamics. Mathematical Finance, 7(2):127–155, 1997. H.J. Bungartz and T. Dornseifer. Sparse grids: Recent developments for elliptic partial differential equations. In W. Hackbusch and G. Wittum, editors, Multigrid Methods V, Lecture Notes in Computational Science and Engineering, pages 45–70, Berlin Heidelberg, 1998. Springer. J. Cox, S. Ross, and M. Rubinstein. Option pricing, a simplified approach. J Financial Econ, 7:229–263, 1979. J. Crank and P. Nicolson. A practical method for numerical evaluation of solutions of partial differential equations of the heat-condution type. Mathematical Proceedings of the Cambridge Philosophical Society, 43:50–67, 1949. J. Dongarra, A. Lumsdaine, R. Pozo, and K. Remington. IML++ v. 1.2 Iterative Methods Library. Available at: http://math.nist.gov/iml++/. A. Etherage. Financial Calculus. Cambridge University Press, 2002. J. Garcke. Sparse grid tutorial. http://wwwmaths.anu.edu.au/˜garcke/ paper/sparseGridTutorial.pdf, 2005. M. Griebel, M. Schneider, and C. Zenger. A combination technique for the solution of sparse grid problems. In Proceedings of the IMACS International Symposium on Iterative Methods in Linear Algebra, pages 263–281, Amsterdam, 1992. Elsevier. URL citeseer.ist.psu.edu/griebel92combination.html. J. Hull. Options, Futures and other Derivatives. Prentice Hall, 1999. 70
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Page 1 and 2:
SPARSE GRID METHOD IN THE LIBOR MAR
Page 3 and 4:
Acknowledgements This project would
Page 5 and 6:
6.3.1 Valuation Results. . . . . .
Page 7 and 8:
6.18 2D Digital Option. Full and sp
Page 9 and 10:
Chapter 1 Introduction The modern f
Page 11 and 12:
Chapter 2 Asset Pricing Overview Th
Page 13 and 14:
Risk-Neutral Pricing Another import
Page 15 and 16:
S 0 u d u S 0 S u 2 0 Su 3 0 S du 2
Page 17 and 18:
or log(S T ) d −→ log(S 0 ) +
Page 19 and 20:
There is an important difference be
Page 21 and 22:
Delta. In order to set up a riskfre
Page 23 and 24:
Theorem 2.3.2. Let W P (t) = (W1 P
Page 25 and 26:
Chapter 3 LIBOR Market Model Having
Page 27 and 28: The right-hand side of the equality
Page 29 and 30: At this point of the text all neces
Page 31 and 32: pays off at expiry. Conveniently, t
Page 33 and 34: 1. Tenor structure of N interest ra
Page 35 and 36: and weight factor parts from the co
Page 37 and 38: we can substitute into the equation
Page 39 and 40: with ɛ i being independent standar
Page 41 and 42: a good compromise on the size of ɛ
Page 43 and 44: Three different θ values represent
Page 45 and 46: Chapter 5 Sparse Grids In the previ
Page 47 and 48: T 0 , 0 T 0 , 1 T 0 , 2 T 0 , 3 |i|
Page 49 and 50: 00 03 02 03 01 03 02 03 00 30 30 20
Page 51 and 52: Chapter 6 Numerical Results. Valuat
Page 53 and 54: 6.1.1 Convergence of MC, Full and S
Page 55 and 56: Full Solution. Level 6 Option Price
Page 57 and 58: 6.1.2 Discussion: Convergence of Pr
Page 59 and 60: 1 Full Delta Value Sparse Delta Val
Page 61 and 62: 0.03 0.025 Full vega Value Sparse v
Page 63 and 64: L1=5.62% Sparse Solution Swaption P
Page 65 and 66: Level L 2 =1.87% L 2 =1.875% L 2 =5
Page 67 and 68: Figures (6.14) and (6.15) show the
Page 69 and 70: 6.3 Discontinuous Payoff. 2D Digita
Page 71 and 72: Level L 1 =3.75% L 1 =4.68% L 1 =5.
Page 73 and 74: Figures (6.21) and (6.22) show the
Page 75 and 76: Chapter 7 Conclusion and Future Wor
Page 77: Appendix A Implementation Details I
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