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Financial Engineering with Finite Elements 1st Edition
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"Financial Engineering with Finite Elements is packed with state of the art valuation methods. Written in a clear and intuitive way makes it a must have for anyone wanting to stay ahead of the game. The book stands out from the crowd with a lot of information I have never seen published in any other finance book." Espen Gaarder Haug, Trader, J.P. Morgan, New York
"Finite elements have for a long time been a preferred numerical scheme for the solution of differential equations arising in the hard sciences. Now Jürgen Topper shows us how to apply the technique effectively to solve equations from the financial arena including the pricing of derivatives. He includes sections on multi-asset options, non-linear equations, exit times and exotics. A very welcome addition to the literature on numerical analysis in finance." Paul Wilmott, fund mananger and mathematician, London
"Jürgen Topper fills an important gap in the burgeoning literature on mathematical finance by providing a systematic and accessible description of the Method of Finite Elements and its applications. Since this important computational technique has a lot of potential in financem the book is very timely." Alexander Lipton, Citadel Investment Group, L.L.C., Chicago
- Item Weight : 1.9 pounds
- Hardcover : 378 pages
- ISBN-10 : 0471486906
- ISBN-13 : 978-0471486909
- Dimensions : 6.9 x 1.1 x 9.7 inches
- Publisher : Wiley; 1st edition (April 1, 2005)
- Language: : English
- Best Sellers Rank: #4,557,846 in Books (See Top 100 in Books)
- Customer Reviews:
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p. 50 3.258 Should be S=E*exp(x)
p. 51 3.279 Should be '+w(i-1,j)' not '-'
p. 61 4.32 Should be u(x,-525/23) instead of -523
p. 64 4.50 Should be a3 = -(163*a4 +3,200,000)/880
p. 66 4.75 and 4.75 should be a5*0.05^4 and a5*0.15^4 respectively instead of a4
p. 74 4.124 Should be (x^3 -4x) not (x^4-4x)
p. 74 middle of the page first 'L(u)=...a2*u...'
should be 'L(u)=...a2(x)*u...'
p. 100 formula (4.343) has to be '...ln(xmin/xmax))' for values in Table 4.9 to be correct.
I'm sure what Table 4.9 'First Exit Time' values represent and have not gone deeper into what is being done. I.e. time is not an input
parameter and the values returned aren't premium.
p. 105 It looks like the graph line for Figure 4.15(b) is missing unless it is the single right-hand vertical line near x=1.0. However it is the
small curved line near U= -0.0000.
p. 161 8th line should be 'see Definition 11 in Appendix A, not Definition 9
p. 177 above 6.48, 'All triangular elements in Figure 6.4...' not 6.5 ?
p. 181 to 183 I don't see Figure 6.10 referenced. Probably did not need to be but transform method did not seem to be explained.
p. 191 under (6.97) & 6.104 Where did 'b' come from ?
p. 191 6.103 and 6.104 should a3 and a4 be a1 and a2 ?
p.192 5th to last line should be 'The last two columns of Table 6.5...' not 6.2
p. 192 scale for Figure (6.15) is 'u-uritz (10^-3)' I assume that was just the result of a label in the code for generating the graph
p. 216 someone else mentioned the 'V' on the right side of (9.14)-(9.16) and time 't' valuations
don't seem right. [Another person pointed this out to me and] asked "what is the meaning of the variable/parameter 'V' on the
right side of these equations? I cannot find a reference to it (maybe it is described
somewhere ) but it might be the solution of the respective BS PDE in two factors. This means
when solving the 3d case we have to solve a 2d case on each face of the cube?" Later
The same person said "I think indeed that it is the solution of the 2d PDE case (just as the 2-factor
reduces to the 1-factor on the boundary). If this is so we must do a lot of computation; at each
time level we solve for the BCs (which are also PDEs)."
p. 221 before (10.5) should be 'Inserting...' not 'Integrating...'
p. 229 3rd to last line should be 'Equivalent .. Equation (10.49)...' not 10.50
p. 229 eq. 10.35 'H' in summation not defined. Stands for 'Holding Period' ?
p. 232 5th line should be 'Inserting ...equation 10.64' not 10.65
p. 234 line above 10.95 should be 'Inserting equation 10.91 not 10.90. Also sign changed from 10.91 to 10.92. Correct ? i.e. should 10.93 be +x*sigma^2 *d^2(v)/dx^2---which seems to change your argument
p. 245 eq (10.138) = 4.3638 [correct values for sigma_min]; what is (10.139) value of .55<2.29 ? [2.29 is the FE value but the eq (10.138) is not the 0.55 [the wings at sigma_min and body at
sigma_max is .56---is this the 0.55 on line (10.139?].
p. 319 B.86 [y',p_sub(y')] should be [y',p]_sub(y') Sorry for the notation. _sub(y') means a
subscript on the variable shown, here on 'p' and '[...]' respectively.
p. 324 are equations B.131 and B.133 missing a division sign after c*sigma1 and sigma2 respectively ?
p. 349 for the Shreve entry it has 'Journal of Finance and Stochastics' instead of just 'Finance and Stochastics.' I think I've seen that for at least one other bibliographic entry.
p. 330 under Theorem 35, 'as defined in Definition 18...' is correct, not 'Definition 15'
p. 338 under C.56, should be '...positive definite (see Theorem 35)...' not 34.
The use of C^1 elements does not allow continuous computation of the Greek known as Gamma. (This is typically the second derivative of the value function with respect to the underlying price.) Using C^2 element functions would have resulted in smooth Gamma and higher order truncation errors. That would also mean more accuracy with fewer elements.
There is a frustrating lack of clear titles for many of the tables given in the book. Often too many redundant entries of tables are given with little indication of accuracy.
All told this is an interesting book but must be augmented with experimental computation and other works (not mentioned here) to be of lasting value.