Financial calculus Introduction to Financial Option Valuation 6 ppt
Financial calculus Introduction to Financial Option Valuation_2 pdf
... that led to (6. 8) and show that the same continuous model arises. 6. 3. Explain why the model (6. 2) is ‘statistically the same if σ is replaced by −σ ’. 6. 4. Verify (6. 5) and (6. 6). [Hint: ... 3.7.] 6. 5. Show that S(t) in (6. 8) has density function (6. 10). [Hint: use the characterization P(a ≤ S(t) ≤ b) = b a f (x) dx from (3.3).] 6. 6. Using (3.8), show that (6....
Ngày tải lên: 21/06/2014, 09:20
Financial calculus Introduction to Financial Option Valuation_3 doc
... given that no active market for options existed. But coincidentally, a month before the formula appeared, the Chicago Board Options Exchange had begun to list stock options for trading. Soon, Texas ... we find, to four decimal places, d 1 = 1. 060 5, d 2 = 0. 760 5, N (d 1 ) = 0.8555, N (d 2 ) = 0.7 765 , N (−d 1 ) = 0.1445, N (−d 2 ) = 0.2235. Here, we used MATLAB’s erf function in order...
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Financial calculus Introduction to Financial Option Valuation_4 pptx
... Speculator A would find the Black– Scholes option value more attractive than Speculator B. This does not contradict the previous theory. A speculator who is willing to accept some risk may value an option ... there is a large group of investors who view options as an excellent means to alleviate their exposure to risk, and another large group who see options as a great way to specu...
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Financial calculus Introduction to Financial Option Valuation_5 doc
... end of the program we reset the display to the default with format. Output from ch13 is Newton error 1.5 465 e-01 8. 362 2e-03 2.4 964 e-05 2.2279e-10 1.1102e- 16 This is consistent with the quadratic ... possible, for exam- ple, to design a hybrid algorithm that uses a safe method, like bisection, until the iterates are close to an x and then switches to Newton’s method to get t...
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Financial calculus Introduction to Financial Option Valuation_6 ppt
... costly. To reduce the error to, say, 10 −4 would take of the order of 10 8 samples, and to reduce it to 10 6 would take of the order of 10 12 samples; see Exercise 15.4. ♦ 15.3 Monte Carlo for option ... price Option price 5125 475 5225 405 5325 340 5425 280 1 2 5525 2 26 562 5 179 1 2 5725 139 5825 105 5100 5200 5300 5400 5500 560 0 5700 5800 5900 0.172 0.174 0.1 76 0.178 0.18...
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Financial calculus Introduction to Financial Option Valuation_8 potx
... 10 2 [0.0 469 , 0. 167 1] [0.0397, 0.1387] [0.0 569 , 0.1813] M = 10 3 [0.0 961 , 0.1347] [0.07 56, 0.1104] [0.07 26, 0.10 46] M = 10 4 [0.1042, 0.1 163 ] [0.0997, 0.1112] [0.09 26, 0.1038] M = 10 5 [0.1097, 0.11 36] ... applied to any of the generalized path-dependent options men- tioned in Sections 19.2, 19.3, 19.4. 1 96 Exotic options The binomial method does not naturally extend to...
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Financial calculus Introduction to Financial Option Valuation_9 potx
... σ is computed in order to value an option, then a widely quoted rule of thumb is to make the historical data time-frame Mt equal to that of the option: to value an option that expires in six ... references 209 20 40 60 80 100 120 140 160 180 0 0.2 0.4 0 .6 0.8 1 Days Vol Daily 20 40 60 80 100 120 140 160 180 200 0 0.2 0.4 0 .6 0.8 1 Weeks Vol Weekly Fig. 20.1. Historical vo...
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Financial calculus Introduction to Financial Option Valuation_10 ppt
... widths 10 2 [0.8247, 1.2819] [0.9518, 1 .67 67] 0 .6 10 3 [0.9713, 1.1574] [1.0 166 , 1.1244] 1.7 10 4 [0. 964 7, 1.0137] [0.9945, 1.0243] 1 .6 10 5 [0.9953, 1.0115] [0.9955, 1.00 46] 1.8 21.7 Multivariate case The ... in Chapter 6, • derivation of the binomial method in Chapter 16, • extension of Monte Carlo to path-dependent option valuation in Chapter 19. The plan is to comput...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_13 pot
... the top and bottom, corresponding to those zero boundary conditions. PROGRAMMING EXERCISES P23.1. Using colon subarray notation, as in ch 16, orotherwise, alter ch23 so that FTCS is used. Toy with ... finite differences to option valuation. We saw in Chapter 18 that the problem of valuing an American option can be couched in terms of a linear complementarity problem. It is possible...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_14 pot
... 249–252, 257– 261 , 265 for American option, 263 for Black–Scholes PDE, 257– 260 FTCS, 240–249, 252, 257– 260 , 265 instability, 243 local accuracy, 2 46 247, 249, 251, 252 penalty method, 263 stencil, ... 238–239, 262 , 265 hedging, 74, 76 78, 82, 87–93, 1 06, 1 16, 145, 164 , 188 historical volatility, 203–209 IBM daily data, 208 IBM weekly data, 208 maximum likelihood, 2 06 207, 210...
Ngày tải lên: 20/06/2014, 18:20