Financial calculus Introduction to Financial Option Valuation 4 pptx

... 5 0 0.1 0.2 0.3 0 .4 IBM Daily Histogram −5 0 5 0 0.5 1 Cumulative Density −5 0 5 4 −2 0 2 4 Quantiles −5 0 5 0 0.1 0.2 0.3 0 .4 IBM Weekly −5 0 5 0 0.5 1 −5 0 5 4 −2 0 2 4 −5 0 5 0 0.1 0.2 0.3 0 .4 Rand. ... Chapter 4 and walkthrough 43 PROGRAMMING EXERCISES P4.1. Adapt ch 04. m to the case where ξ i in (4. 7) are from the exponential distri- bution with parameter λ = 1. [Hi...

Ngày tải lên: 21/06/2014, 09:20

... 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 ... RITCHIE, option trader, source (Bass, 1999) 74 Black–Scholes PDE and formulas The key idea in this chapter is hedging to eliminate risk.Toreinforce the idea, and emphasize that it is a...

Ngày tải lên: 21/06/2014, 09:20

... 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 1 2 3 Asset path E 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 Delta 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.5 1 1.5 2 Cash 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 1 1.5 2 Portfolio Fig. ... hedging 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 1 2 3 Asset path E 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 Delta 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 1 2 Cash 0 0.5 1 1.5 2 2.5 3 3.5 4...

Ngày tải lên: 21/06/2014, 09:20

... to the default with format. Output from ch13 is Newton error 1. 546 5e-01 8.3622e-03 2 .49 64e-05 2.2279e-10 1.1102e-16 This is consistent with the quadratic convergence discussed in Section 13 .4 ... approach to finding a fair option value, there are a number of related points to make. (i) Formulas (12.2) and (12 .4) were derived without any reference to the idea of hedging to el...

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... abs(increment); end sigma Fig. 14. 3. Program of Chapter 14: ch 14. m. PROGRAMMING EXERCISES P 14. 1. Alter ch 14 to deal with a put option. P 14. 2. Acquire some real option data, either electronically ... 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. ♦...

Ngày tải lên: 21/06/2014, 09:20

... from 100 to 40 0. Solid line is 1/M. Lower picture: same data on a log–log scale. 0 2 4 6 8 10 12 14 16 18 20 0 1 2 3 4 5 6 7 8 9 10 t = T /4 S American put value Fig. 18.3. Value P Am (S, T /4) for ... = 10 −2 t = 10 −3 t = 10 4 M = 10 2 [0. 046 9, 0.1671] [0.0397, 0.1387] [0.0569, 0.1813] M = 10 3 [0.0961, 0.1 347 ] [0.0756, 0.11 04] [0.0726, 0.1 046 ] M = 10 4 [0.1 042 , 0....

Ngày tải lên: 21/06/2014, 09:20

... σ  is computed in order to value an option, then a widely quoted rule of thumb is to make the historical data time-frame Mt equal to that of the option: to value an option that expires in six ... and 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. Historica...

Ngày tải lên: 21/06/2014, 09:20

... of widths 10 2 [0.8 247 , 1.2819] [0.9518, 1.6767] 0.6 10 3 [0.9713, 1.15 74] [1.0166, 1.1 244 ] 1.7 10 4 [0.9 647 , 1.0137] [0.9 945 , 1.0 243 ] 1.6 10 5 [0.9953, 1.0115] [0.9955, 1.0 046 ] 1.8 21.7 Multivariate ... widths 10 2 [1.8 841 , 2.0752] [1.9601, 2.0031] 4. 4 10 3 [1.9538, 2.0087] [1.9951, 2.00 84] 4. 1 10 4 [1.9890, 2.0062] [1.99 94, 2.0036] 4. 1 10 5 [1.9969, 2.0023] [1.999...

Ngày tải lên: 21/06/2014, 09:20

... data ( 24. 2) or ( 24. 3) and the boundary values V i 0 and V i N x for all 1 ≤ i ≤ N t specified by the boundary conditions ( 24. 4) or ( 24. 5). To obtain a generalized version of FTCS for the PDE ( 24. 1) ... O(h 4 ). (23. 14) 23.7 Von Neumann stability and convergence 247 0 5 10 15 0 2 4 6 8 10 0 0.2 0 .4 0.6 0.8 1 x BTCS: ν = 6.6 t Fig. 23.7. BTCS solution on the heat equation (2...

Ngày tải lên: 20/06/2014, 18:20

... neutrality, 115, 118–120, 144 , 146 , 151, 1 54, 163, 167, 180, 181, 1 94, 232 cash-or-nothing, 167–168 sample mean, 34, 48 , 64, 141 , 146 , 2 04, 215 sample variance, 34, 48 SDE, see stochastic differential ... 265 instability, 243 local accuracy, 246 – 247 , 249 , 251, 252 penalty method, 263 stencil, 242 , 244 , 249 upwind, 262 von Neumann stability, 247 – 249 , 251, 252, 260, 265 fin...

Ngày tải lên: 20/06/2014, 18:20