Financial calculus Introduction to Financial Option Valuation 3 doc

... is expected to cost the young city trader involved his job. The deal amounted to 30 0m rather than £3m and flashed across stock market screens just as the stock market was about to close, causing ... 34 3.5 0 0.5 1 1.5 t =3 f ( x ) σ = 0 .3 σ = 0.5 σ = 0 .3 σ = 0.5 σ = 0 .3 σ = 0.5 σ = 0 .3 σ = 0.5 σ = 0 .3 σ = 0.5 Fig. 6.1. Lognormal density (6.10) for µ = 0.05, S 0 = 1, with σ...

Ngày tải lên: 21/06/2014, 09:20

... (S, t) corresponds to the value of a European call or put. 73 66 Asset price model: Part II 0 0.1 0.2 0 .3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.2 0.4 0.6 0.8 1 Fig. ... 10 3 d t = 5 × 10 −4 Asset paths 0 0.1 0.2 0 .3 0.4 0.5 0 0.01 0.02 0. 03 0.04 0.05 Sum-of-square returns σ 2 /2 σ 2 /2σ 2 /2 0 0.1 0.2 0 .3 0.4 0.5 0.8 0.9 1 1.1 Ass...

Ngày tải lên: 21/06/2014, 09:20

... symbol. 99 9 .3 Delta at expiry 91 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 0.5 1 1.5 2 Cash 0 0.5 1 1.5 2 2.5 3 3.5 ... 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 4.5 5 1...

Ngày tải lên: 21/06/2014, 09:20

... walkthrough In ch 13, listed in Figure 13. 3, we apply Newton’s method to N(x) + e x = 2. The line exact = fzero(inline(‘0.5*(1+erf(x/sqrt(2))) + exp(x)- 2’),1); %CH 13 Program for Chapter 13 % % Apply ... F(x mid ) must then match either F(x a ) or 1 23 128 Solving a nonlinear equation 13. 3.  To compute the errors that are shown in Figure 13. 2 it was ne- cessary to obtain the e...

Ngày tải lên: 21/06/2014, 09:20

... The errors for M = 2 16 and M = 2 17 are 5 .31 × 10 3 and 3. 64 × 10 3 , respectively. The ratio of these errors is ≈ 1.5, which is close to the asymptotic (M →∞)value of √ 2. This computation ... 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 Mont...

Ngày tải lên: 21/06/2014, 09:20

... is 0.09 83 t = 10 −2 t = 10 3 t = 10 −4 M = 10 2 [0.0469, 0.1671] [0. 039 7, 0. 138 7] [0.0569, 0.18 13] M = 10 3 [0.0961, 0. 134 7] [0.0756, 0.1104] [0.0726, 0.1046] M = 10 4 [0.1042, 0.11 63] [0.0997, ... to the option, and hence for each S, t one of (18.1) and (18.2) is at equality. (18 .3) The three components (18.1), (18.2) and (18 .3) are the key features in the the- ory of...

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 ... this case (20.4) produced σ  = 0 .36 10 with a 95% confidence interval of [0 .32 63, 0 .39 57]. We found that a M =−4.0 × 10 3 and the estimate (20.10) gave σ  = 0 .36 21. Overall, t...

Ngày tải lên: 21/06/2014, 09:20

... widths 10 2 [0.0878, 0 .32 19] [0.1 239 , 0 .30 61] 1 .3 10 3 [0.2285, 0 .33 33] [0.2 238 , 0.2 936 ] 1.5 10 4 [0.24 43, 0.2764] [0. 237 0, 0.2580] 1.5 10 5 [0. 235 9, 0.2458] [0. 237 3, 0.2440] 1.5 21.10 Program of ... correspond to asset price.) In the case L = π with g(x) = sin(x), a(t) = b(t) = 0, ( 23. 5) it is easy to verify that u(x, t) = e −t sin(x) ( 23. 6) solves ( 23. 2), (...

Ngày tải lên: 21/06/2014, 09:20

... form ( 23. 9). 23. 4.  Verify that BTCS, ( 23. 10), may be written in the form ( 23. 11). 23. 5.  Using Table 23. 1, show that the local accuracy of BTCS, defined in ( 23. 15), satisfies ( 23. 16). 23. 6. By ... methods 0 5 10 15 0 50 100 150 200 0 0.2 0.4 0.6 0.8 1 x FTCS: ν = 0 .3 t Fig. 23. 4. FTCS solution on the heat equation ( 23. 2), ( 23. 3) and ( 23. 4) with initial and bound...

Ngày tải lên: 20/06/2014, 18:20

... Company, The, 70 pseudo-random numbers, 33 34 , 40, 43, 48, 63, 64, 88, 141, 145, 148, 205, 218, 219, 225, 230 , 231 put–call parity, 13 14, 17, 83, 102, 131 cash-or-nothing, 165, 169 put–call supersymmetry, ... 111 quadratic convergence, 125 quadrature method, 232 quantile, 36 quantile–quantile plot, 37 , 38 , 48 quasi Monte Carlo, 233 random number generators, 33 see also pseudo-r...

Ngày tải lên: 20/06/2014, 18:20