An Introduction to Financial Option Valuation 1 potx
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_13 pot
... derivatives in (24 .10 ) leads to the finite difference formula W i +1 j − W i j k + 1 2 σ 2 W i +1 j +1 − 2W i +1 j + W i +1 j 1 h 2 + (r − 1 2 σ 2 ) W i +1 j +1 − W i +1 j 1 2h = 0. (24 .11 ) Setting h 2 = ... eliminating the W i +1 j terms in (24 .11 ), and the formula then reduces to W i j = p W i +1 j +1 + (1 − p )W i +1 j 1 , (24 .12 ) where p = 1...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_14 pot
... neutrality, 11 5, 11 8 12 0, 14 4, 14 6, 15 1, 15 4, 16 3, 16 7, 18 0, 18 1, 19 4, 232 cash-or-nothing, 16 7 16 8 sample mean, 34, 48, 64, 14 1, 14 6, 204, 215 sample variance, 34, 48 SDE, see stochastic differential ... Carlo method, 14 1 14 8, 215 –224, 229–232 for American put, 18 0 18 2 for exotics, 19 4 19 6 for Greeks, 14 5 14 8 Index 273 New York Stock Exchange, 6, 5...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_1 pot
... formulas 10 5 11 .1 Motivation 10 5 11 .2 Where is µ? 10 5 11 .3 Time dependency 10 6 11 .4 The big picture 10 6 11 .5 Change of variables 10 8 11 .6 Notes and references 11 1 11 .7 Program of Chapter 11 and walkthrough ... walkthrough 11 1 12 Risk neutrality 11 5 12 .1 Motivation 11 5 12 .2 Expected payoff 11 5 12 .3 Risk neutrality 11 6 12 .4 Notes and references...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_3 pptx
... DENNEY AND STEVEN GAINES (Denney and Gaines, 2000) 36 Computer simulation 0 0.5 1 0 0.5 1 1.5 10 00 samples 0 0.5 1 0 0.5 1 1.5 10 000 samples 0 0.5 1 0 0.5 1 1.5 10 0000 samples 0 0.5 1 0 0.5 1 1.5 10 00000 ... samples and N(0 ,1) quantiles 1 0 1 2 1 −0.5 0 0.5 1 1.5 2 U(0 ,1) samples and U(0 ,1) quantiles Fig. 4.4. Quantile–quantile plots using M = 10 0 samples...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_4 ppt
... small, then e 1. 96σ √ t+(µ− 1 2 σ 2 )t ≈ e 1. 96σ √ t ≈ 1 − 1. 96σ √ t and e 1. 96σ √ t+(µ− 1 2 σ 2 )t ≈ e 1. 96σ √ t ≈ 1 + 1. 96σ √ t. So the confidence interval is approximately [S 0 (1 − 1. 96σ √ t), S 0 (1 ... Part II 0 0.5 1 1.5 2 2.5 3 0.9 1 1 .1 1.2 1. 3 1. 4 1. 5 Discrete asset path t i S i Fig. 7 .1. Discrete asset path of the form (7 .1) . Discrete points...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_5 ppt
... = 1, if x > 0, 0, if x = 0, 1, if x < 0. 7.4 Notes and references 69 0 0 .1 0.2 0.3 0.4 0.5 0.6 0.8 1 1.2 1. 4 1. 6 d t = 5 × 10 −3 d t = 5 × 10 −4 Asset paths 0 0 .1 0.2 0.3 0.4 ... (Bj ¨ ork, 19 98; Duffie, 20 01; Karatzas and Shreve, 19 98; Nielsen, 19 99; Øksendal, 19 98). It is possible to weaken the boundary conditions (8 .17 ) and (8 .18 ) in the Blac...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_7 pdf
... zlabel(’C(S,t)’) Fig. 11 .6. Program of Chapter 11 : ch 11. m. PROGRAMMING EXERCISES P 11. 1. Edit ch 11. m so that it applies to a European put option, as in Figure 11 .4. P 11. 2. Edit ch 11. m so that it applies to the ... this model, you had these numbers, 11 .7 Program of Chapter 11 and walkthrough 11 1 11 .6 Notes and references Colour versions of Figures 11 .3, 11 .4 and...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_8 pptx
... EXERCISES P15 .1. Adapt ch15 to produce a picture like that in Figure 15 .2. P15.2. Adapt ch15 to produce an estimate of the delta. 15 .2 Monte Carlo 14 3 10 1 10 2 10 3 10 4 10 5 10 6 10 0 .1 10 0.2 10 0.3 10 0.4 Num ... Black–Scholes formula. 14 .5 Implied volatility with real data 13 5 0 0.5 1 1.5 2 2.2 2.4 2.6 2.8 σ C( σ) starting value iterates 0 2 4 6 8 1...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_9 pot
... Ae −r(T−t) . (17 .10 ) 17 .2. Show that C cash (S, t) in (17 .4) satisfies (17 .1) , (17 .2) and (17 .3). 17 .3. Differentiate (17 .4) to establish (17 .5), (17 .6) and (17 .7). 17 .4. Using (17 .4) and (17 .10 ), ... practice 15 5 Table 16 .1. European put value approximations from binomial method Option value M = 10 0 1. 4 716 M = 200 1. 4762 M = 400 1. 4726 Black–Scho...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_1 doc
... Puts Option Oct Nov Dec Oct Nov Dec Royal Bk Scot. 16 00 67.092.5 10 9.529.049.062.5 (16 34.0) 17 00 19 .543.559.082.0 10 0.0 11 2.5 The number 16 34.0isthe closing price of The Royal Bank of Scotland’s ... gained an amount S(t 1 ) at time t = t 1 from the short sale, (b) paid out an amount S(t 2 ) at time t = t 2 from the buy back. 1. 6 Notes and references 7 30 40 50 60 7...
Ngày tải lên: 21/06/2014, 07:20