Financial calculus Introduction to Financial Option Valuation 4 pptx

Financial calculus Introduction to Financial Option Valuation_2 pdf

... 500.10.20.30 .4 IBM DailyHistogram−50 500.51Cumulative Density−50 5 4 −202 4 Quantiles−50 500.10.20.30 .4 IBM Weekly−5 0 500.51−50 5 4 −202 4 −50 500.10.20.30 .4 Rand. ... Chapter 4 and walkthrough 43 PROGRAMMING EXERCISESP4.1. Adapt ch 04. m to the case where ξiin (4. 7) are from the exponential distri-bution with parameter λ = 1. [Hint: make use of Exercise 3 .4 and ... ch05 shows one way to compute a quantile–quantile plot, as seen in Figures 4. 4, 4. 6 and5.3. It is listed in Figure 5 .4. We use MATLAB’s N(0, 1) pseudo-random number generator, randn.The line...

22
1,402
0

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 ... RITCHIE, option trader, source (Bass, 1999) 74 Black–Scholes PDE and formulasThe key idea in this chapter is hedging to eliminate risk.Toreinforce the idea,and emphasize that it is a concrete tool ... 0.50.60.811.21 .4 1.6dt = 5 × 10−3dt = 5 × 10 4 Asset paths0 0.1 0.2 0.3 0 .4 0.500.010.020.030. 04 0.05Sum-of-square returnsσ2/2 σ2/2σ2/20 0.1 0.2 0.3 0 .4 0.50.80.911.1Asset...

Financial calculus Introduction to Financial Option Valuation_4 pptx

... 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50123Asset pathE0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 500.51Delta0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.511.52Cash0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 511.52PortfolioFig. ... hedging0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50123Asset pathE0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 500.51Delta0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5012Cash0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 511.52PortfolioFig. ... 0.2586Cvega = 0. 647 0P=0 .49 53Pdelta = -0. 741 4Pvega = 0. 647 0PROGRAMMING EXERCISESP10.1. Adapt function ch10.m to return more Greeks.P10.2. Investigate the use of MATLAB’s symbolic toolbox to conﬁrm...

Financial calculus Introduction to Financial Option Valuation_5 doc

... to the default with format.Output from ch13 isNewton error1. 546 5e-018.3622e-032 .49 64e-052.2279e-101.1102e-16This 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 eliminate risk.(ii) ... possible, for exam-ple, to design a hybrid algorithm that uses a safe method, like bisection, untilthe iterates are close to an xand then switches to Newton’s method to get thebeneﬁt of rapid...

Financial calculus Introduction to Financial Option Valuation_6 ppt

... abs(increment);endsigmaFig. 14. 3. Program of Chapter 14: ch 14. m.PROGRAMMING EXERCISESP 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 108samples, and to reduce it to 10−6would takeof the order of 1012samples; see Exercise 15 .4. ♦15.3 Monte Carlo for option ... form∂2C∂σ2=T − t 4 3(σ 4 − σ 4 )∂C∂σ, ( 14. 6)see Exercise 14. 2. The identity ( 14. 6) shows us that C(σ ) is convex for σ<σand concave for σ>σ. This will allow us to get a globally...

Financial calculus Introduction to Financial Option Valuation_8 potx

... 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 200123 4 5678910t=T /4 SAmerican put valueFig. 18.3. Value PAm(S, T /4) for ... = 10−2t = 10−3t = 10 4 M = 102[0. 046 9, 0.1671] [0.0397, 0.1387] [0.0569, 0.1813]M = 103[0.0961, 0.1 347 ] [0.0756, 0.11 04] [0.0726, 0.1 046 ]M = 10 4 [0.1 042 , 0.1163] [0.0997, 0.1112] ... applied to any of the generalized path-dependent options men-tioned in Sections 19.2, 19.3, 19 .4. 196 Exotic optionsThe binomial method does not naturally extend to path-dependent options,...

Financial calculus Introduction to Financial Option Valuation_9 potx

... σis computed in order to value an option, then a widely quoted rule ofthumb 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 20920 40 60 80 100 120 140 160 18000.20 .4 0.60.81DaysVolDaily20 40 60 80 100 120 140 160 180 20000.20 .4 0.60.81WeeksVolWeeklyFig. 20.1. Historical volatility estimates ... reduction. One way to summarize the potentialadvantage is:215212 Historical volatility0 200 40 0 600 800 1000 1200 140 0 1600 1800 200000.050.10.150.20.250.30.350 .4 0 .45 0.5tVolatilityFig....

Financial calculus Introduction to Financial Option Valuation_10 ppt

... of widths102[0.8 247 , 1.2819] [0.9518, 1.6767] 0.6103[0.9713, 1.15 74] [1.0166, 1.1 244 ] 1.710 4 [0.9 647 , 1.0137] [0.9 945 , 1.0 243 ] 1.6105[0.9953, 1.0115] [0.9955, 1.0 046 ] 1.821.7 Multivariate ... widths102[1.8 841 , 2.0752] [1.9601, 2.0031] 4. 4103[1.9538, 2.0087] [1.9951, 2.00 84] 4. 110 4 [1.9890, 2.0062] [1.99 94, 2.0036] 4. 1105[1.9969, 2.0023] [1.9993, 2.0006] 4. 1Table 22.2. Ninety-ﬁve ... 0.3061] 1.3103[0.2285, 0.3333] [0.2238, 0.2936] 1.510 4 [0. 244 3, 0.27 64] [0.2370, 0.2580] 1.5105[0.2359, 0. 245 8] [0.2373, 0. 244 0] 1.521.10 Program of Chapter 21 and walkthrough 22521.9...

An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_13 pot

... data ( 24. 2) or ( 24. 3) and the boundary values Vi0and ViNxfor all 1 ≤ i ≤ Ntspeciﬁed 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 05101502 4 681000.20 .4 0.60.81xBTCS: ν = 6.6tFig. 23.7. BTCS solution on the heat equation (23.2), (23.3) and (23 .4) ... differences to option valuation. We saw in Chapter 18 that the problem of valuing an American option can becouched in terms of a linear complementarity problem. It is possible to develop 24. 2 FTCS,...

An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_14 pot

... neutrality, 115, 118–120, 144 , 146 , 151, 1 54, 163,167, 180, 181, 1 94, 232cash-or-nothing, 167–168sample mean, 34, 48 , 64, 141 , 146 ,2 04, 215sample variance, 34, 48 SDE, see stochastic differential ... 265instability, 243 local accuracy, 246 – 247 , 249 , 251, 252penalty method, 263stencil, 242 , 244 , 249 upwind, 262von Neumann stability, 247 – 249 , 251, 252, 260,265finite difference operator, 237–238, 240 , ... hypothesis, 45 46 , 49 , 51, 52, 54, 61,70, 72error bar, 143 error function, 41 inverse, 41 European call option, 163definition, 1delta, 87European put option definition, 2delta, 87European-style option, ...

Xem thêm