An Introduction to Financial Option Valuation Mathematics Stochastics and Computation 4 docx

... 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 (23.2), (23.3) and (23 .4) ... 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 vers...

Ngày tải lên: 20/06/2014, 18:20

... 60 true random numbers, 40 unbiased, 142 , 148 uniform distribution, 22, 24, 28 up -and- in call, 190, 223 up -and- in put, 190 up -and- out call, 190, 1 94, 195, 197 up -and- out put, 190 variance, 24, 142 variance ... 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, 3...

Ngày tải lên: 20/06/2014, 18:20

... MathWorks, Inc. AN INTRODUCTION TO FINANCIAL OPTION VALUATION Mathematics, Stochastics and Computation This is a lively textbook providing a solid introduction to financial option valuation for ... Chapter 24 and walkthrough 265 References 267 Index 271 viii Contents 4 Computer simulation 33 4. 1 Motivation 33 4. 2 Pseudo-random numbers 33 4. 3 Statistical te...

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... rand and randn to generate U(0, 1) and N(0, 1) samples, respectively. To make the experiments reproducible, we set the random number generator seed to 100; that is, we used rand(‘state’,100) and ... samples from N(0, 1) and U(0, 1) random number generators. 3 Random variables OUTLINE • discrete and continuous random variables • expected value and variance • uniform and nor...

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... way to compute a quantile–quantile plot, as seen in Figures 4. 4, 4. 6 and 5.3. It is listed in Figure 5 .4. We use MATLAB’s N(0, 1) pseudo-random number generator, randn. The line samples = randn(M,1), ... known to investors, and hence any change in the price is due to new information. We may build this into our model by adding a ran- dom ‘fluctuation’ increment to the interest...

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... the company and has many insights into the practical issues involved in collecting and analysing vast amounts of financial data. EXERCISES 7.1. Confirm the results (7 .4) and (7.5). 7.2.  By analogy ... see (Rogers and Zane, 1999), for example. A completely different approach is to abandon any attempt to understand the processes that drive asset prices (in particular to pay n...

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... problem and it is marvelously intuitive. MARK P. KRITZMAN (Kritzman, 2000) To put it simply, if there is an arbitrage price, any other price is too dangerous to quote. MARTIN BAXTER AND ANDREW ... prices, and counting the proportion that are in-the-money. P12.2. Investigate the use of quad and quadl for evaluating integrals of the form (12 .4) . 12 .4 Notes and references 119...

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... a and variance var(X) = b 2 are not known. Suppose • we are interested in computing an approximation to a (and possibly b), and • we are able to take independent samples of X using a pseudo-random ... From ( 14. 1) and ( 14. 2), values of C(σ ) must lie between max(0, S − Ee −r(T −t) ) and S.Itfollows that C(σ ) = C  has a solution if and only if max(S − Ee −r(T −t) , 0) ≤ C...

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... 250 1 .46 1 .48 1.5 1.52 M European put 200 220 240 260 280 300 320 340 360 380 40 0 1 .47 2 1 .47 3 1 .47 4 1 .47 5 1 .47 6 1 .47 7 M European put Fig. 16.2. Convergence of the binomial method for a European ... Chapter 8 that led to the Black–Scholes PDE can be adapted to cover an American put option. We write P Am (S, t) to denote the American put option value at asset price...

Ngày tải lên: 20/06/2014, 18:20

... arguments to those above can be used to obtain simple upper and lower bounds on the values C and P of European call and put options. To study the call option, consider two portfolios: π A : one call option ... than π B at time 0 then it would be possible to sell π A (that is, sell the call option and borrow the cash) and buy π B (that is, buy one put option and one...

Ngày tải lên: 21/06/2014, 07:20