An Introduction to Financial Option Valuation Mathematics Stochastics and Computation 11 doc

... in the matrix–vector forms (23.9) and (23 .11) , and the Crank–Nicolson method is given by (24.8). The τ = 0 condition (19.2) specifies V 0 j = max(B + jh − E, 0) and the left-hand boundary condition ... problem of valuing an American option can be couched in terms of a linear complementarity problem. It is possible to develop 24.2 FTCS, BTCS and Crank–Nicolson for Black–Scholes...

Ngày tải lên: 20/06/2014, 18:20

... G. and E. J. Stapleton (1998) Fast accurate binomial pricing of options. Finance and Stochastics, 2:3–17. Rogers, L. C. G. and O. Zane (1999) Saddle-point approximations to option prices. Annals ... Economic Dynamics and Control, 21:1267–1321. Broadie, Mark and Paul Glasserman (1998) Introduction to Chapter III: Volatility and correlation. In Mark Broadie and Paul Glass...

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... 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 ... picture 106 11. 5 Change of variables 108 11. 6 Notes and references 111 11. 7 Program of Chapter 11 and walkthrough 111 12 Risk neutrality 115 12.1 Motivati...

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... 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 normal distributions • ... by i.i.d. random variables and hence the overall effect can be reasonably modelled by a single normal random vari- able with an appropriate mean and variance. This is why normal ran...

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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 rate...

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... 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 no heed to the efficient ... 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...

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... this model, you had these numbers, 11. 7 Program of Chapter 11 and walkthrough 111 11. 6 Notes and references Colour versions of Figures 11. 3, 11. 4 and 11. 5 can be downloaded from this book’s website, ... 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 quot...

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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 ... highly relevant is (Hammersley and Handscombe, 1964), whilst a short and very accessible modern perspective is given by (Madras, 2002). Monte Carlo, pseudo-random number generatio...

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... the Black–Scholes analysis, places analytic formulas out of reach, and puts a strain on computational methods. 18.2 American call and put An American option is like a European option except that ... 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 S and...

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... 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