An Introduction to Financial Option Valuation_2 potx

... 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 25...

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...

Ngày tải lên: 20/06/2014, 18:20

... The 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 ... Upper and lower bounds on option values 14 2.7 Notes and references 16 2.8 Program of Chapter 2 and walkthrough 17 3 Random variables 21 3.1 Motivation 21 3.2 Rando...

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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...

Ngày tải lên: 20/06/2014, 18:20

... 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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... 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 ... is to scale the option values by the asset price, by letting c := C S , for a call option, and p := P S , for a put option. In these new variables, d 1 and d 2 in (8.20) and (...

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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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... 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 time t, and use (S(t)) ... 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 Eur...

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... sample means and variances approach the true values 0 and 1. A more enlightening approach to testing a random number generator is to divide the x-axis into subintervals, or bins,oflength x and count ... 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 random...

Ngày tải lên: 21/06/2014, 04:20

... movement The book (Lo and MacKinlay, 1999) is a good source of practical information for stock market data analysis. Many exchanges have informative websites, including the American Stock Exchange: www.amex.com/, ... Stock Exchange: www.amex.com/, the Chicago Board Options Exchange: www. cboe.com/Home/, the London Stock Exchange: www.londonstockexchange. com/, the New York Stock Exchange: www...

Ngày tải lên: 21/06/2014, 04:20

... of us to carry out hedging. On one side there is a large group of investors who view options as an excellent means to alleviate their exposure to risk, and another large group who see options ... rapidly, the Fed managed to persuade a consortium of major banks and in- vestment houses to bail out LTCM in order to prevent the very real possibility of a total meltdown of the financi...

Ngày tải lên: 21/06/2014, 04:20

... two threads together and introduce the Monte Carlo approach to valuing an option. As we will see in Chapter 19, this provides a powerful means to compute option values in cases where no analytical ... showed that valuing an option can be regarded as computing an ex- pected value. The idea of using pseudo-random number generators to compute estimates of expected values was to...

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... 19.6. 19.5 Bermudan and shout options A Bermudan option differs from the corresponding American option in only one respect. While the American option allows the holder to exercise at any time in [0, ... deals with points (i) and (iii). 180 American options 18.6 Monte Carlo for an American put We have seen that the binomial method has a natural extension from European to American o...

Ngày tải lên: 21/06/2014, 04:20

... 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 ... important aspects of practical option valuation, and it remains an active research topic, see (Poon and Granger, 2003), for example. More sophisticated time-varying volatility m...

Ngày tải lên: 21/06/2014, 04:20