introduction to financial econometrics
Introduction to Financial Econometrics Hypothesis Testing in the Market Model
... of δ is found to be statistically greater than zero we might then want to go on to test the hypothesis that the up market beta is greater than one Since the up market beta is equal to β + δ this ... whereas if it is less than the data are in support of the null hypothesis1 To determine how big | tα=0 | needs to be to reject the null, we use the fact that under the statistical assumptions ... over time it is of interest to know if α and β change over time To illustrate, suppose we have a ten year sample of monthly data (T = 120) on returns that we split into two five year subsamples...
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Mathematics for Finance: An Introduction to Financial Engineering docx
... called the forward price An investor who agrees to buy the asset is said to enter into a long forward contract or to take a long forward position If an investor agrees to sell the asset, we speak ... resources to fulfil the resulting obligations and, in particular, to close the short position in risky assets, that is, to repurchase the stock and return it to the owner Similarly, the investor must ... return KS on stock will be 25% if stock goes up, or 5% if stock goes down (Observe that both stock prices at time happen to be higher than that at time 0; ‘going up’ or ‘down’ is relative to the other...
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springer, mathematics for finance - an introduction to financial engineering [2004 isbn1852333308]
... called the forward price An investor who agrees to buy the asset is said to enter into a long forward contract or to take a long forward position If an investor agrees to sell the asset, we speak ... resources to fulfil the resulting obligations and, in particular, to close the short position in risky assets, that is, to repurchase the stock and return it to the owner Similarly, the investor must ... return KS on stock will be 25% if stock goes up, or 5% if stock goes down (Observe that both stock prices at time happen to be higher than that at time 0; ‘going up’ or ‘down’ is relative to the other...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_13 pot
... + U ij−1 h2 = It is convenient to write this as a process that goes from time level i to i + 1, that is, to increase the time index by 1, which allows the method to be written U i+1 = U ij + ν ... at the top and bottom, corresponding to those zero boundary conditions PROGRAMMING EXERCISES P23.1 Using colon subarray notation, as in ch16, or otherwise, alter ch23 so that FTCS is used Toy with ... Chapter 23, it is possible to convert the Black–Scholes PDE for European calls and puts into the heat equation form (23.2) Hence, it is perfectly reasonable to convert to that form before applying...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_14 pot
... Biology, Princeton, NJ: Princeton University Press Duffie, Darrell (2001) Dynamic Asset Pricing Theory, 3rd edn Princeton, NJ: Princeton University Press Elder, Alexander (2002) Come into My Trading ... Columbia, New York Bass, Thomas A (1999) The Predictors London: Penguin Baxter, Martin and Andrew Rennie (1996) Financial Calculus: An Introduction to Derivative Pricing Cambridge: Cambridge University ... matrix–vector form Confirm that the transformations given in Section 24.4 convert (8.15) to (24.10) Suppose that a constant diffusion coefficient, σ , is introduced into the heat equation (23.2) to give...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_1 pot
... intentionally left blank AN INTRODUCTION TO FINANCIAL OPTION VALUATION Mathematics, Stochastics and Computation This is a lively textbook providing a solid introduction to financial option valuation ... Mathematics for his research contributions to a broad range of problems in numerical analysis AN INTRODUCTION TO FINANCIAL OPTION VALUATION Mathematics, Stochastics and Computation DESMOND J HIGHAM ... helped to shape my views on how to present this material to a wide audience MATLAB programs I firmly believe that the best way to check your understanding of a computational algorithm is to examine,...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_3 pptx
... the density function Note that the powering operator, ^, and the division operator, /, are preceded by full stops This notation allows MATLAB to work directly on arrays by interpreting the commands ... can more quickly progress to the topics that are central to this book 33 34 Computer simulation Table 4.1 Ten pseudo-random numbers from a U(0, 1) and an N(0, 1) generator U(0, 1) N(0, 1) 0.3929 ... built-in functions 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)...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_4 ppt
... familiar to anybody who has seen stock market data displayed in graphical form To examine this data, it is reasonable to treat it on the same level as the output from a pseudo-random number generator ... involved his job The deal amounted to £300m rather than £3m and flashed across stock market screens just as the stock market was about to close, causing a precipitous fall in the Footsie, the barometer ... the information 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 random ‘fluctuation’ increment to the interest rate...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_5 ppt
... would predict One approach is to allow the volatility to be stochastic, see (Duffie, 2001; Hull, 2000; Hull and White, 1987), for example Another is to allow the asset to undergo ‘jumps’, see (Duffie, ... be able to transform this knowledge into money Finance is consistent in its ability to build good models and consistent in its inability to make easy money The purpose of the model is to understand ... approach is to abandon any attempt to understand the processes that drive asset prices (in particular to pay no heed to the efficient market hypothesis) and instead to test as many models as possible...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_7 pdf
... xb − xa < ε then stop Use (xa + xb ) as the approximation to x Otherwise return to Step Note that we must choose a value ε > for our stopping criterion xb − xa < ε It is easy to see that the value ... the iterates are close to an x and then switches to Newton’s method to get the benefit of rapid convergence Also, the residual |F(xn )| gives a measure of how close xn is to a solution, and this ... can be incorporated into the stopping criterion Furthermore, although we have considered only a single nonlinear equation, it is possible to generalize Newton’s method to the case of many equations...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_8 pptx
... pseudo-random number generators to compute estimates of expected values was touched on in Chapter Here we pull these two threads together and introduce the Monte Carlo approach to valuing an option ... volatility is the wrong number to put in the wrong formula to obtain the right price RICCARDO REBONATO It is the strong opinion of the author that most traders (Rebonato, 1999) 14.7 Program of Chapter ... 14.1 Newton’s method for the implied volatility Upper picture: iterates Lower picture: errors σ = 0.15 in order to compute the Black–Scholes value for C, and then applied Newton’s method to see...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_9 pot
... superimposed To emphasize that large deltas can arise, we chose an asset that stumbles towards the strike price E near expiry The ‘near infinite’ deltas close to expiry are too much for the plotter to handle ... approximations appear to converge as M increases, the convergence is by no means monotonic – taking a slightly bigger M may worsen the error – and there is a general ‘sawtooth’ pattern to the sequence ... 1996; Rogers and Stapleton, 1998) give explanations for the effect and propose fixes Applying the binomial method may be shown to be equivalent to using a finite difference method to approximate the...
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An Introduction to Financial Option Valuation_1 potx
... the density function Note that the powering operator, ^, and the division operator, /, are preceded by full stops This notation allows MATLAB to work directly on arrays by interpreting the commands ... can more quickly progress to the topics that are central to this book 33 34 Computer simulation Table 4.1 Ten pseudo-random numbers from a U(0, 1) and an N(0, 1) generator U(0, 1) N(0, 1) 0.3929 ... built-in functions 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)...
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An Introduction to Financial Option Valuation_2 potx
... familiar to anybody who has seen stock market data displayed in graphical form To examine this data, it is reasonable to treat it on the same level as the output from a pseudo-random number generator ... involved his job The deal amounted to £300m rather than £3m and flashed across stock market screens just as the stock market was about to close, causing a precipitous fall in the Footsie, the barometer ... the information 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 random ‘fluctuation’ increment to the interest rate...
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An Introduction to Financial Option Valuation_4 pot
... is possible to simulate an asset path and implement discrete hedging To write down the resulting algorithm, we use {ξi } to denote samples from an N(0, 1) pseudo-random number generator that are ... out-of-the-money close to expiry then the payoff is very likely to be zero whatever happens to the asset – there is no risk, so we should not be holding any asset The analogous results to (9.7) for a ... The fund used leverage – investing borrowed money – to scale up these tiny margins into large profits One commentator likened their trades to ‘picking up nickels in front of bulldozers’ (Lowenstein,...
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An Introduction to Financial Option Valuation_6 ppt
... pseudo-random number generators to compute estimates of expected values was touched on in Chapter Here we pull these two threads together and introduce the Monte Carlo approach to valuing an option ... volatility is the wrong number to put in the wrong formula to obtain the right price RICCARDO REBONATO It is the strong opinion of the author that most traders (Rebonato, 1999) 14.7 Program of Chapter ... 14.1 Newton’s method for the implied volatility Upper picture: iterates Lower picture: errors σ = 0.15 in order to compute the Black–Scholes value for C, and then applied Newton’s method to see...
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An Introduction to Financial Option Valuation_8 pdf
... S is large, since there would be no payoff, it cannot be worthwhile to exercise an American put; it is optimal to hold on to the option On the other hand, in the limit S → 0, the payoff from ... is optimal to exercise Interpolating between these two extremes, we might expect there to be a well-defined optimal exercise boundary, S (t), such that • for S(t) < S (t) it is optimal to exercise, ... may be expressed as P Am (S0 , 0) = sup E e−r τ (S(τ )) , 0≤τ ≤T (18.8) where τ is a stopping time To define a stopping time precisely requires technicalities that have not been developed in this...
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An Introduction to Financial Option Valuation_9 doc
... involved may not be properly understood even by the most sophisticated of investors Some of these instruments appear to be specifically designed to enable institutions to take gambles which they would ... 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 months’ time, take six months of historical data There is ... proportional to M This makes it an expensive business to improve the approximation by taking more samples To get an extra digit of accuracy, that is, to shrink a confidence interval by a factor of 10,...
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An Introduction to Financial Option Valuation_11 pdf
... + U ij−1 h2 = It is convenient to write this as a process that goes from time level i to i + 1, that is, to increase the time index by 1, which allows the method to be written U i+1 = U ij + ν ... at the top and bottom, corresponding to those zero boundary conditions PROGRAMMING EXERCISES P23.1 Using colon subarray notation, as in ch16, or otherwise, alter ch23 so that FTCS is used Toy with ... Chapter 23, it is possible to convert the Black–Scholes PDE for European calls and puts into the heat equation form (23.2) Hence, it is perfectly reasonable to convert to that form before applying...
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An Introduction to Financial Option Valuation_12 pptx
... Biology, Princeton, NJ: Princeton University Press Duffie, Darrell (2001) Dynamic Asset Pricing Theory, 3rd edn Princeton, NJ: Princeton University Press Elder, Alexander (2002) Come into My Trading ... Columbia, New York Bass, Thomas A (1999) The Predictors London: Penguin Baxter, Martin and Andrew Rennie (1996) Financial Calculus: An Introduction to Derivative Pricing Cambridge: Cambridge University ... matrix–vector form Confirm that the transformations given in Section 24.4 convert (8.15) to (24.10) Suppose that a constant diffusion coefficient, σ , is introduced into the heat equation (23.2) to give...
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