an introduction to financial markets business finance and portfolio management

... risk management specialists and auditors and middle-office staff who monitor and measure risks and exposures and profits; f information technology professionals who develop and manage the bank’s ... of Equity, FX and Interest-rate Options Riccardo Rebonato Risk Managem ent and Analy sis vol 1: Measuring and Modelling Financial R isk Carol Alexander (ed.) R isk Managem ent and Analy sis vol ... issuers and the investors, and the role of the banks in bringing issues to the market and in trading bonds Investors and traders in bonds have to understand how the securities are priced and how...

Ngày tải lên: 31/03/2017, 09:51

... Theory G Smith and O Tabachnikova Topologies and Uniformities I.M James Vector Calculus P.C Matthews Marek Capi´ ski and Tomasz Zastawniak n Mathematics for Finance An Introduction to Financial Engineering ... Jones and J.M Jones Introduction to Laplace Transforms and Fourier Series P.P.G Dyke Introduction to Ring Theory P.M Cohn Introductory Mathematics: Algebra and Analysis G Smith Linear Functional Analysis ... hand, and Markowitz portfolio optimisation and the Capital Asset Pricing Model on the other hand Models based on the principle of no arbitrage can also be developed to study interest rates and...

Ngày tải lên: 22/03/2014, 09:20

... Theory G Smith and O Tabachnikova Topologies and Uniformities I.M James Vector Calculus P.C Matthews Marek Capi´ ski and Tomasz Zastawniak n Mathematics for Finance An Introduction to Financial Engineering ... Jones and J.M Jones Introduction to Laplace Transforms and Fourier Series P.P.G Dyke Introduction to Ring Theory P.M Cohn Introductory Mathematics: Algebra and Analysis G Smith Linear Functional Analysis ... hand, and Markowitz portfolio optimisation and the Capital Asset Pricing Model on the other hand Models based on the principle of no arbitrage can also be developed to study interest rates and...

Ngày tải lên: 08/05/2014, 10:07

... = 50 and Nt = 500, so k = × 10−3 and h = 0.2, we found that err0 = 1.5 × 10−3 for FTCS and err0 = 1.7 × 10−3 for BTCS With Crank– Nicolson we were able to reduce Nt to 50, so k = × 10−2 , and ... written in the matrix–vector forms (23.9) and (23.11), and the Crank–Nicolson method is given by (24.8) The τ = condition (19.2) specifies V j0 = max(B + j h − E, 0) and the left-hand boundary condition ... accuracy expansions (23.14) and (23.16) causes the O(k) term to vanish.) 23.10 Program of Chapter 23 and walkthrough The program ch23 implements BTCS for the heat equation (23.2) with initial and boundary...

Ngày tải lên: 20/06/2014, 18:20

... American options Mathematical Finance, 12:271–286 Rogers, L C 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) ... Hodder & Stoughton Lo, Andrew W and Craig MacKinlay (1999) A Non-Random Walk Down Wall Street Princeton, NJ: Princeton University Press Longstaff, F A and E S Schwartz (2001) Valuing American options ... Black–Scholes model: a note Journal of Finance, 38:227–230 Mantegna, Rosario N and H Eugene Stanley (2000) An Introduction to Econophysics: Correlations and Complexity in Finance Cambridge: Cambridge University...

Ngày tải lên: 20/06/2014, 18:20

... 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 ... accompanying stand-alone MATLAB code listing to illustrate a key idea The author has made heavy use of figures and examples, and has included computations based on real stock market data Solutions to ... parity 2.6 Upper and lower bounds on option values 2.7 Notes and references 2.8 Program of Chapter and walkthrough 11 11 11 12 13 13 14 16 17 Random variables 3.1 Motivation 3.2 Random variables,...

Ngày tải lên: 20/06/2014, 18:20

... 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 ... pseudo-random numbers Our justification for this omission is that random number generation is a highly advanced, active, research topic and it is unreasonable to expect non-experts to understand and ... samples and N(0,1) quantiles N(0,1) samples and U(0,1) quantiles 5 0 −5 −5 −5 −5 U(0,1) samples and N(0,1) quantiles U(0,1) samples and U(0,1) quantiles 1.5 0.5 −0.5 −5 −5 −1 −1 Fig 4.4 Quantile–quantile...

Ngày tải lên: 20/06/2014, 18:20

... 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 equation and making ... 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), ... www.maths.warwick.ac.uk/wiberg/MathFinance/ to manipulate and display real stock market data 5.6 Program of Chapter and walkthrough 51 %CH05 Program for Chapter % % Illustrates quantile plot clf randn(’state’,100) M...

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 7.2 Confirm the results (7.4) and (7.5) By analogy ... 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...

Ngày tải lên: 20/06/2014, 18:20

... for a put option and In these new variables, d1 and d2 in (8.20) and (8.21) simplify to d1 = m τ + τ and d2 = m τ − , τ (11.1) and, from (8.19) and (8.24), the re-scaled call and put values become ... added in the left-hand plot 13.6 Notes and references 127 x0 = and stopped when |xn+1 − xn | < 10−5 We see that only iterations were required to produce an error of around 10−12 , and the error ... points to make (i) Formulas (12.2) and (12.4) were derived without any reference to the idea of hedging to eliminate risk (ii) Formulas (12.2) and (12.4) were derived without any reference to the...

Ngày tải lên: 20/06/2014, 18:20

... number, not a random variable, so p is either in I or outside it, and it is meaningless to speak of the probability of p lying in I (the Bayesians, on the other hand, consider p a random variable ... Notes and references There are many texts that discuss general Monte Carlo simulation A ‘golden oldie’ that is still highly relevant is (Hammersley and Handscombe, 1964), whilst a short and very ... introduce another computational approach The binomial method is straightforward to describe and implement, and, as we will see in Chapters 18 and 19, has the advantage that it is readily adapted to...

Ngày tải lên: 20/06/2014, 18:20

... (16.10) has zero mean and unit variance, we recover the continuous asset price model in the limit δt → Set µ = r and p = and show that requiring E(Yi ) = and var(Yi ) = in (16.10) leads to √ √ u = + ... reach, and puts a strain on computational methods 18.2 American call and put An American option is like a European option except that the holder may exercise at any time between the start date and ... as depicted in Figures 16.2 and 16.3, have been widely reported The references (Leisen and Reimer, 1996; Rogers and Stapleton, 1998) give explanations for the effect and propose fixes Applying the...

Ngày tải lên: 20/06/2014, 18:20

... including • what range of expiry dates and exercise prices are typically offered, • how dividends and stock splits are dealt with, and • how money and products actually change hands Section 5.5 ... Similar 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 ... than π B at time 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 share) This brings us an instantaneous...

Ngày tải lên: 21/06/2014, 07:20

... 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 7.2 Confirm the results (7.4) and (7.5) By analogy ... 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...

Ngày tải lên: 21/06/2014, 07:20

... 191 Up and out European Call value E B S Fig 19.3 Time-zero up -and- out call value (19.5) as a function of S payoff cannot exceed B − E, and hence can be bought for much less than the European version ... (19.9) for ≤ n ≤ i and ≤ i ≤ M − The overall method is then defined by (16.1), (16.2) and (19.9) 19.7 Notes and references The texts (Kwok, 1998) and (Wilmott et al., 1995), and any of the Wilmott ... lookbacks, barriers and Asians early exercise options: Bermudans and shouts Monte Carlo and binomial methods 19.1 Motivation So far, we have seen European options and American-style options A bewildering...

Ngày tải lên: 21/06/2014, 07:20

... first coin and tails for the second Now define random variables X and Y as follows Let X take the value if the first coin lands heads and otherwise, and let Y take the value if the first and second ... and it follows immediately that if X and Y are independent then cov(X, Y ) = Loosely, from (21.1), if the covariance is positive then X and Y tend to be smaller than their means or larger than ... independent, normal random variables with mean (µ − σ ) t and variance σ t From this point of view, getting hold of historical asset price data and forming the log ratios is 203 204 Historical volatility...

Ngày tải lên: 21/06/2014, 07:20

... end aM = mean(V); bM = std(V); conf = [aM - 1.96*bM/sqrt(M), aM + 1.96*bM/sqrt(M)] aManti = mean(Vanti); bManti = std(Vanti); confanti = [aManti - 1.96*bManti/sqrt(M), aManti + 1.96*bManti/sqrt(M)] ... long and distinguished history in numerical analysis, and many methods have been developed Monte Carlo 22.4 Notes and references 233 Table 22.3 Ninety-five per cent confidence intervals with standard ... 1998) and the survey (Boyle et al., 1997) give pointers to recent literature Both variance reduction and hedging share the aim of making a random variable more predictable, and this connection can...

Ngày tải lên: 21/06/2014, 07:20

... = 50 and Nt = 500, so k = × 10−3 and h = 0.2, we found that err0 = 1.5 × 10−3 for FTCS and err0 = 1.7 × 10−3 for BTCS With Crank– Nicolson we were able to reduce Nt to 50, so k = × 10−2 , and ... written in the matrix–vector forms (23.9) and (23.11), and the Crank–Nicolson method is given by (24.8) The τ = condition (19.2) specifies V j0 = max(B + j h − E, 0) and the left-hand boundary condition ... accuracy expansions (23.14) and (23.16) causes the O(k) term to vanish.) 23.10 Program of Chapter 23 and walkthrough The program ch23 implements BTCS for the heat equation (23.2) with initial and boundary...

Ngày tải lên: 21/06/2014, 07:20

... American options Mathematical Finance, 12:271–286 Rogers, L C 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) ... Hodder & Stoughton Lo, Andrew W and Craig MacKinlay (1999) A Non-Random Walk Down Wall Street Princeton, NJ: Princeton University Press Longstaff, F A and E S Schwartz (2001) Valuing American options ... Black–Scholes model: a note Journal of Finance, 38:227–230 Mantegna, Rosario N and H Eugene Stanley (2000) An Introduction to Econophysics: Correlations and Complexity in Finance Cambridge: Cambridge University...

Ngày tải lên: 21/06/2014, 07:20

... left-handed and righthanded particles, respectively, and are separately conserved The two currents j (x) and j (x) are the Noether currents corresponding to the two transformations (x) ! ei (x) and ... easiest to analyze this theory by considering (x) and (x), rather than the real and imaginary parts of (x), as the basic dynamical variables (a) Find the conjugate momenta to (x) and (x) and the canonical ... electron and muon have spins parallel to their directions of motion they are \right-handed" The antiparticles, similarly, are \left-handed" The electron and positron spins add up to one unit of angular...

Ngày tải lên: 17/03/2014, 14:38