an introduction to financial option valuation 12

An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_13 pot

An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_13 pot

Ngày tải lên : 20/06/2014, 18:20
... = 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 ... Neumann stability and convergence A fundamental, and seemingly modest, requirement of a finite difference method is that of convergence – the error should tend to zero as k and h are decreased to ... which simplifies to ≤ ν sin2 ( βh) ≤ 2 For βh ∈ [−π, π] the quantity sin2 ( βh) takes values between and 1, and hence stability in the sense of von Neumann for FTCS is equivalent to ν ≤ (23.17)...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_14 pot

An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_14 pot

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 ... American options Working paper, University of Columbia, New York Bass, Thomas A (1999) The Predictors London: Penguin Baxter, Martin and Andrew Rennie (1996) Financial Calculus: An Introduction to...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_1 pot

An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_1 pot

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 for ... issues 123 123 123 123 124 127 x Contents 13.6 Notes and references 13.7 Program of Chapter 13 and walkthrough 127 128 14 Implied volatility 14.1 Motivation 14.2 Implied volatility 14.3 Option ... contributions to a broad range of problems in numerical analysis AN INTRODUCTION TO FINANCIAL OPTION VALUATION Mathematics, Stochastics and Computation DESMOND J HIGHAM Department of Mathematics...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_3 pptx

An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_3 pptx

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 ... 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 ... simulation to experiment with and visualize our ideas, and also to estimate quantities that cannot be determined analytically This chapter introduces the tools that we will apply 4.2 Pseudo-random...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_4 ppt

An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_4 ppt

Ngày tải lên : 20/06/2014, 18:20
... data analysis Many exchanges have informative websites, including the American Stock Exchange: www.amex.com/, the Chicago Board Options Exchange: www cboe.com/Home/, the London Stock Exchange: ... 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),...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_5 ppt

An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_5 ppt

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...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_7 pdf

An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_7 pdf

Ngày tải lên : 20/06/2014, 18:20
... 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 ... program ch12, listed in Figure 12. 2, illustrates risk neutrality in the manner of Figure 12. 1 We fix S,E,r,sigma and T and an array of 200 values for mu A for loop is then used to compute an array ... 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. 5 Program of Chapter 12 and walkthrough 121 %CH12...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_8 pptx

An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_8 pptx

Ngày tải lên : 20/06/2014, 18:20
... Chapter 12 showed that valuing an option can be regarded as computing an expected value The idea of using pseudo-random number generators to compute estimates of expected values was touched on ... 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 ... look at the implied volatility for call options traded on the London International Financial Futures and Options Exchange (LIFFE), as reported in the Financial Times on Wednesday, 22 August 2001...
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An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_9 pot

An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_9 pot

Ngày tải lên : 20/06/2014, 18:20
... Chapter 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)) ... 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 ... better than gaining S(t) − E at time t Since it is never optimal to exercise an American call option before the expiry date, an American call option must have the same value as a European call option...
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An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_1 doc

An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_1 doc

Ngày tải lên : 21/06/2014, 07:20
... 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 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 ... 1 Options OUTLINE • European call and put options • payoff diagrams • how and why options are traded 1.1 What are options? Throughout the book we use the term asset to describe any financial...
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An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_4 docx

An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_4 docx

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...
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An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_9 ppt

An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_9 ppt

Ngày tải lên : 21/06/2014, 07:20
... 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, ... 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 ... the case of an American call option Show that the Black–Scholes European call option formula (8.19) satisfies the relevant analogues of (18.2)–(18.6) Deduce that an American call option has the...
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An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_10 doc

An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_10 doc

Ngày tải lên : 21/06/2014, 07:20
... 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 models, including autoregressive ... 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 ... 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...
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An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_11 doc

An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_11 doc

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)] ... rather than about , the antithetic estimate uses −Ui , rather than − Ui Of course, −Ui is also an N(0, 1) random variable The above analysis that gave us (21.16) can then be repeated to give ... 21.6 Normal case 221 when f is monotonic In words: For monotonic f , the variance in the antithetic sample is always less than or equal to half that in the standard sample Of course, this is only...
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An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_12 pot

An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_12 pot

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 ... Neumann stability and convergence A fundamental, and seemingly modest, requirement of a finite difference method is that of convergence – the error should tend to zero as k and h are decreased to ... which simplifies to ≤ ν sin2 ( βh) ≤ 2 For βh ∈ [−π, π] the quantity sin2 ( βh) takes values between and 1, and hence stability in the sense of von Neumann for FTCS is equivalent to ν ≤ (23.17)...
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An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_13 pdf

An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_13 pdf

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 ... American options Working paper, University of Columbia, New York Bass, Thomas A (1999) The Predictors London: Penguin Baxter, Martin and Andrew Rennie (1996) Financial Calculus: An Introduction to...
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An Introduction to Financial Option Valuation_1 potx

An Introduction to Financial Option Valuation_1 potx

Ngày tải lên : 21/06/2014, 04:20
... 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 ... 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 ... simulation to experiment with and visualize our ideas, and also to estimate quantities that cannot be determined analytically This chapter introduces the tools that we will apply 4.2 Pseudo-random...
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An Introduction to Financial Option Valuation_2 potx

An Introduction to Financial Option Valuation_2 potx

Ngày tải lên : 21/06/2014, 04:20
... data analysis Many exchanges have informative websites, including the American Stock Exchange: www.amex.com/, the Chicago Board Options Exchange: www cboe.com/Home/, the London Stock Exchange: ... 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),...
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An Introduction to Financial Option Valuation_4 pot

An Introduction to Financial Option Valuation_4 pot

Ngày tải lên : 21/06/2014, 04:20
... most 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 ... 200 000 option transactions (that is separate option tickets) over 12 years and studying about 70 000 risk management reports, I felt that I needed to sit down and reflect on the thousands of ... Give a financial argument that explains why ∂ P(S, t)/∂ S → −1 at expiry for an in-the-money put option and ∂ P(S, t)/∂ S → at expiry for an outof-the-money put option 9.7 Program of Chapter and walkthrough...
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An Introduction to Financial Option Valuation_6 ppt

An Introduction to Financial Option Valuation_6 ppt

Ngày tải lên : 21/06/2014, 04:20
... Chapter 12 showed that valuing an option can be regarded as computing an expected value The idea of using pseudo-random number generators to compute estimates of expected values was touched on ... 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 ... look at the implied volatility for call options traded on the London International Financial Futures and Options Exchange (LIFFE), as reported in the Financial Times on Wednesday, 22 August 2001...
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