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<p>Preface xxiii</p> <p><b>1 Products and Markets: Equities, Commodities, Exchange Rates, Forwards and Futures 1</b></p> <p>1.1 Introduction 2</p> <p>1.2 Equities 2</p> <p>1.3 Commodities 9</p> <p>1.4 Currencies 9</p> <p>1.5 Indices 11</p> <p>1.6 The time value of money 11</p> <p>1.7 Fixed-income securities 17</p> <p>1.8 Inflation-proof bonds 17</p> <p>1.9 Forwards and futures 19</p> <p>1.10 More about futures 22</p> <p>1.11 Summary 24</p> <p><b>2 Derivatives 27</b></p> <p>2.1 Introduction 28</p> <p>2.2 Options 28</p> <p>2.3 Definition of common terms 33</p> <p>2.4 Payoff diagrams 34</p> <p>2.5 Writing options 39</p> <p>2.6 Margin 39</p> <p>2.7 Market conventions 39</p> <p>2.8 The value of the option before expiry 40</p> <p>2.9 Factors affecting derivative prices 41</p> <p>2.10 Speculation and gearing 42</p> <p>2.11 Early exercise 44</p> <p>2.12 Put-call parity 44</p> <p>2.13 Binaries or digitals 47</p> <p>2.14 Bull and bear spreads 48</p> <p>2.15 Straddles and strangles 50</p> <p>2.16 Risk reversal 52</p> <p>2.17 Butterflies and condors 53</p> <p>2.18 Calendar spreads 53</p> <p>2.19 LEAPS and FLEX 55</p> <p>2.20 Warrants 55</p> <p>2.21 Convertible bonds 55</p> <p>2.22 Over the counter options 56</p> <p>2.23 Summary 57</p> <p><b>3 The Binomial Model 59</b></p> <p>3.1 Introduction 60</p> <p>3.2 Equities can go down as well as up 61</p> <p>3.3 The option value 63</p> <p>3.4 Which part of our ‘model’ didn’t we need? 65</p> <p>3.5 Why should this ‘theoretical price’ be the ‘market price’? 65</p> <p>3.6 How did I know to sell 1 2 of the stock for hedging? 66</p> <p>3.7 How does this change if interest rates are non-zero? 67</p> <p>3.8 Is the stock itself correctly priced? 68</p> <p>3.9 Complete markets 69</p> <p>3.10 The real and risk-neutral worlds 69</p> <p>3.11 And now using symbols 73</p> <p>3.12 An equation for the value of an option 75</p> <p>3.13 Where did the probability p go? 77</p> <p>3.14 Counter-intuitive? 77</p> <p>3.15 The binomial tree 78</p> <p>3.16 The asset price distribution 78</p> <p>3.17 Valuing back down the tree 80</p> <p>3.18 Programming the binomial method 85</p> <p>3.19 The greeks 86</p> <p>3.20 Early exercise 88</p> <p>3.21 The continuous-time limit 90</p> <p>3.22 Summary 90</p> <p><b>4 The Random Behavior of Assets 95</b></p> <p>4.1 Introduction 96</p> <p>4.2 The popular forms of ‘analysis’ 96</p> <p>4.3 Why we need a model for randomness: Jensen’s inequality 97</p> <p>4.4 Similarities between equities, currencies, commodities and indices 99</p> <p>4.5 Examining returns 100</p> <p>4.6 Timescales 105</p> <p>4.7 Estimating volatility 109</p> <p>4.8 The random walk on a spreadsheet 109</p> <p>4.9 The Wiener process 111</p> <p>4.10 The widely accepted model for equities, currencies, commodities and indices 112</p> <p>4.11 Summary 115</p> <p><b>5 Elementary Stochastic Calculus 117</b></p> <p>5.1 Introduction 118</p> <p>5.2 A motivating example 118</p> <p>5.3 The Markov property 120</p> <p>5.4 The martingale property 120</p> <p>5.5 Quadratic variation 120</p> <p>5.6 Brownian motion 121</p> <p>5.7 Stochastic integration 122</p> <p>5.8 Stochastic differential equations 123</p> <p>5.9 The mean square limit 124</p> <p>5.10 Functions of stochastic variables and Itô’s lemma 124</p> <p>5.11 Interpretation of Itô’s lemma 127</p> <p>5.12 Itô and Taylor 127</p> <p>5.13 Itô in higher dimensions 130</p> <p>5.14 Some pertinent examples 130</p> <p>5.15 Summary 136</p> <p><b>6 The Black–Scholes Model 139</b></p> <p>6.1 Introduction 140</p> <p>6.2 A very special portfolio 140</p> <p>6.3 Elimination of risk: delta hedging 142</p> <p>6.4 No arbitrage 142</p> <p>6.5 The Black–Scholes equation 143</p> <p>6.6 The Black–Scholes assumptions 145</p> <p>6.7 Final conditions 146</p> <p>6.8 Options on dividend-paying equities 147</p> <p>6.9 Currency options 147</p> <p>6.10 Commodity options 148</p> <p>6.11 Expectations and Black–Scholes 148</p> <p>6.12 Some other ways of deriving the Black–Scholes equation 149</p> <p>6.13 No arbitrage in the binomial, Black–Scholes and ‘other’ worlds 150</p> <p>6.14 Forwards and futures 151</p> <p>6.15 Futures contracts 152</p> <p>6.16 Options on futures 153</p> <p>6.17 Summary 153</p> <p><b>7 Partial Differential Equations 157</b></p> <p>7.1 Introduction 158</p> <p>7.2 Putting the Black–Scholes equation into historical perspective 158</p> <p>7.3 The meaning of the terms in the Black–Scholes equation 159</p> <p>7.4 Boundary and initial/final conditions 159</p> <p>7.5 Some solution methods 160</p> <p>7.6 Similarity reductions 163</p> <p>7.7 Other analytical techniques 163</p> <p>7.8 Numerical solution 164</p> <p>7.9 Summary 164</p> <p><b>8 The Black–Scholes Formulæ and the ‘Greeks’ 169</b></p> <p>8.1 Introduction 170</p> <p>8.2 Derivation of the formulæ for calls, puts and simple digitals 170</p> <p>8.3 Delta 182</p> <p>8.4 Gamma 184</p> <p>8.5 Theta 187</p> <p>8.6 Speed 187</p> <p>8.7 Vega 188</p> <p>8.8 Rho 190</p> <p>8.9 Implied volatility 191</p> <p>8.10 A classification of hedging types 194</p> <p>8.11 Summary 196</p> <p><b>9 Overview of Volatility Modeling 203</b></p> <p>9.1 Introduction 204</p> <p>9.2 The different types of volatility 204</p> <p>9.3 Volatility estimation by statistical means 205</p> <p>9.4 Maximum likelihood estimation 211</p> <p>9.5 Skews and smiles 215</p> <p>9.6 Different approaches to modeling volatility 217</p> <p>9.7 The choices of volatility models 221</p> <p>9.8 Summary 221</p> <p><b>10 How to Delta Hedge 225</b></p> <p>10.1 Introduction 226</p> <p>10.2 What if implied and actual volatilities are different? 227</p> <p>10.3 Implied versus actual, delta hedging but using which volatility? 228</p> <p>10.4 Case 1: Hedge with actual volatility, σ 228</p> <p>10.5 Case 2: Hedge with implied volatility, ˜σ 231</p> <p>10.6 Hedging with different volatilities 235</p> <p>10.7 Pros and cons of hedging with each volatility 238</p> <p>10.8 Portfolios when hedging with implied volatility 239</p> <p>10.9 How does implied volatility behave? 241</p> <p>10.10 Summary 245</p> <p><b>11 An Introduction to Exotic and Path-dependent Options 247</b></p> <p>11.1 Introduction 248</p> <p>11.2 Option classification 248</p> <p>11.3 Time dependence 249</p> <p>11.4 Cashflows 250</p> <p>11.5 Path dependence 252</p> <p>11.6 Dimensionality 254</p> <p>11.7 The order of an option 255</p> <p>11.8 Embedded decisions 256</p> <p>11.9 Classification tables 258</p> <p>11.10 Examples of exotic options 258</p> <p>11.11 Summary of math/coding consequences 266</p> <p>11.12 Summary 267</p> <p><b>12 Multi-asset Options 271</b></p> <p>12.1 Introduction 272</p> <p>12.2 Multidimensional lognormal random walks 272</p> <p>12.3 Measuring correlations 274</p> <p>12.4 Options on many underlyings 277</p> <p>12.5 The pricing formula for European non-path-dependent options on dividend-paying assets 278</p> <p>12.6 Exchanging one asset for another: a similarity solution 278</p> <p>12.7 Two examples 280</p> <p>12.8 Realities of pricing basket options 282</p> <p>12.9 Realities of hedging basket options 283</p> <p>12.10 Correlation versus cointegration 283</p> <p>12.11 Summary 284</p> <p><b>13 Barrier Options 287</b></p> <p>13.1 Introduction 288</p> <p>13.2 Different types of barrier options 288</p> <p>13.3 Pricing methodologies 289</p> <p>13.4 Pricing barriers in the partial differential equation framework 290</p> <p>13.5 Examples 293</p> <p>13.6 Other features in barrier-style options 300</p> <p>13.7 Market practice: what volatility should I use? 302</p> <p>13.9 Summary 307</p> <p><b>14 Fixed-income Products and Analysis: Yield, Duration and Convexity 319</b></p> <p>14.1 Introduction 320</p> <p>14.2 Simple fixed-income contracts and features 320</p> <p>14.3 International bond markets 324</p> <p>14.4 Accrued interest 325</p> <p>14.5 Day-count conventions 325</p> <p>14.6 Continuously and discretely compounded interest 326</p> <p>14.7 Measures of yield 327</p> <p>14.8 The yield curve 329</p> <p>14.9 Price/yield relationship 329</p> <p>14.10 Duration 331</p> <p>14.11 Convexity 333</p> <p>14.12 An example 335</p> <p>14.13 Hedging 335</p> <p>14.14 Time-dependent interest rate 338</p> <p>14.15 Discretely paid coupons 339</p> <p>14.16 Forward rates and bootstrapping 339</p> <p>14.17 Interpolation 344</p> <p>14.18 Summary 346</p> <p><b>15 Swaps 349</b></p> <p>15.1 Introduction 350</p> <p>15.2 The vanilla interest rate swap 350</p> <p>15.3 Comparative advantage 351</p> <p>15.4 The swap curve 353</p> <p>15.5 Relationship between swaps and bonds 354</p> <p>15.6 Bootstrapping 355</p> <p>15.7 Other features of swaps contracts 356</p> <p>15.8 Other types of swap 357</p> <p>15.9 Summary 358</p> <p><b>16 One-factor Interest Rate Modeling 359</b></p> <p>16.1 Introduction 360</p> <p>16.2 Stochastic interest rates 361</p> <p>16.3 The bond pricing equation for the general model 362</p> <p>16.4 What is the market price of risk? 365</p> <p>16.5 Interpreting the market price of risk, and risk neutrality 366</p> <p>16.6 Named models 366</p> <p>16.7 Equity and FX forwards and futures when rates are stochastic 369</p> <p>16.8 Futures contracts 370</p> <p>16.9 Summary 372</p> <p><b>17 Yield Curve Fitting 373</b></p> <p>17.1 Introduction 374</p> <p>17.2 Ho & Lee 374</p> <p>17.3 The extended Vasicek model of Hull & White 375</p> <p>17.4 Yield-curve fitting: For and against 376</p> <p>17.5 Other models 380</p> <p>17.6 Summary 380</p> <p><b>18 Interest Rate Derivatives 383</b></p> <p>18.1 Introduction 384</p> <p>18.2 Callable bonds 384</p> <p>18.3 Bond options 385</p> <p>18.4 Caps and floors 389</p> <p>18.5 Range notes 392</p> <p>18.6 Swaptions, captions and floortions 392</p> <p>18.7 Spread options 394</p> <p>18.8 Index amortizing rate swaps 394</p> <p>18.9 Contracts with embedded decisions 397</p> <p>18.10 Some examples 398</p> <p>18.11 More interest rate derivatives 400</p> <p>18.12 Summary 401</p> <p><b>19 The Heath, Jarrow & Morton and Brace, Gatarek & Musiela Models 403</b></p> <p>19.1 Introduction 404</p> <p>19.2 The forward rate equation 404</p> <p>19.3 The spot rate process 404</p> <p>19.4 The market price of risk 406</p> <p>19.5 Real and risk neutral 407</p> <p>19.6 Pricing derivatives 408</p> <p>19.7 Simulations 408</p> <p>19.8 Trees 410</p> <p>19.9 The Musiela parameterization 411</p> <p>19.10 Multi-factor HJM 411</p> <p>19.11 Spreadsheet implementation 411</p> <p>19.12 A simple one-factor example: Ho & Lee 412</p> <p>19.13 Principal Component Analysis 413</p> <p>19.14 Options on equities, etc. 416</p> <p>19.15 Non-infinitesimal short rate 416</p> <p>19.16 The Brace, Gatarek & Musiela model 417</p> <p>19.17 Simulations 419</p> <p>19.18 PVing the cashflows 419</p> <p>19.19 Summary 420</p> <p><b>20 Investment Lessons from Blackjack and Gambling 423</b></p> <p>20.1 Introduction 424</p> <p>20.2 The rules of blackjack 424</p> <p>20.3 Beating the dealer 426</p> <p>20.4 The distribution of profit in blackjack 428</p> <p>20.5 The Kelly criterion 429</p> <p>20.6 Can you win at roulette? 432</p> <p>20.7 Horse race betting and no arbitrage 433</p> <p>20.8 Arbitrage 434</p> <p>20.9 How to bet 436</p> <p>20.10 Summary 438</p> <p><b>21 Portfolio Management 441</b></p> <p>21.1 Introduction 442</p> <p>21.2 Diversification 442</p> <p>21.3 Modern portfolio theory 445</p> <p>21.4 Where do I want to be on the efficient frontier? 447</p> <p>21.5 Markowitz in practice 450</p> <p>21.6 Capital Asset Pricing Model 451</p> <p>21.7 The multi-index model 454</p> <p>21.8 Cointegration 454</p> <p>21.9 Performance measurement 455</p> <p>21.10 Summary 456</p> <p><b>22 Value at Risk 459</b></p> <p>22.1 Introduction 460</p> <p>22.2 Definition of Value at Risk 460</p> <p>22.3 VaR for a single asset 461</p> <p>22.4 VaR for a portfolio 463</p> <p>22.5 VaR for derivatives 464</p> <p>22.6 Simulations 466</p> <p>22.7 Use of VaR as a performance measure 468</p> <p>22.8 Introductory Extreme Value Theory 469</p> <p>22.9 Coherence 470</p> <p>22.10 Summary 470</p> <p><b>23 Credit Risk 473</b></p> <p>23.1 Introduction 474</p> <p>23.2 The Merton model: equity as an option on a company’s assets 474</p> <p>23.3 Risky bonds 475</p> <p>23.4 Modeling the risk of default 476</p> <p>23.5 The Poisson process and the instantaneous risk of default 477</p> <p>23.6 Time-dependent intensity and the term structure of default 481</p> <p>23.7 Stochastic risk of default 482</p> <p>23.8 Positive recovery 484</p> <p>23.9 Hedging the default 485</p> <p>23.10 Credit rating 486</p> <p>23.11 A model for change of credit rating 488</p> <p>23.12 Copulas: pricing credit derivatives with many underlyings 488</p> <p>23.13 Collateralized debt obligations 490</p> <p>23.14 Summary 492</p> <p><b>24 RiskMetrics and CreditMetrics 495</b></p> <p>24.1 Introduction 496</p> <p>24.2 The RiskMetrics datasets 496</p> <p>24.3 Calculating the parameters the RiskMetrics way 496</p> <p>24.4 The CreditMetrics dataset 498</p> <p>24.5 The CreditMetrics methodology 501</p> <p>24.6 A portfolio of risky bonds 501</p> <p>24.7 CreditMetrics model outputs 502</p> <p>24.8 Summary 502</p> <p><b>25 CrashMetrics 505</b></p> <p>25.1 Introduction 506</p> <p>25.2 Why do banks go broke? 506</p> <p>25.3 Market crashes 506</p> <p>25.4 CrashMetrics 507</p> <p>25.5 CrashMetrics for one stock 508</p> <p>25.6 Portfolio optimization and the Platinum hedge 510</p> <p>25.7 The multi-asset/single-index model 511</p> <p>25.8 Portfolio optimization and the Platinum hedge in the multi-asset model 519</p> <p>25.9 The multi-index model 520</p> <p>25.10 Incorporating time value 521</p> <p>25.11 Margin calls and margin hedging 522</p> <p>25.12 Counterparty risk 524</p> <p>25.13 Simple extensions to CrashMetrics 524</p> <p>25.14 The CrashMetrics Index (CMI) 525</p> <p>25.15 Summary 526</p> <p><b>26 Derivatives **** Ups 527</b></p> <p>26.1 Introduction 528</p> <p>26.2 Orange County 528</p> <p>26.3 Proctor and Gamble 529</p> <p>26.4 Metallgesellschaft 532</p> <p>26.5 Gibson Greetings 533</p> <p>26.6 Barings 536</p> <p>26.7 Long-Term Capital Management 537</p> <p>26.8 Summary 540</p> <p><b>27 Overview of Numerical Methods 541</b></p> <p>27.1 Introduction 542</p> <p>27.2 Finite-difference methods 542</p> <p>27.3 Monte Carlo methods 544</p> <p>27.4 Numerical integration 546</p> <p>27.5 Summary 547</p> <p><b>28 Finite-difference Methods for One-factor Models 549</b></p> <p>28.1 Introduction 550</p> <p>28.2 Grids 550</p> <p>28.3 Differentiation using the grid 553</p> <p>28.4 Approximating θ 553</p> <p>28.5 Approximating � 554</p> <p>28.6 Approximating Ɣ 557</p> <p>28.7 Example 557</p> <p>28.8 Bilinear interpolation 558</p> <p>28.9 Final conditions and payoffs 559</p> <p>28.10 Boundary conditions 560</p> <p>28.11 The explicit finite-difference method 562</p> <p>28.12 The Code #1: European option 567</p> <p>28.13 The Code #2: American exercise 571</p> <p>28.14 The Code #3: 2-D output 573</p> <p>28.15 Upwind differencing 575</p> <p>28.16 Summary 578</p> <p><b>29 Monte Carlo Simulation 581</b></p> <p>29.1 Introduction 582</p> <p>29.2 Relationship between derivative values and simulations: equities, indices, currencies, commodities 582</p> <p>29.3 Generating paths 583</p> <p>29.4 Lognormal underlying, no path dependency 584</p> <p>29.5 Advantages of Monte Carlo simulation 585</p> <p>29.6 Using random numbers 586</p> <p>29.7 Generating Normal variables 587</p> <p>29.8 Real versus risk neutral, speculation versus hedging 588</p> <p>29.9 Interest rate products 590</p> <p>29.10 Calculating the greeks 593</p> <p>29.11 Higher dimensions: Cholesky factorization 594</p> <p>29.12 Calculation time 596</p> <p>29.13 Speeding up convergence 596</p> <p>29.14 Pros and cons of Monte Carlo simulations 598</p> <p>29.15 American options 598</p> <p>29.16 Longstaff & Schwartz regression approach for American options 599</p> <p>29.17 Basis functions 603</p> <p>29.18 Summary 603</p> <p><b>30 Numerical Integration 605</b></p> <p>30.1 Introduction 606</p> <p>30.2 Regular grid 606</p> <p>30.3 Basic Monte Carlo integration 607</p> <p>30.4 Low-discrepancy sequences 609</p> <p>30.5 Advanced techniques 613</p> <p>30.6 Summary 614</p> <p>A All the Math You Need .and No More (An Executive Summary) 617</p> <p>A. 1 Introduction 618</p> <p>A. 2 e 618</p> <p>A. 3 log 618</p> <p>A. 4 Differentiation and Taylor series 620</p> <p>A. 5 Differential equations 623</p> <p>A. 6 Mean, standard deviation and distributions 623</p> <p>A. 7 Summary 626</p> <p>B Forecasting the Markets? A Small Digression 627</p> <p>B. 1 Introduction 628</p> <p>B. 2 Technical analysis 628</p> <p>B. 3 Wave theory 637</p> <p>B. 4 Other analytics 638</p> <p>B. 5 Market microstructure modeling 640</p> <p>B. 6 Crisis prediction 641</p> <p>B. 7 Summary 641</p> <p>C A Trading Game 643</p> <p>C. 1 Introduction 643</p> <p>C. 2 Aims 643</p> <p>C. 3 Object of the game 643</p> <p>C. 4 Rules of the game 643</p> <p>C. 5 Notes 644</p> <p>C. 6 How to fill in your trading sheet 645</p> <p>D Contents of CD accompanying Paul Wilmott Introduces Quantitative Finance, second edition 649</p> <p>E What you get if (when) you upgrade to PWOQF2 653</p> <p>Bibliography 659</p> <p>Index 683</p>

<p><b>Paul Wilmott, </b>described by the <i>Financial Times </i>as ‘cult derivatives lecturer,’ is one of the world’s leading experts on quantitative finance and derivatives. <p>He is the proprietor of an innovative magazine on quantitative finance and a highly popular community website <b>(www.wilmott.com). </b>He was formerly a partner in a successful volatility arbitrage hedge fund and is currently the principal of the financial consultancy and training firm, Wilmott Associates, and Course Director for the Certificate in Quantitative Finance. Dr Wilmott has researched and published widely on financial engineering. <p><I>PWIQF2 </I>is an accessible introduction to the classical side of quantitative finance specifically for university students. Adapted from the comprehensive, even epic work, <i>Paul Wilmott on Quantitative Finance, Second Edition</i>, itself an update to <i>Derivatives</i>, the book includes carefully selected chapters to give the student a thorough understanding of futures, options and numerical methods. Software is included to help visualize the most important ideas and to show how techniques are implemented in practice.

<p><B>IN PRAISE OF PAUL WILMOTT AND HIS PREVIOUS WORKS</B> <p>Some people write for fame, some for fortune. Academics write books to impress the professor down the corridor so that one day they will be the professor down the corridor everyone is trying to impress. Uniquely, Paul Wilmott writes to inform and educate his readers, to convey ideas, and, most importantly, to show them <i>how to do it</i>. <p>His most enthusiastic admirers are his readers. So, instead of endorsements from the great and the good, here are the words of his fans. Their sometimes unique spelling and grammar has been retained. <p>‘I found it to be easily the best book that I have read/worked through on the subject.’<p> ‘I thought it might amuse you to know that I think your book got me a job!’ <p>‘I’d like to say that this is a great book but you already know that!’ <p>‘I’m a junior derivatives trader in Mexico City. I’ve seen your book and I have only one comment: SEXY!’ <p>‘Loved your book, which is a breath of fresh air, amongst all those arid derivatives books!! It really is in a class of its own. I have wasted so much money on stupid derivative books which too elementary or way too complicated.’ <p>‘Purchased both <i>Quant Finance </i>and <i>Derivatives </i>a couple of days ago. Will not be able to afford steak or wine for weeks as a result.’ <p>‘BTW, I want to congratulate you for the *best* book in Financial Engineering I’ve read in the last years.’ <p>‘After reading the book I’d like to follow one of your courses, but they are way too expensive.’ <p>‘Congratulations for your brilliant book.’ <p>‘What I like about it is that it has this no-nonsense kind of approach that you’d expect in a physics text and it spells out the “stuff between the equations”.’ <p>‘Congratulation to your book <i>Derivatives </i>!!! The way you describe, present, and deliver Derivative knowledge is unique! One can feel your passion on the topic. It’s a pleasure to read, study, re-read...’ <p>‘Congratulations on a great new book – ‘<i>PW on Quant Finance</i>’. I bought the DERIVATIVES one but cannot afford this one!!’ <p>‘I am fanatical follower of your book “<i>Derivatives</i>”. You are best and this not flattery. Sorry from my English!’ <p>‘We use it for the part of our Banking and Risk Management course and it’s much more comprehensive than the books that we have recommended in our study guide.’ <p>‘Your book “<i>Derivatives: the Theory and Practice of Financial Engineering</i>” is the best in the market so far.’ <p>‘I shall waste no more precious words but to say that I am very simpathetic to your humor and irony...what most don’t always seem to understand: irony is one of the GREAT filters to access knowledge in this world and an elegant one for that matter.’ <p>‘Your book rocks.’ <p>‘Congratulations to the success of your book (I got my copy of it for Christmas).’ ‘I would like to thank you for writing <i>Derivatives</i>.’ <p>‘<i>Derivatives </i>is the Greatest! Thank you, thank you, thank you! Just read the first 7 chapters of <i>Derivatives</i>, and it speaks to me.’ <p>‘Complete, brilliant and amusing, stimulating for some original ideas and examples, didactically ready to be used by Students; it employs mathematical tools as tools only, not as a target; it is the last but the best book on derivatives in my library.’ <p>‘You’re book truly struck me as fun, informative and brilliant! Us American would say “Awesome Dude!!!”’ <p>‘I had a course on derivatives and your book was not suggested by the teacher (a stupid teacher).’ <p>‘Love you for ever, baby. xxx M’

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