A Practical Guide to Quantitative Finance Interviews
Contents

Table of Contents

  1. Chapter 1 General Principles1
  2. 1. Build a broad knowledge base1
  3. 2. Practice your interview skills1
  4. 3. Listen carefully2
  5. 4. Speak your mind2
  6. 5. Make reasonable assumptions2
  7. Chapter 2 Brain Teasers3
  8. 2.1 Problem Simplification3
  9. Screwy pirates3
  10. Tiger and sheep4
  11. 2.2 Logic Reasoning5
  12. River crossing5
  13. Birthday problem5
  14. Card game6
  15. Burning ropes7
  16. Defective ball7
  17. Trailing zeros9
  18. Horse race9
  19. Infinite sequence10
  20. 2.3 Thinking Out of the Box10
  21. Box packing10
  22. Calendar cubes11
  23. Door to offer12
  24. Message delivery13
  25. Last ball13
  26. Light switches14
  27. Quant salary15
  28. 2.4 Application of Symmetry15
  29. Coin piles15
  30. Mislabeled bags16
  31. Wise men17
  32. 2.5 Series Summation17
  33. Clock pieces18
  34. Missing integers18
  35. Counterfeit coins I19
  36. 2.6 The Pigeon Hole Principle20
  37. Matching socks21
  38. Handshakes21
  39. Have we met before?21
  40. Ants on a square22
  41. Counterfeit coins II22
  42. ii
  43. 2.7 Modular Arithmetic23
  44. Prisoner problem24
  45. Division by 925
  46. Chameleon colors26
  47. 2.8 Math Induction27
  48. Coin split problem27
  49. Chocolate bar problem28
  50. Race track29
  51. 2.9 Proof by Contradiction31
  52. Irrational number31
  53. Rainbow hats31
  54. Chapter 3 Calculus and Linear Algebra33
  55. 3.1 Limits and Derivatives33
  56. Basics of derivatives33
  57. Maximum and minimum34
  58. L'Hospital's rule35
  59. 3.2 Integration36
  60. Basics of integration36
  61. Applications of integration38
  62. Expected value using integration40
  63. 3.3 Partial Derivatives and Multiple Integrals40
  64. 3.4 Important Calculus Methods41
  65. Taylor's series41
  66. Newton's method44
  67. Lagrange multipliers45
  68. 3.5 Ordinary Differential Equations46
  69. Separable differential equations47
  70. First-order linear differential equations47
  71. Homogeneous linear equations48
  72. Nonhomogeneous linear equations49
  73. 3.6 Linear Algebra50
  74. Vectors50
  75. QR decomposition52
  76. Determinant, eigenvalue and eigenvector53
  77. Positive semidefinite/definite matrix56
  78. LU decomposition and Cholesky decomposition57
  79. Chapter 4 Probability Theory59
  80. 4.1 Basic Probability Definitions and Set Operations59
  81. Coin toss game61
  82. Card game61
  83. Drunk passenger62
  84. iii
  85. N points on a circle63
  86. 4.2 Combinatorial Analysis64
  87. Poker hands65
  88. Hopping rabbit66
  89. Screwy pirates 267
  90. Chess tournament68
  91. Application letters69
  92. Birthday problem71
  93. 100th digit71
  94. Cubic of integer72
  95. 4.3 Conditional Probability and Bayes' formula72
  96. Boys and girls73
  97. All-girl world?74
  98. Unfair coin74
  99. Fair probability from an unfair coin75
  100. Dart game75
  101. Birthday line76
  102. Dice order78
  103. Monty Hall problem78
  104. Amoeba population79
  105. Candies in a jar79
  106. Coin toss game80
  107. Russian roulette series81
  108. Aces82
  109. Gambler's ruin problem83
  110. Basketball scores84
  111. Cars on road85
  112. 4.4 Discrete and Continuous Distributions86
  113. Meeting probability88
  114. Probability of triangle89
  115. Property of Poisson process90
  116. Moments of normal distribution91
  117. 4.5 Expected Value, Variance & Covariance92
  118. Connecting noodles93
  119. Optimal hedge ratio94
  120. Dice game94
  121. Card game95
  122. Sum of random variables95
  123. Coupon collection97
  124. Joint default probability98
  125. 4.6 Order Statistics99
  126. Expected value of max and min99
  127. Correlation of max and min100
  128. Random ants102
  129. Chapter 5 Stochastic Process and Stochastic Calculus105
  130. iv
  131. 5.1 Markov Chain105
  132. Gambler's ruin problem107
  133. Dice question108
  134. Coin triplets109
  135. Color balls113
  136. 5.2 Martingale and Random walk115
  137. Drunk man116
  138. Dice game117
  139. Ticket line117
  140. Coin sequence119
  141. 5.3 Dynamic Programming121
  142. Dynamic programming (DP) algorithm122
  143. Dice game123
  144. World series123
  145. Dynamic dice game126
  146. Dynamic card game127
  147. 5.4 Brownian Motion and Stochastic Calculus129
  148. Brownian motion129
  149. Stopping time/ first passage time131
  150. Ito's lemma135
  151. Chapter 6 Finance137
  152. 6.1. Option Pricing137
  153. Price direction of options137
  154. Put-call parity138
  155. American v.s. European options139
  156. Black-Scholes-Merton differential equation142
  157. Black-Scholes formula143
  158. 6.2. The Greeks149
  159. Delta149
  160. Gamma152
  161. Theta154
  162. Vega156
  163. 6.3. Option Portfolios and Exotic Options158
  164. Bull spread159
  165. Straddle159
  166. Binary options160
  167. Exchange options161
  168. 6.4. Other Finance Questions163
  169. Portfolio optimization163
  170. Value at risk164
  171. Duration and convexity165
  172. Forward and futures167
  173. Interest rate models168
  174. v
  175. Chapter 7 Algorithms and Numerical Methods171
  176. 7.1. Algorithms171
  177. Number swap172
  178. Unique elements173
  179. Horner's algorithm174
  180. Moving average174
  181. Sorting algorithm174
  182. Random permutation176
  183. Search algorithm177
  184. Fibonacci numbers179
  185. Maximum contiguous subarray180
  186. 7.2. The Power of Two182
  187. Power of 2?182
  188. Multiplication by 7182
  189. Probability simulation182
  190. Poisonous wine183
  191. 7.3 Numerical Methods184
  192. Monte Carlo simulation184
  193. Finite difference method189