Table of Contents
Chapter 1 General Principles (1)
1. Build a broad knowledge base (1)
2. Practice your interview skills (1)
3. Listen carefully (2)
4. Speak your mind (2)
5. Make reasonable assumptions (2)
Chapter 2 Brain Teasers (3)
2.1 Problem Simplification (3)
Screwy pirates (3)
Tiger and sheep (4)
2.2 Logic Reasoning (5)
River crossing (5)
Birthday problem (5)
Card game (6)
Burning ropes (7)
Defective ball (7)
Trailing zeros (9)
Horse race (9)
Infinite sequence (10)
2.3 Thinking Out of the Box (10)
Box packing (10)
Calendar cubes (11)
Door to offer (12)
Message delivery (13)
Last ball (13)
Light switches (14)
Quant salary (15)
2.4 Application of Symmetry (15)
Coin piles (15)
Mislabeled bags (16)
Wise men (17)
2.5 Series Summation (17)
Clock pieces (18)
Missing integers (18)
Counterfeit coins I (19)
2.6 The Pigeon Hole Principle (20)
Matching socks (21)
Handshakes (21)
Have we met before? (21)
Ants on a square (22)
Counterfeit coins II (22)
Contents
ii 2.7 Modular Arithmetic (23)
Prisoner problem (24)
Division by 9 (25)
Chameleon colors (26)
2.8 Math Induction (27)
Coin split problem (27)
Chocolate bar problem (28)
Race track (29)
2.9 Proof by Contradiction (31)
Irrational number (31)
Rainbow hats (31)
Chapter 3 Calculus and Linear Algebra (33)
3.1 Limits and Derivatives (33)
Basics of derivatives (33)
Maximum and minimum (34)
L’Hospital’s rule (35)
3.2 Integration (36)
Basics of integration (36)
Applications of integration (38)
Expected value using integration (40)
3.3 Partial Derivatives and Multiple Integrals (40)
3.4 Important Calculus Methods (41)
Taylor’s series (41)
Newton’s method (44)
Lagrange multipliers (45)
3.5 Ordinary Differential Equations (46)
Separable differential equations (47)
First-order linear differential equations (47)
Homogeneous linear equations (48)
Nonhomogeneous linear equations (49)
3.6 Linear Algebra (50)
Vectors (50)
QR decomposition (52)
Determinant, eigenvalue and eigenvector (53)
Positive semidefinite/definite matrix (56)
LU decomposition and Cholesky decomposition (57)
Chapter 4 Probability Theory (59)
4.1 Basic Probability Definitions and Set Operations (59)
Coin toss game (61)
Card game (61)
Drunk passenger (62)
A Practical Guide To Quantitative Finance Interviews
N points on a circle (63)
4.2 Combinatorial Analysis (64)
Poker hands (65)
特斯拉股价
Hopping rabbit (66)
Screwy pirates 2 (67)
Chess tournament (68)
Application letters (69)
Birthday problem (71)
100th digit (71)
Cubic of integer (72)
4.3 Conditional Probability and Bayes’ formula (72)
Boys and girls (73)
All-girl world? (74)
Unfair coin (74)
Fair probability from an unfair coin (75)
Dart game (75)
Birthday line (76)
Dice order (78)
Monty Hall problem (78)
Amoeba population (79)
Candies in a jar (79)
Coin toss game (80)
Russian roulette series (81)
Aces (82)
Gambler’s ruin problem (83)
Basketball scores (84)
Cars on road (85)
4.4 Discrete and Continuous Distributions (86)
Meeting probability (88)
Probability of triangle (89)
Property of Poisson process (90)
Moments of normal distribution (91)
4.5 Expected Value, Variance & Covariance (92)
Connecting noodles (93)
Optimal hedge ratio (94)
Dice game (94)
Card game (95)
Sum of random variables (95)
Coupon collection (97)
Joint default probability (98)
4.6 Order Statistics (99)
Expected value of max and min (99)
Correlation of max and min (100)
Random ants (102)
Chapter 5 Stochastic Process and Stochastic Calculus (105)
iii
Contents
iv 5.1 Markov Chain (105)
Gambler’s ruin problem (107)
Dice question (108)
Coin triplets (109)
Color balls (113)
5.2 Martingale and Random walk (115)
Drunk man (116)
Dice game (117)
Ticket line (117)
Coin sequence (119)
5.3 Dynamic Programming (121)
Dynamic programming (DP) algorithm (122)
Dice game (123)
World series (123)
Dynamic dice game (126)
Dynamic card game (127)
5.4 Brownian Motion and Stochastic Calculus (129)
Brownian motion (129)
Stopping time/ first passage time (131)
Ito’s lemma (135)
Chapter 6 Finance (137)
6.1. Option Pricing (137)
Price direction of options (137)
Put-call parity (138)
American v.s. European options (139)
Black-Scholes-Merton differential equation (142)
Black-Scholes formula (143)
6.2. The Greeks (149)
Delta (149)
Gamma (152)
Theta (154)
Vega (156)
6.3. Option Portfolios and Exotic Options (158)
Bull spread (159)
Straddle (159)
Binary options (160)
Exchange options (161)
6.4. Other Finance Questions (163)
Portfolio optimization (163)
Value at risk (164)
Duration and convexity (165)
Forward and futures (167)
Interest rate models (168)
A Practical Guide To Quantitative Finance Interviews Chapter 7 Algorithms and Numerical Methods (171)
7.1. Algorithms (171)
Number swap (172)
Unique elements (173)
Horner's algorithm (174)
Moving average (174)
Sorting algorithm (174)
Random permutation (176)
Search algorithm (177)
Fibonacci numbers (179)
Maximum contiguous subarray (180)
7.2. The Power of Two (182)
Power of 2? (182)
Multiplication by 7 (182)
Probability simulation (182)
Poisonous wine (183)
7.3 Numerical Methods (184)
Monte Carlo simulation (184)
Finite difference method (189)
v