Mathematical Techniques in Finance. Amir Sadr
A.3 LINEAR REGRESSION ANALYSIS
17 APPENDIX B: Useful Excel Functions
18 About the Companion Website
19 Index
List of Tables
1 Chapter 1TABLE 1.1 Balance sheet of the United States at 2020 year end.TABLE 1.2 Households sector balance sheet as of 2020 year end.TABLE 1.3 Market size ($Trillions).TABLE 1.4 U.S. bond market ($Trillions).TABLE 1.5 Global derivatives market size ($Trillions).TABLE 1.6 Market participants and financial products.
2 Chapter 2TABLE 2.1 Future Value of $100,000 for a 2 year (
3 Chapter 3TABLE 3.1 St. Petersburg game.TABLE 3.2 MVP portfolio for two risky assets.TABLE 3.3 Regression statistics.
4 Chapter 4TABLE 4.1 3‐month evolution of an asset and its forward price.
5 Chapter 6TABLE 6.1 Properties of normal and lognormal random variables.TABLE 6.2 Six‐month call option prices with different strikes.TABLE 6.3 Six‐month put option prices with different strikes.TABLE 6.4 BSM formulas and Greeks.TABLE 6.5 10 x 1000‐path simulation runs, random.seed(2021).
6 Chapter 7TABLE 7.1 Fixed leg's cash flows of a $100M 1‐year 4% fixed versus floating ...TABLE 7.2 Floating leg's cash flows of a $100M 1‐year 4% fixed versus floati...TABLE 7.3 Discount factor curve, forward 6‐month rate curve, and swap rates ...TABLE 7.4 1‐year forward start 1‐year quarterly cap with strike
List of Illustrations
1 Chapter 2FIGURE 2.1 Bond price versus yield with coupon rate = 2% p.a.FIGURE 2.2 Price of bond versus remaining years to maturity.FIGURE 2.3 Pull to par effect for a 2‐year, 4% semiannual coupon bond.FIGURE 2.4 Cash flows of a 2‐year 4% semiannual coupon bond versus a 2‐year ...FIGURE 2.5 Newton‐Raphson method.FIGURE 2.6 PV01, PVBP, and modified duration of a coupon bond.FIGURE 2.7 Interest and principal payments of a level pay loan.FIGURE 2.8 A pool of loans with low prepayment speed.FIGURE 2.9 A pool of loans with high prepayment speed.FIGURE 2.10 Negative convexity due to increased prepayments when rates are l...FIGURE 2.11 U.S. Treasury yield curve.
2 Chapter 3FIGURE 3.1 Compound lottery.FIGURE 3.2 Risk attitude and utility function.FIGURE 3.3 Risk premium for a risk‐averse investor.FIGURE 3.4 Conic sections.FIGURE 3.5 Feasible region for two risky assets.FIGURE 3.6 Feasible regions for different correlations.FIGURE 3.7 Feasible region for three or more risky assets.FIGURE 3.8 Method of Lagrange multipliers.FIGURE 3.9 Relationship between CML and the feasible region of risky assets....FIGURE 3.10 Proof of the CAPM formula.FIGURE 3.11 PCA identification of eigenvectors.FIGURE 3.12 Utility indifference curves.FIGURE 3.13 5‐year monthly price history of Amazon (AMZN), Walmart (WMT).FIGURE 3.14 Walmart (WMT) versus Amazon (AMZN).FIGURE 3.15 Z‐Score for Amazon‐Walmart pair trade.FIGURE 3.16 10,000 risky portfolios.
3 Chapter 4FIGURE 4.1 Contango versus backwardation.FIGURE 4.2 3‐month evolution of an asset's spot and forward prices.
4 Chapter 5FIGURE 5.1 Economic value of European‐style call and put options at expirati...FIGURE 5.2 One‐step binomial model.FIGURE 5.3 Lack of arbitrage.FIGURE 5.4 Two‐step binomial model.FIGURE 5.5 Two‐period evolution of the replicating portfolio for a call opti...FIGURE 5.6 A symmetric random walk is a martingale.
5 Chapter 6FIGURE 6.1 Standard Brownian motion.FIGURE 6.2 Geometric Brownian motion.FIGURE 6.3 Random walk with drift (top); exponentiated random walk with drif...FIGURE 6.4 Normal and lognormal random variables with same mean and variance...FIGURE 6.5 European‐style option payoffs.FIGURE 6.6 Skew and smile effect for out‐of‐the‐money options.FIGURE 6.7 Call option value and its delta.FIGURE 6.8 Put option value and its delta.FIGURE 6.9 Convexity PnL versus time decay for a delta‐hedged call option.FIGURE 6.10 Delta as a function of time to expiration,
6 Chapter 7FIGURE 7.1 Forward‐rate, zero‐coupon, and discount‐factor curves.FIGURE 7.2 Cash flows of a 1‐year USD fixed versus floating interest rate sw...FIGURE 7.3 Payoff of a
7 Appendix AFIGURE A.1 Probability density function of a normal
Guide
6 Preface
8
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