1.
Introduction1.1.1.2.1.3.1.4.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Numerical Accuracy & Errors....................................................Core Math’s Classes ...................................................................1.2.1. Root Finding - Interval Bisection..................................1.2.2. Newton’s Method...........................................................Statistical Classes........................................................................1.3.1. Measures of Dispersion .................................................Application Classes.....................................................................1.4.1. Internal Rate of Return ..................................................1.4.2. Deriving Yield Approximations – Bisection Method ...1.4.3. Deriving Yield Approximations
-the Newton Raphson Method .......................................1.4.4. Portfolio Management....................................................1.4.5. Portfolio Risk Measurement ..........................................1
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2.
Interest2.1.2.2.2.3.2.4.Rate Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Compound Interest......................................................................2.1.1. Nominal and Effective Interest......................................Present Value (PV) .....................................................................2.2.1. Compounding Cashflows...............................................2.2.2. Perpetuity and Annuity ..................................................Internal Rate of Return ...............................................................Term Structures...........................................................................2.4.1. Rate Interchanges...........................................................2.4.2. Spot Rates ......................................................................2.4.3. Deriving the Spot Curve ................................................33
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3.
Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.1. Bonds – Fixed Interest................................................................3.2. Bond Prices .................................................................................3.2.1. Interest Yields ................................................................3.2.2. Yield to Maturity ...........................................................3.3. Static Spread ...............................................................................3.4. Credit Spreads.............................................................................59
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Contents
3.5.
3.6.
Bond Volatility Measures........................................................... 81
3.5.1. Price Value of a Point.................................................... 85
Bond Pricing Characteristics ...................................................... 88
4.
Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.1. Macaulay Duration ..................................................................... 99
4.2. Effective Duration....................................................................... 105
5.
Futures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.1. Forward & Futures Pricing......................................................... 108
5.2. Forward Price.............................................................................. 112
5.3. Pricing On Different Markets..................................................... 115
5.3.1. Stock Index .................................................................... 115
5.3.2. Currencies....................................................................... 117
5.4. Commodity Futures .................................................................... 118
6.
Options.6.1.6.2.6.3.6.4.6.5.6.6.6.7.6.8.6.9.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .125
Option Types............................................................................... 125
Option Specifications.................................................................. 127
Pricing Specification................................................................... 128
6.3.1. Dividends and Stock Splits............................................ 130
6.3.2. Option Quotes ................................................................ 131
6.3.3. Margin Accounts............................................................ 132
Arbitrage in Option Prices.......................................................... 133
6.4.1. Main Components of Pricing......................................... 133
6.4.2. Limits for Pricing........................................................... 136
Early Exercise of American Options.......................................... 141
Option Convexity........................................................................ 143
Put Call Parity............................................................................. 145
Strategies ..................................................................................... 149
6.8.1. Hedge with a Protected Put ........................................... 150
6.8.2. Reverse Protected Put Hedge ........................................ 150
6.8.3. Hedge with a Covered Call ........................................... 150
6.8.4. Reverse Covered Call Hedge......................................... 150
Profit Diagrams........................................................................... 155
7.
Modelling Stock Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7.1. The Stochastic Process ............................................................... 163
7.1.1. Random Walks............................................................... 163
7.1.2. Brownian Motion ........................................................... 164
7.1.3. Wiener Process............................................................... 164
7.1.4. Ito Differential................................................................ 168
7.2. Lognormal Modelling of Stock Prices ....................................... 170
7.2.1. Handling Empirical Data ............................................... 171
7.2.2. Simulation with Monte Carlo ........................................ 177
7.3. The Lognormal Property ............................................................ 182