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Financial risk management: samenvatting

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5 vendu
168 pages
2025/2026 Rédigé pour l'année scolaire
Établissement Universiteit Antwerpen (UA)
Cours Financial Risk Management (2104TEWFIN)
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Aperçu 4 sur 168 pages

This summary is based on the topics covered in the Financial Risk Management course taught by Prof. De Ceuster at the Faculty of Business and Economics at the University of Antwerp. It covers the material from all the lecture videos made available via EduCloud. By studying this summary, which I compiled myself, and completing all the accompanying exercises, I achieved a score of 18/20 for this course.

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FINANCIAL RISK MANAGEMENT
2025-2026




This summary is based on the topics covered in the Financial Risk Management course taught by Prof. De Ceuster at
the Faculty of Business and Economics at the University of Antwerp. It covers the material from all the lecture videos
made available via EduCloud.



1

,Introduction

1. Different kinds of risks
Market risk = the risk that financial variables in the market change

Credit risk = the risk that there will be a default by the borrower of funds, to that the interest and principal are not paid to
the lender as promised (determines the interest rate)

Operational risk = the risk that systems or processes might fail

Systemic risk = the risk that a default by one financial institution will create a ‘‘ripple effect’’ that leads to defaults by other
financial institutions and threatens the stability of the financial system.


2. Different kinds of products
Linear products = products where the holder of the product can win or lose
→ zero-sum game

Non-linear products = products where one party gets a gain and the other party loses
→ kinked pay-off profile (eg. options)




2

,CLASS 1: introduction to derivatives
Section 1: Derivatives

1. What are derivatives?
Characteristics of derivatives
●​ derive value: value of derivative is a function of the underlying ​
→ underlying can be tradable (eg. financial instruments) or non-tradable (eg. index, temperature ...)
●​ uncertainty about future cash flows

Derivative = contingent claim = instrument whose payoff depends on one or several other uncertain underlying variables
→ eg. forwards and futures, swaps, options, real options … while bonds and equity are not derivatives

Other derivative classifications
●​ based on the underlying
○​ equity derivatives (stock)
○​ interest rate derivatives (eg. EURIBOR)
○​ currency derivatives (eg. value written on the dollar)
○​ commodity derivatives (eg. electricity)
○​ credit derivatives
○​ property derivatives
●​ based on the nature of the market​
→ exchange traded, OTC (Over The Counter, outside of an exchange)


1.1 Importance of derivatives
Derivatives are the biggest financial markets we have
●​ swap markets are larger than the GDP of large countries
●​ biggest financial markets with outstanding notionals that are a multiple of world GDP

A lot of people use derivatives
●​ derivatives enable us to transfer risks efficiently (eg. hedging, arbitrage)

Many financial products have embedded derivatives
●​ embedded derivatives: bonds, structured products, …
●​ eg. you buy a 30-year treasury bond with the option for the state to buy the bond back after 15 years at
a fixed price (embedded call option) so you actually buy a portfolio of a bond and an option

In capital budgeting, real options allow enhanced NPV calculations by including value creation through flexibility
●​ real call options: option to wait, option to expand or shrink, option to grow
●​ real put options: option to stop, option to change input or output


1.2 Users of derivatives
A lot of people use derivatives
●​ hedgers = person who enters into financial contracts to reduce risk from price fluctuations with the goal
of protecting their investments from potential losses by offsetting price volatility
●​ speculators = person who bets on future movements in the price of an asset hoping to make a profit
●​ arbitrageurs = person who simultaneously buys and sells financial instruments in different markets or in
derivative forms to take advantage of differing prices for the same asset in two different markets
3

, Section 2: Spot contracts, forwards, futures and swaps

1. The spot contract
Spot contract = an agreement concluded today in which two counterparties agree to buy or sell a well specified asset at a
certain price with an almost immediate delivery and payment (max. within 3 days)

If you hold an asset, you have a long position in that asset (buyer). You will gain if the asset price increases.
Short selling allows you to take a short position (seller). You will gain if the asset price decreases.
→ short selling = selling borrowed securities (on an up-tick, except for indices) by security lending or a repo


Payoff = CF at a certain moment T in the future
S = spot price at maturity

If you have an asset, you will sell it at a future price at
which it is traded on the exchange market.

e.g. you buy something at €20 and sell it at €30
●​ profit = 30 - 20 = 10
●​ payoff = 30 (unaffected by past costs)

45° degree line
→ if the share value increases with €1, the value of the
spot contract will also increase by €1




2. The forward contract
Forward contract = an agreement concluded between two counterparties in the OTC market in which they agree to
buy or sell an underlying asset at a certain time in the future (maturity date) for a contracted delivery price
●​ delivery price is determined at time 0, but will be paid at time T
●​ forward contracts can only be purchased at a financial institution (OTC), not exchange traded


Positions
●​ long = obligation to buy
●​ short = obligation to sell




The value of the contract is 0 because there is no premium paid at the moment of concluding the contract.
●​ the value of the underlying is the spot price at moment T​
→ net CF of the forward contract = ST - DP0 where ST is uncertain
●​ dangerous: if something uncertain happens, you can’t do anything because you have an agreement

Who wins at moment T?
●​ if ST (spot price at time T) has risen during the period between “now” and “T”, the seller loses ​
→ DP0 (delivery price) < ST
●​ if ST has dropped during the period between “now” and “T”, the buyer loses and the seller wins​
→ DP0 > ST



4

Table des matières

  1. 01 Introduction 2
    1. 1. Different kinds of risks 2
    2. 2. Different kinds of products 2
  2. 02 Section 1: Derivatives 3
    1. 1. What are derivatives? 3
  3. 03 Section 2: Spot contracts, forwards, futures and swaps 4
    1. 1. The spot contract 4
    2. 2. The forward contract 4
    3. 3. Futures 7
    4. 4. Swaps (not discussed in class) 7
  4. 04 Section 3: Options 7
    1. 1. What are options? 7
    2. 2. Why use options? 8
    3. 3. Terminology 8
    4. 4. The payoff of the option contract 9
    5. 5. Payoff diagrams of options 9
    6. 6. The profit diagram 11
    7. 7. The role of exchanges in option trading 11
    8. 8. Dividends and stock splits 11
  5. 05 Section 4: Derivatives use revised 12
    1. 1. Hedging example 12
    2. 2. Speculation example (not discussed in class) 12
    3. 3. Structured products 12
  6. 06 Section 5: Exercises 14
  7. 07 Section 1: History 15
    1. 1. The origins of forwards are very old 15
    2. 2. Financial futures are relatively new 15
  8. 08 Section 2: Where are futures traded? At the exchanges! 15
    1. 1. US 15
    2. 2. Europe 15
  9. 09 Section 3: What is Traded? The contract specifications 15
    1. 1. The underlying 15
    2. 2. Quantity 16
    3. 3. Quality 16
    4. 4. Other delivery specifications 17
  10. 10 Section 4: Prices and quotes 18
    1. 1. Futures quotes 18
    2. 2. Price patterns 18
  11. 11 Section 5: How are futures traded? The functioning of the exchanges 19
    1. 1. Economic functions of a futures exchange 19
  12. 12 Section 6: OTC transactions 24
  13. 13 Section 7: Exercises 25
  14. 14 SUMMARY: forward vs futures contracts 25
  15. 15 Section 1: Simple interest rate 26
  16. 16 Section 2: Compounded interest 26
    1. 1. Annual compounding 26
    2. 2. Calculating compounded values 26
    3. 3. Numerative examples 27
    4. 4. Bond pricing 27
    5. 5. The new normal 28
    6. 6. The IRR 28
  17. 17 Section 3: Compounding at a non-annual frequency 28
    1. 1. Compounded interest: discrete time compounding 28
  18. 18 Section 4: Continuous compounding 29
    1. 1. Exploring the limit of a particular function 29
  19. 19 Section 5: Conversion of interest rates 30
  20. 20 Section 6: Zero bonds 30
    1. 1. Pricing a zero bond 30
    2. 2. Determining the zero coupon yield 30
    3. 3. Spot rates 31
    4. 4. Market quotation 31
  21. 21 Section 7: Term structure 32
    1. 1. Shapes of the term structure 32
    2. 2. Spot rates and forward rates 33
  22. 22 Section 8: Coupon bonds 36
    1. 1. Pricing a coupon bond on the term structure 36
  23. 23 Section 9: Extracting spot rates from fixed income instruments 36
    1. 1. Bootstrapping the zero curve 36
  24. 24 Section 10: Parameterization of the term structure 37
    1. 1. Splines 37
    2. 2. Smoothing the bootstrap 38
  25. 25 Section 11: The yield to maturity 38
    1. 1. Bond pricing using a Yield (to Maturity) 38
    2. 2. Bond portfolio yields 39
    3. 3. Par vs non par bonds 40
  26. 26 Section 12: The price-yield relationship 40
  27. 27 Section 13: Price sensitivity 41
    1. 1. Bond price sensitivity 41
    2. 2. Bond price prediction 41
    3. 3. Duration 42
  28. 28 Section 1: Recap 46
    1. 1. Illustrative example 46
  29. 29 Section 2: The replication principle and the assumption of no arbitrage 46
    1. 1. The nature of the underlying 47
  30. 30 Section 3: Determining the forward price of investment assets 48
    1. 1. Underlying is a non dividend paying investment asset 48
    2. 2. Underlying is a dividend paying investment asset 50
    3. 3. Underlying is a continuous dividend paying investment asset 52
  31. 31 Section 4: The off-market forward 53
    1. 1. Example of an off-market forward 53
  32. 32 Section 5: The marked-to-market value of a forward (investment asset) 53
    1. 1. Value of a forward contract 53
  33. 33 Section 6: Determining the delivery price of consumption assets 54
    1. 1. Hybrids 54
    2. 2. Pure consumption assets 55
    3. 3. The implied repo rate (not discussed in class) 55
  34. 34 Section 7: Exercises 57
  35. 35 Section 8: Futures pricing 57
    1. 1. Valuing futures 57
    2. 2. Exercise 59
  36. 36 Section 1: regression of a scatter plot 60
    1. 1. Scatterplot 60
    2. 2. Regression in Excel 60
  37. 37 Section 2: Hedging 62
    1. 1. Setting up a hedge 62
    2. 2. Long and short hedges 63
    3. 3. Rolling the hedge: timing problems 64
    4. 4. Commodity mismatch 65
    5. 5. Optimal hedging 65
    6. 6. Hedging effectiveness 67
    7. 7. Optimal hedging: tailing the hedge 68
    8. 8. Cross hedging equity portfolios with stock index futures 69
  38. 38 Section 3: Exercises 70
  39. 39 OVERVIEW 71
  40. 40 Section 1: interest rate forwards as forward rate agreements (FRA) NIET KENNEN 71
    1. 1. The FRA 71
    2. 2. Pricing a new FRA 73
    3. 3. Valuing an existing FRA 74
    4. 4. Hedging with FRAs 74
  41. 41 Section 2: interest rate futures - eurodollar futures NIET KENNEN 74
    1. 1. Eurodollar deposits 74
    2. 2. Eurodollar futures 75
    3. 3. Hedging with Eurodollar futures 76
    4. 4. Eurodollar futures versus FRAs 77
    5. 5. The LIBOR zero curve (not discussed in class) 78
  42. 42 Section 3: bond futures 78
    1. 1. Bond futures quotation 78
    2. 2. Impact of the delivery option 79
    3. 3. Bond future valuation: step by step 79
    4. 4. Duration of a future 80
  43. 43 INTRODUCTION 83
    1. 1. Market size 83
    2. 2. Definition of a swap 83
  44. 44 INTEREST RATE SWAP 83
    1. 1. What 83
    2. 2. Why do companies use interest rate swaps? 84
    3. 3. Par yield 87
    4. 4. Valuation 88
    5. 6. Swap rates and zero curves 89
    6. 6. Overnight indexed swaps 90
  45. 45 CURRENCY SWAPS 91
    1. 1. What 91
    2. 2. Why do companies use currency swaps? 92
    3. 3. Valuation 92
  46. 46 OTHER SWAPS 93
    1. 1. Case study: the P&G-BT “5/30” swap 93
    2. 2. Exercise 94
  47. 47 INTRODUCTION 95
    1. 1. Competition between OTC and Exchanges 95
    2. 2. Contract specifications 95
    3. 3. Cash dividends and stock splits 95
  48. 48 Section 0: exercises 95
  49. 49 Section 1: same old friends 96
    1. 1. Payoff diagrams 96
  50. 50 Section 2: taxonomy trading strategies 97
    1. 1. Trading strategies 97
  51. 51 Section 3: hedges 98
    1. 1. Covered call 98
    2. 2. Protective put 98
  52. 52 Section 4: spreads 99
    1. 1. Vertical spreads based on two option series 99
    2. 2. Vertical spreads based on three or more option series 101
  53. 53 Section 5: combinations 102
    1. 1. Comparing a straddle with a strangle 103
  54. 54 Section 6: exercises 103
  55. 55 Section 7: reverse engineering 103
    1. 1. Replicating the payoff profile of a bull spread 103
    2. 2. Replicating the payoff profile of a butterfly spread 104
    3. 3. A more difficult situation… 104
  56. 56 Section 0: introduction 106
    1. 1. Is there an arbitrage opportunity? 106
  57. 57 Section 1: European Call (no dividends) 106
    1. 1. The upper bound 106
    2. 2. The lower bounds 106
    3. 3. Summary 107
  58. 58 Section 2: European Call (with dividends during the lifetime of the option) 107
    1. 1. The new bounds 107
    2. 2. Summary 108
  59. 59 Section 3: American Call (no dividends) 108
    1. 1. The upper bound 108
    2. 2. The lower bounds 108
    3. 3. Summary 109
    4. 4. What about early exercise? 109
  60. 60 Section 4: American Call (discrete dividends) 109
    1. 1. The new bounds 110
    2. 2. Summary 110
    3. 3. Early exercise condition 110
  61. 61 Section 5: European put 111
    1. 1. Restrictions - no dividend case 111
    2. 2. The intrinsic value of the put 112
    3. 3. Restrictions - discrete dividend case 112
  62. 62 Section 6: American put 113
    1. 1. Restrictions - no dividend case 113
    2. 2. Another view on early exercise 113
  63. 63 Section 7: Exercises 114
  64. 64 Section 0: introduction 115
    1. 1. European put-call parity 115
    2. 2. American put-call parity (no dividends) 116
    3. 3. American put-call parity (dividends case) 116
  65. 65 Section 1: Exercises 117
  66. 66 Section 0: introduction 118
    1. 1. Determinants 118
    2. 2. Overview 118
  67. 67 Section 0: discrete time and continuous time 120
  68. 68 Section 1: the one period binomial model 120
    1. 1. The CRR (1979) example 121
    2. 2. The pricing recipe 122
    3. 3. The CRR (1979) example 123
    4. 4. Remarks 123
    5. 5. Risk neutral valuation 127
  69. 69 Section 2: the multi period binomial model for European options 128
    1. 1. The two period binomial model 128
    2. 2. The three period model 130
    3. 3. The N-period model 130
    4. 4. Black Scholes formula 134
    5. 5. For those who don’t like manual work 134
  70. 70 Section 3: American options 135
    1. 1. American style 135
    2. 2. Pricing an American put 136
  71. 71 Section 4: Exercises 136
  72. 72 Section 1: basic concepts 137
    1. 1. Evolution of a riskless asset in continuous time 137
    2. 2. Evolution of a risky asset in time 138
  73. 73 Section 2: examples of (continuous time) stochastic processes 138
    1. 1. Gaussian White Noise 138
    2. 2. The Wiener process 140
    3. 3. An Ito-process 143
    4. 4. Stochastic processes in Excel 145
  74. 74 Section 3: working with random functions 146
    1. 1. The derivative of a function 146
    2. 2. The derivative of a random function 146
    3. 3. The Ito-Döblin Lemma (Ito’s Lemma) 146
  75. 75 Section 4: finance related examples 147
    1. 1. Forward contracts 147
    2. 2. Continuous returns 148
    3. 3. The lognormal distribution 149
    4. 4. Confidence intervals 149
  76. 76 Section 4: Exercises 150
  77. 77 APPENDICES 150
    1. 1. The Markov Property 150
    2. 2. Distribution of annualized log returns 150
  78. 78 Section 0: introduction 152
    1. 1. Recall Ito’s Lemma 152
    2. 2. The fundamental Partial Differential Equation (PDE) 152
  79. 79 Section 1: Risk Neutral Valuation (under the ? measure) 153
    1. 1. Forward contract RNV 154
    2. 2. European call option RNV - proof of the Black-Scholes Model 154
    3. 3. Black-SCholes put pricing model 156
  80. 80 Section 2: applying the Black-Scholes model 157
    1. 1. Input parameters 157
    2. 2. Time to maturity estimation 157
    3. 3. Volatility estimation 157
  81. 81 Section 3: option pricing & dividends 158
    1. 1. Recall 158
    2. 2. Continuous dividend yield 159
    3. 3. Discrete dividends 160
    4. Conclusion 160
  82. 82 Section 0: delta hedging 162
    1. 1. Motivation 162
    2. 2. Dynamic delta hedging 163
  83. 83 Section 1: Greek for risk managers 164
    1. 1. The delta 164
    2. 2. The gamma 165
    3. 3. The theta 166
    4. 4. The vega 167
    5. 5. The rho 168
    6. 6. Overview 168

Infos sur le Document

Cours
Business Engineering: Financial Engineering
Publié le
5 février 2026
Nombre de pages
168
Écrit en
2025/2026
Type
Resume
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