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Index
Market Consistency
Contents
Preface
Acknowledgements
Abbreviations
Notation
1 Introduction
1.1 Market consistency
1.2 The primacy of the ‘market’
1.3 Calibrating to the ‘market’
1.4 Structure of the book
1.5 Terminology
2 When is and when isn’t Market Consistency Appropriate?
2.1 Introduction
2.2 Drawing lessons from the characteristics of money itself
2.2.1 The concept of ‘value’
2.2.2 The time value of money
2.2.3 Axioms of additivity, scalability and uniqueness
2.2.4 Market consistent valuations
2.2.5 Should financial practitioners always use market consistent valuations?
2.2.6 Equity between parties
2.2.7 Embedded values and franchise values
2.2.8 Solvency calculations
2.2.9 Pension fund valuations
2.2.10 Bid–offer spreads
2.3 Regulatory drivers favouring market consistent valuations
2.4 Underlying theoretical attractions of market consistent valuations
2.5 Reasons why some people reject market consistency
2.6 Market making versus position taking
2.7 Contracts that include discretionary elements
2.8 Valuation and regulation
2.9 Marking-to-market versus marking-to-model
2.10 Rational behaviour?
3 Different Meanings given to ‘Market Consistent Valuations’
3.1 Introduction
3.2 The underlying purpose of a valuation
3.3 The importance of the ‘marginal’ trade
3.4 Different definitions used by different standards setters
3.4.1 Introduction
3.4.2 US accounting – FAS 157
3.4.3 Guidance on how to interpret FAS, IAS, IFRS, etc.
3.4.4 EU insurance regulation – ‘Solvency II’
3.4.5 Market consistent embedded values
3.4.6 UK pension fund accounting and solvency computation
3.5 Interpretations used by other commentators
3.5.1 Introduction
3.5.2 Contrasting ‘market consistent’ values with ‘real world’ values
3.5.3 Stressing the aim of avoiding subjectivity where possible
3.5.4 Extending ‘market consistency’ to other activities
3.5.5 Application only if obvious market observables exist
3.5.6 Hedgeable liabilities
3.5.7 Fair valuation in an asset management context
4 Derivative Pricing Theory
4.1 Introduction
4.2 The principle of no arbitrage
4.2.1 No arbitrage
4.2.2 Valuation of symmetric derivatives
4.2.3 Valuation of asymmetric derivatives
4.2.4 Valuation of path dependent derivatives
4.3 Lattices, martingales and ˆIto calculus
4.3.1 Lattice valuation approaches
4.3.2 Stochastic (ˆIto) calculus
4.3.3 The martingale formulation
4.3.4 Hedging
4.3.5 Path dependent derivatives
4.4 Calibration of pricing algorithms
4.4.1 Market conventions versus underlying market beliefs
4.4.2 Why calculate market implied parameters such as implied volatility?
4.4.3 The volatility smile or skew
4.5 Jumps, stochastic volatility and market frictions
4.5.1 Mileage options
4.5.2 Jump processes
4.5.3 Stochastic volatility
4.5.4 Non-zero dealing costs
4.5.5 Interpretation in the context of Modern Portfolio Theory
4.6 Equity, commodity and currency derivatives
4.7 Interest rate derivatives
4.8 Credit derivatives
4.9 Volatility derivatives
4.10 Hybrid instruments
4.11 Monte Carlo techniques
4.12 Weighted Monte Carlo and analytical analogues
4.12.1 Weighted Monte Carlo
4.12.2 Analytical weighted Monte Carlo
4.13 Further comments on calibration
5 The Risk-free Rate
5.1 Introduction
5.2 What do we mean by ‘risk-free’?
5.3 Choosing between possible meanings of ‘risk-free’
5.3.1 Real world or market consistent?
5.3.2 Choice between different reference rates
5.3.3 How risk-free is government debt?
5.3.4 Impact of choice of reference rate
6 Liquidity Theory
6.1 Introduction
6.2 Market experience
6.3 Lessons to draw from market experience
6.3.1 Consideration of ‘extreme’ events
6.3.2 Or maybe not such extreme events?
6.3.3 Contagion
6.4 General principles
6.5 Exactly what is liquidity?
6.5.1 Different points of view
6.5.2 Funding versus market liquidity
6.5.3 The impact of these different points of view
6.5.4 Modelling liquidity premia on different instruments
6.6 Liquidity of pooled funds
6.7 Losing control
7 Risk Measurement Theory
7.1 Introduction
7.2 Instrument-specific risk measures
7.3 Portfolio risk measures
7.3.1 Introduction
7.3.2 Ex-post (i.e. historic, backward-looking, retrospective) risk measures
7.3.3 Ex-ante (i.e. forward-looking, prospective) risk measures
7.4 Time series-based risk models
7.4.1 Risk ‘models’ versus risk ‘systems’
7.4.2 Mathematical characterisation of different types of risk model
7.4.3 Intrinsic ways of estimating risk models from past data
7.4.4 Matrix analysis
7.4.5 The link back to pricing algorithms
7.4.6 Choice of underlying distributional form
7.4.7 Monte Carlo methods
7.4.8 Summary
7.5 Inherent data limitations applicable to time series-based risk models
7.5.1 The sparsity of the data available
7.5.2 Idiosyncratic risk
7.6 Credit risk modelling
7.6.1 Introduction
7.6.2 Credit ratings
7.6.3 Market consistency
7.6.4 Collateralised debt obligations (CDOs)
7.6.5 An accident waiting to happen?
7.6.6 Conduits and structured investment vehicles (SIVs)
7.7 Risk attribution
7.7.1 Intrinsic rationale
7.7.2 Traditional (covariance-based) risk attribution
7.7.3 Risk attribution applied to other types of risk measure
7.7.4 ‘Stand-alone’ risk statistics
7.8 Stress testing
7.8.1 Introduction
7.8.2 Different interpretations
7.8.3 Further comments
8 Capital Adequacy
8.1 Introduction
8.2 Financial stability
8.3 Banking
8.3.1 The Basel Accords
8.3.2 Market risk
8.3.3 Credit risk
8.3.4 Operational risk
8.4 Insurance
8.4.1 Solvency II
8.4.2 Underlying approach
8.4.3 Best estimate calculations
8.4.4 Surrender rates
8.4.5 UK regulatory capital computations for insurers
8.4.6 Categorising risks
8.5 Pension funds
8.6 Different types of capital
9 Calibrating Risk Statistics to Perceived ‘Real World’ Distributions
9.1 Introduction
9.2 Referring to market values
9.3 Backtesting
9.3.1 Introduction
9.3.2 In-sample versus out-of-sample backtesting
9.3.3 Testing backtest quality statistically
9.3.4 Intra-period position movements
9.3.5 Calibration of credit default models
9.4 Fitting observed distributional forms
9.5 Fat-tailed behaviour in individual return series
9.5.1 Identifying the true underlying return series
9.5.2 Fat tails
9.5.3 Skew, kurtosis and the (fourth-moment) Cornish-Fisher approach
9.5.4 Weaknesses of the Cornish-Fisher approach
9.5.5 Improving on the Cornish-Fisher approach
9.5.6 Time-varying volatility
9.5.7 Crowded trades
9.5.8 Bounded rationality
9.6 Fat-tailed behaviour in multiple return series
9.6.1 Introduction
9.6.2 Visualising fat tails in multiple return series
9.6.3 Copulas, Sklar’s theorem and quantiles
9.6.4 Fractile–fractile (i.e. quantile–quantile box) plots
9.6.5 Time-varying volatility
9.6.6 Differentiating between return series
10 Calibrating Risk Statistics to ‘Market Implied’ Distributions
10.1 Introduction
10.2 Market implied risk modelling
10.2.1 Refining the granularity-based approach to risk modelling
10.2.2 Time horizons
10.2.3 Additivity, scalability and coherence
10.3 Fully market consistent risk measurement in practice
10.3.1 Comparison with current risk management practices
10.3.2 The CDO analogy
11 Avoiding Undue Pro-cyclicality in Regulatory Frameworks
11.1 Introduction
11.2 The 2007–09 credit crisis
11.3 Underwriting of failures
11.4 Possible pro-cyclicality in regulatory frameworks
11.5 Re-expressing capital adequacy in a market consistent framework
11.6 Discount rates
11.7 Pro-cyclicality in Solvency II
11.8 Incentive arrangements
11.9 Systemic impacts of pension fund valuations
11.10 Sovereign default risk
12 Portfolio Construction
12.1 Introduction
12.2 Risk–return optimisation
12.2.1 Introduction
12.2.2 The basic mathematics of risk–return optimisation
12.2.3 Mean–variance optimisation
12.2.4 Constraint-less mean–variance optimisation
12.2.5 Alpha–beta separation
12.2.6 Multi-period mean–variance optimisation
12.3 Other portfolio construction styles
12.4 Risk budgeting
12.4.1 Introduction
12.4.2 Information ratios
12.4.3 Sensitivity to the input assumptions
12.4.4 Sensitivity to the universe from which ideas are drawn
12.5 Reverse optimisation and implied view analysis
12.5.1 Implied alphas
12.5.2 Consistent implementation of investment ideas across portfolios
12.6 Calibrating portfolio construction techniques to the market
12.7 Catering better for non-normality in return distributions
12.7.1 Re-normalising historic return distributions
12.7.2 Using co-skew, co-kurtosis and other co-moments
12.8 Robust optimisation
12.8.1 Black-Litterman
12.8.2 Re-sampling
12.9 Taking due account of other investors’ risk preferences
13 Calibrating Valuations to the Market
13.1 Introduction
13.2 Price formation and price discovery
13.2.1 The price formation process
13.2.2 Price discovery
13.3 Market consistent asset valuations
13.3.1 Introduction
13.3.2 Relatively simple assets independent of the firm
13.3.3 More complex assets independent of the firm
13.3.4 Assets that include risk exposures linked to the firm
13.3.5 Further comments
13.4 Market consistent liability valuations
13.4.1 Introduction
13.4.2 Sure promises from infinitely well-capitalised entities
13.4.3 Uncertain promises from finitely capitalised entities
13.4.4 The solvency put option
13.4.5 Bid and offer prices
13.4.6 Annuities
13.4.7 Unit-linked life insurance
13.4.8 With-profits (i.e. participating) business
13.4.9 Other non-profit non-linked life insurance
13.4.10 Non-life (i.e. property/casualty) insurance
13.4.11 Bank deposits
13.5 Market consistent embedded values
13.6 Solvency add-ons
13.6.1 Introduction
13.6.2 Current methodologies
13.6.3 Full market consistency
13.6.4 Correlations
13.6.5 Equity market and yield curve movements (market risk)
13.6.6 Credit risk
13.6.7 Liquidity risk
13.6.8 Bid–offer spreads
13.6.9 Expense risk
13.6.10 Systemic mortality and longevity risks (insurance risk)
13.6.11 Other demographic risks
13.6.12 Operational risk
13.6.13 Non-life (i.e. property/casualty) insurance risk
13.7 Defined benefit pension liabilities
13.7.1 Introduction
13.7.2 Solvency valuations
13.7.3 Ongoing valuations
13.7.4 Transfer values
13.8 Unit pricing
14 The Final Word
14.1 Conclusions
14.2 Market consistent principles
Bibliography
Index
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