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Unified Financial Analysis Risk & Finance Lab

This chapter provides an overview of market risk factors and their analysis modes. It covers important terms, different categories of risk factors, and their role in determining expected cash flows. The chapter also discusses the concepts of risk neutrality and risk-free rates for discounting.

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Unified Financial Analysis Risk & Finance Lab

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  1. Unified Financial Analysis Risk & Finance Lab Chapter 4: Market Risk Factors Willi Brammertz / Ioannis Akkizidis

  2. Table of Content Market Risk Factors Overview Some Important Terms Market Risk Factors and Different Analysis Modes

  3. Risk factors • Contract evens are state contingent!

  4. Double role of market risk factors • Market risk factors determine expected cash flows • Market risk factors used for discounting (interest rates, FX, stock indices, ....)

  5. Main categories • Interest rates • Term structures • Product rates • FX rates • Stock prices and indices • Commodity prices and indices • CreditRating spreads • Indices

  6. Table of Content Market Risk Factors Overview Some Important Terms Market Risk Factors and Different Analysis Modes

  7. Arbitrage free • There is no free lunch • There is no possibility to make systematic gain without taking risk (1 + r1)(1 + r1,2) = (1 + r2)2

  8. Risk neutral and risk free • Risk free • Risk does not exist • This is generally not the case • A risk free world can be constructed in some cases (call/put) • Risk neutrality • Risk does not matter (in decisions) • Risk has a zero prize • In a risk free world • Risk neutrality “applies” • Risk free rate for discounting • In a risky world • Risk neutrality does not exist • Risk neutral models still applied for convenience reasons • Credit-Risk spread as a correction

  9. Risk in Reality:St. Petersburg paradox • A coin of unit 1 is tossed until head appears • The payoff is 2^(i-1) if the first i-1 tosses were tails • How much are you ready to pay for the game? • How much should the fair pay-off be? = ∞

  10. Another example from financeWhy do smiles exist? • Implied volatilities tweak probabilities (σ) in order to get observed prices using risk free rates (same function as spreads) Implied Volatility Forward Strike

  11. Another exampleForward rates and forecasts • Forward rates are based on arbitrage considerations • Example: (1 + r1)(1 + r1,2) = (1 + r2)2 • Predominant upward slope of yield curves embed upward bias • Possible explanation: Mismatch between liquidity preferences and long term un-certainty • “Risk free” yield curves contain some risk premium • Arbitrage free models <> unbiased forecast

  12. Conclusions on risk • The world is not risk neutral • People prefer low but more likely gains to high but very unlikely pay-offs • If people take risks, they want to be paid for it • Nevertheless the bulk of finance (theory) is within a risk-neutral setting • Risk neutrality is primarily reflected within market evolutions models • Risk neutrality is achieved by arbitrary “tweaking” of parameters within models • Risk neutrality is convenient: Easy mathematical solutions • Real world models need “richer environment” (Ariadne)

  13. Table of Content Market Risk Factors Overview Some Important Terms Market Risk Factors and Different Analysis Modes

  14. Different types of market modelling Risk is assumed Real world models Arbitrage free models (forward rates)

  15. Static models (type I)Canonical A yield curve and its derivations • Zero coupons • Discount factors • Forward rates is sufficient in a static risk-free world with linear instruments • Border cases • BS model for options • Parametric VaR

  16. Clsong the GapCR-Spreads • Spreads are mini-yield curves (same mathematical treatment) • Spreads to model risk aversion (non risk neutral behavior)

  17. Stress tests – Type IIStatic What-If, MC What-If Same like type I but • Initial position calculated with actual market conditions • Stress applied on actual market conditions • Position recalculated with stressed conditions • Stressed VaR • Stress initial conditions • Yield curves, FX-rates • Volatilities • Apply standard VaR techniques

  18. Stochastic arbitrage free models (type III)Special Case of Dynamic MC Complex non-linear instruments need a distribution of the underlying dynamic risk factors paths for valuation Simple instruments can be solved analytically

  19. From type III to type VAnother important property • Forward rates are not economic forecasted rates • Forward rates are biased if taken for forecasting • We need “real world” models

  20. Real world models (Type V) Real world models are the models a typical economist would construct • What-If • Historical • Monte Carlo Scenarios (e.g. Ornstein Uhlenbeck) • Mean • Variance • Mean reversion Taking all economic knowledge into account (Mi, GDP, Unemployment etc.)

  21. Markets Counter-parties Behavior Contracts Arbitrage Free and Real World Modelling Real world models Arbitrage free models

  22. Parallel valuation techniques Arbitrage free models and real world models must coexist (example : determination of value within dynamic simulation) Needs strict separation of cash flow generation and discounting! For a „real“ real world case see chapter 17.4

  23. Synopsis of valuation techniques

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