Consistent Multinational Assumptions

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Consistent MultinationalAssumptions

• Stochastic Investment Models
• Working Party

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Autoregressionwithout a Free Lunch

• Keith Guthrie, Robert Howie
• Shyam Mehta Andrew Smith
• Stochastic Investment Models
• Working Party

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Presentation Overview

• Why did we write this paper?
• Autoregression and efficiency
• Using autoregressive models for pricing
• Deflators for a modified Wilkie model
• Discussion

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Motivation for the Paper
actuarial auto-regressive models
banking random walk models
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Regression Efficiency

• What do we mean by
• Autoregressive models
• Efficient markets
• What are the relationships between these ideas?

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Last years return was poor
This year we expect
more poor returns
average returns
extra good returns
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Efficiency Question of Degree
Objective to quantify the implied efficiency of
a model (making use of cross-sectional data)
free lunch
no risk premium
See supporting paper for definitions and
quantitative measures of efficiency.
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Autoregression Efficiency
Inefficiency S
positive autoregression
negative autoregression
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Example Model

• Long rate A, short rate B
• Parameters sA, sB, r
• Random error terms eA, eB
• N(0,1) with correlation r
• Functions mA and mB of At and Bt
• Recurrence relations
• At1 mAexpsAeAsA2/2
• Bt1 mBexpsBeB-sB2/2

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Short Rate Simulations
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Long Rate Simulations
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Models for Pricing

• Require deflators
• or equivalently, risk neutral law
• Only arbitrage-free models permit this
• inefficiency no obstacle (in theory)
• We know financial models that do this
• But are our favourite actuarial models up to the
  job?

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Finding a Deflator

• Model already implies some market inefficiencies
• Not necessarily an obstacle to pricing
• Provided arbitrage-free (which it is)
• Seek deflator
• Incomplete market problem
• Resolve ambiguity by applying minimum
  inefficiency principle
• Equivalent to utility formulation
• Read our paper for the formulas
• Equity and other markets see Kemp(2001)

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Simulated Deflators
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So in theory,

• We welcome Wilkies model to the fold of finance
  theory models
• Our modified Wilkie model implies (like other
  finance models)
• 100 of equities worth 100 of bonds
• Modigliani-Miller proposition
• (in absence of frictional costs)

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Example Application

• Can use deflators to price any cash flow
• In particular, a fixed cash flow
• Hence a spot curve family consistent with
  Wilkie-style models
• This solves the problem of finding arbitrage-free
  yield curves for the Wilkie model
• See some examples from different states
• keeping Wilkies long term parameters

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Implications Yield Curves (1)
50,000 sims
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And another
50,000 sims
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What is going on now?
50,000 sims
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And now the Bad News

• Deflator variability increases with inefficiency
• our quasi-Wilkie model had very variable
  deflators (and we set out to minimise that
  variability)
• Of 50,000 simulations, a few with huge deflators
  dominate valuations
• millions of simulations needed for convergence
• nesting eg for swaptions compounds the problem
• The solution works in theory
• Some computational breakthroughs needed to make
  solutions practical
• In the meantime, practical pricing models exist
  based on efficient FE approaches

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Points for Discussion

• What output is our advice based on?
• distributions?
• implied prices?
• Is it important to derive both?
• within the same model?
• role of market prices in calibration?

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Autoregressionwithout a Free Lunch

• Keith Guthrie, Robert Howie
• Shyam Mehta Andrew Smith
• Stochastic Investment Models
• Working Party