“Financial Risk and Crisis Management after
the Global Financial Crisis” Series No.2 (11/2015)

New Movements of Financial Risk Analysis
in Post-Financial Crisis1

Hisashi Nakamurai
Associate Professor, Graduate School of Commerce and Management,
Hitotsubashi University

1 This document is an English translation of the original Japanese, which appears in theNov. 2015 edition of The Japan Economic Research Institute Monthly Report, publishedby The Japan Economic Research Institute.

Overview
Over the past quarter century, financial markets have witnessed
remarkable growth in financial techniques, including securitization and thedevelopment of derivative products. The free use of these techniques allowed
for subdividing individual business risks and diversifying as well as
disseminating those risks into an enormous capital market. This led to thethought in the mid-2000s that financial markets and real economies had
succeeded in constructing an iron-clad system to manage risk. However, in2007 and the years that followed, the subprime mortgage crisis and thebankruptcy of Lehman Brothers revealed the obfuscatious nature ofdiversified risk when absorbed into the capital market, and unprecedented
losses were inflicted on financial markets and real economies. Given theexperience of this world financial crisis, the previous standard arbitrage-freepricing approach alone is insufficient to completely analyze recent
movements in financial markets and the financial risks found therein. Thishas prompted the construction of a new asset valuation (asset pricing) modelthat can appropriately explain financial risk in the post-global financial
crisis period, which is an urgent issue for both academics and those working
in the financial field. Outlining a brief review of the fundamentals of theasset price research theory, this study presents new movements in the
post-financial crisis financial risk analysis and provides a guide toward
future research.

1. Introduction
Financial techniques have significantly evolved over the past quarter
century, including securitization and derivative product development. The
free use of these techniques allowed for subdividing individual business risks
and diversifying as well as disseminating those risks into an enormous
capital market. This led to the thought in the mid-2000s that financial
markets and real economies had succeeded in constructing an iron-cladsystem to manage risk. However, in 2007 and the years that followed, thesubprime mortgage crisis and the bankruptcy of Lehman Brothers revealed
the obfuscatious nature of diversified risk when absorbed into the capital
market, and unprecedented losses were inflicted on financial markets andreal economies.
Given the experience of this world financial crisis, the previous standard

arbitrage-free pricing approach alone is insufficient to completely analyze
recent movements in financial markets and the financial risks found therein.
Most notably, the presence of asymmetric information (moral hazard,
adverse selection, monitoring), transaction costs, defaults, psychologicalcauses, network effects, and other sources of financial friction rendermarkets incomplete, thus making the analysis of asset pricing a troublesome
affair. Considering these points, the construction of a new asset valuation(asset pricing) model that can appropriately explain financial risk in the
post-global financial crisis period has become an urgent issue for bothacademics and those working in the financial field.
This study serves the following purposes: first, it provides a basic review of
the asset pricing theory; second, it presents new movements in the
post-financial crisis asset pricing theory and financial risk analysis; third, itsuggests the direction of future research in this area. However, theconstruction of a universal asset pricing model in an incomplete market
wherein various sources of financial friction exist is a difficult matter.
Considering this, this study introduces new asset pricing and valuation
models with respect to numerous specific financial friction sources.
Specifically, this study presents nine pieces of research conducted with grantfunding from Japan’s MEXT, which comprise the “Construction of new
Interest/Exchange Valuation Models After the Global Financial Crisis”(Class B, general, headed by Eiji Ogawa, reference number 25285098 ),focusing on the financial friction sources of network effects and moral hazard
in introducing three pieces of research on asset valuation and pricing fromtheoretical, demonstrative, and numerical analytical perspectives. The firstpiece of research is a numerical analysis of network effects-related asset
pricing models based on the study by Kobayashi and Nanpo (2016),
considering a financial market model incorporating causes from behavioral
finance and investment behavior. The second piece of research, based on the
study by Takamizawa (2015), explores demonstrative research on interest
rate volatility forecasting using data found in the yield curve. The third pieceof research, based on the study by Misumi et al. (2015), provides theoretical
validation for the distorting effects of moral hazard on prices in the financial
market. Significant focus is placed on the third area of research as it is basedon my research.
The remainder of this paper is structured as follows: Section 2 reviews
fundamental theory on asset pricing analysis and financial risk analysis.

Section 3 presents new trends in asset pricing analysis and financial risk
analysis as they have unfolded in recent times. Section 4 presents an overall
conclusion and suggests directions for future research.

2. Frameworks for Asset Pricing Analysis: Arbitrage-Free andEquilibrium Approaches
Here, we provide a low-level review of the framework that supports asset
price analysis based on the textbooks of Duffie (2001) and Cochrane (2005);
specifically, we address arbitrage-free and equilibrium methods and related
topics.
2.1 Basic Assumptions
Let us consider a one-period two-date economic model（t ∈｛ 0, 1 ｝）.2 Thiseconomy is exposed to uncertainty, and a finite set of scenarios｛ 1,・・・, S ｝
is possible. Though which scenario will occur is unclear at date 0, it isrevealed at date 1. The chance of each scenario occurring is indicated by
あああああああああ , ああああ. Also, N securities exist within this economy’s
financial market, with security structures reflected by an N × S matrix,
indicated by D =｛ Dis ｝（i ∈｛ 1,・・・,N ｝, s ∈a. In other words, Dis
represents the payoff of security i in scenario s at date 1. The security priceat date 0 has N elements, represented as q, and the security portfolio
purchased at date 0 has N elements, represented as θ. Security portfolio θ ’smarket value is, and payoff is D⊤θ. In other words, an economic
entity purchases security portfolio θ at date 0 for the price of ・θ, receivingD⊤θ at date 1 depending on the scenario. Here, we utilize two presumptions.
Given (1): Payoff space X is.
This presumption relates to market transaction opportunities, which implies
that an economic entity may freely purchase or sell securities at date 0 toform a portfolio.
Given (2): The price for payoff x ∈X is represented as qx, and a π existsthat satisfies x ＝ π（x） at which x1, x2 ∈ and a, b ∈ R (note that R
represents the set of real numbers) can be constructed as.
This is known as the law of one price and implies the linearity of pricing
2

For more details, see Duffie (2001) and Cochrane (2005)

and guarantees that all portfolios with the same payoff also have the same
price; that is, rearranging payoffs will result in no gain.
In the asset pricing theory, we validate what properties π will have whensecurity structure D is observed with security price q. In particular, we mayfind the state-price concept useful in applying characteristics to π. A
state-price security (or Arrow–Debreu security) is defined as one that pays
off a unit of a numeraire if a particular state occurs, with no payoff in otherstates with price vector＝ （1, ・・・, s, ・）.. . Therefore, s ＝ π（1s）thexists. Here, only the s element results in 1, whereas other elements resultin zero in an s-dimensional column vector, which represents theArrow–Debreu security’s payoff in state s. We may notate this as q ＝ D
based on our two given conditions.
2.2 Arbitrage-Free Opportunities and Incomplete Markets
However, we cannot simply utilize π，ψ to assign characteristics in ananalytical or numerically analytical fashion to asset pricing and financial
risk movements for all security structures and market transaction
opportunities. Actual financial operations will analyze asset pricing undermore realistic restrictions on security structures and the market transaction
environment. Arbitrage opportunities are defined as [q・θ≤ 0 ∪ D ⊤θ＞ 0]
and [q・θ＜ 0 ∪ D ⊤θ≥ 0] for portfolio θ. In general, this refers to theopportunity of realizing a gain by the simple act of holding portfolio θ.
Therefore, the nonexistence of arbitrage opportunity (arbitrage-freeopportunity) means that there is no free gain to be made (stochastically).
This is a more stringent restriction compared with our second given
condition. Here, we posit
Theorem 2.1: In the absence of arbitrage opportunity, and only in such anoccasion, a positive state price must exist. However, though this positive
state price exists in this situation, it does not necessarily follow that it is the
only possible state price.
Yet, another classic restriction is that of a complete market. A complete
market means that any payoff pattern may be replicated within the market.
In particular, when the number of states is limited, a market is complete
when the number of market assets is equal to the number of states. This
restriction is more stringent than our first given condition. Here, we posit
Theorem 2.2: When the market is complete, if and only if there is anabsence of arbitrage opportunity, a single positive price state vector will

exist.
Since a single positive state price vector exists in this situation, this canprove useful in analyzing financial market asset pricing. However, therestriction of a complete market is stringent in practice. For example,
transaction costs, asymmetric information, defaults, etc. may render themarket incomplete.
In actual financial risk and asset pricing analyses, these and otherrestrictions provide the basis for analyzing state price characteristics. Morespecifically, analysis methods are largely categorized into arbitrage-free andequilibrium methods. As these are complementary approaches, they must be
utilized under different circumstances. The following is a simple explanationof these two approaches and their reciprocity.
2.3 Arbitrage-free Method
The arbitrage-free method presumes the absence of arbitrage opportunity
in a complete market, extractingπ,from an existing security
structure/price regardless of whether it is explicit or implicit, valuing othersecurities through replication based on risk-neutral probability. A classic
example of this is the Black–Scholes option pricing model. Arbitrage-freepricing models are characterized by their convenience in price valuation for
securities through replication, whereas their applicability in incomplete
markets is restricted. The existence of corporate bankruptcy, imperfect
information (moral hazard, adverse selection, monitoring), transaction cost,and other sources of financial friction will render markets incomplete,making it difficult to directly apply an arbitrage-free approach.3
2.4 Equilibrium Method
A second analytical method is the equilibrium approach. Based on our
fundamental assumptions, when a representative economic entity accesses a
securities market characterized by（D, q） , it will optimally allocate assets
for optimal consumption to achieve maximal expected utility. The
equilibrium approach seeks out a price function π (or) in which thisoptimal allocation allows for market equilibrium in the economy. Althougharbitrage-free methods also take a particular view on equilibrium, the3

There have naturally been significant attempts to apply arbitrage-free pricing approaches toincomplete markets in academia and in the field; however, wide-ranging mathematical limitations
outside of arbitrage opportunity-free scenarios are often imposed.

“equilibrium” in the equilibrium approach refers to (1) maximization of agiven value (here, expected utility) by an economic entity within its
budgetary restrictions, given the use of consumption/investment/asset
allocation, and (2) the state of complete market clearance in financial assets.
If we work through these problems of optimization under the appropriate
mathematical conditions, then we realize that for optimal consumption, state
price is comparable with marginal utility. Consequently, a security’s price
may be characterized as a function of the potential economic environment(output in this scenario). Moreover, even in an incomplete market, asset
pricing becomes possible as long as an optimal solution can be discerned.
Thus, we may build upon these fundamental presumptions by introducing
information problems (moral hazard, adverse selection, monitoring),
transaction costs, and other sources of financial friction in using theequilibrium approach to seek out a state price, thereby being able tostructurally analyze the effects of movements in financial friction sourcesand outputs (market conditions and company performances) on asset pricing
and market risk. If a state price is found through the equilibrium method
when the market is incomplete, then this particular state price is considered
to be one of the multiple appropriate state prices that could be derived anddoes not exclude the presence of other state prices. The equilibrium approach
can be characterized by having the advantage of structurally deriving a state
price without presupposing a complete market while being easily exposed tomodel risk due to the state price’s dependence on the model structure.
Overall, arbitrage-free pricing and equilibrium approaches have limitations
imposed on their application. If we then consider that the assumption ofincomplete markets for risk analysis is inevitable after the financial crisis,
then it is conceivable that a more preferable stance may be to apply either
one approach or the other in a complementary fashion depending on thesituation.

3. Analysis of Post-financial Crisis Asset Pricing/Financial Risk
Using the Equilibrium ApproachThis section presents recent research on the equilibrium method in relation
to asset pricing and financial risk movements under restriction from sourcesof financial friction; specifically, three new analyses of asset
valuation/financial risk are presented. These analyses are based on theresearch conducted with grant funding from Japan’s MEXT, “Construction of
new Interest/Exchange Valuation Models After the Global Financial Crisis”(Class B, general, headed by Eiji Ogawa, reference number 25285098). The
first piece of research is a numerical analysis of network effects-related asset
pricing models based on the study by Kobayashi and Nanpo (2016),
considering a financial market model incorporating causes from behavioral
finance into investment behavior. The second piece of research, based on the
study by Takamizawa (2015), explores demonstrative research on interest
rate volatility forecasting using data found in the yield curve. The third pieceof research, based on the study by Misumi et al. (2015), provides theoretical
validation for the distorting effects of moral hazard on prices in the financial
market. Significant focus is placed on the third area of research as it is basedon my research.
3.1 A Price Fluctuation Model for Financial Markets Constructed from
Investment Behavior
The complex mixture of credit and liquidity problems during the global
financial crisis revealed peculiar price fluctuations in financial markets. As
such, studies thus far have proposed numerous models to tackle the questionof the nature of price variation in stocks and other such items. However, thegreater part of existing models was created ex post facto with stochastic
items to apply to actual price movements; thus, this stochastic format does
not provide a clear explanation beyond statistical effects.
In contrast to the models proposed thus far, we do not presuppose thatmovements that may appear random are of exogenous probability. We
instead utilize the structure created by a swath of investors engaged indeterministic investment behavior to produce a model and reproduce market
price fluctuations among investor interdependence (networks) withnumerical calculations. In other words, we do not engage in stochastic
estimation based on the financial market’s output (price movements) but
construct a financial market model whereby price is determined throughequilibrium between total sales and purchase volumes across all investors in
the market, given that those investors base deterministic investment
strategies on past price movements. Investor behavior has someinterdependence in the market, which leads to network effects. Therefore, we
can increase the number of investors and conduct numerical analyses tovalidate the network effects of investor behavior.

The results indicate that regardless of the absence of random elements ininvestor decision making, deterministic investment behavior feeds onto itself
in the market and deteriorates into a chaotic phenomenon whereby
seemingly random price fluctuations are generated. The results of this study
imply that the act of presupposing a probability model, as in models
proposed thus far, is not the only method for modeling financial markets.
3.2 Predicting Interest Volatility via Information Extracted from the Yield
Curve
Takamizawa (2015) constructed and verified time series models to explain(1) interest rate time series behavior and (2) a cross-section of risk premiums
demanded by investors with respect to interest rate variation factors, thus
clarifying the key conditions necessary for constructing an interest rate
model. In previous studies, a problem of contradiction between time series
and cross-sections was found, and time series analysis did not completely
consider cross-sectional information in the yield curve. In contrast, thisstudy utilizes the US interest rate data comprising LIBOR and swap rates
and empirically explains interest rate volatility using cross-sectional
information inherent to the yield curve. Specifically, it expounds thatinterest rate volatility has a uniformly non-linear function across all interest
rate factors (three were used in the proof) versus yield curve information.
The following three items represent the major results of that analysis. First,(the non-linear function of) interest rate factors suffice well to explain thevolatility of the yield curve’s “slope.” Second, (the non-linear function of)interest rate factors can explain the volatility of the yield curve’s “curvature”
when combined with volatility factors. Third, though interest rate models
that satisfy arbitrage-free conditions have been said to face troubles insimultaneously explaining the data’s cross-sectional directionality and timeseries directionality, discoveries here reveal that resolving the mutual
exclusion problem of time series and cross-sectional areas without needlessly
increasing the number of factors is possible. Though this study does not
absolutely presuppose an equilibrium approach, its demonstrative uniform
explanation of both cross-sectional and time series areas in a reduced form
conceivably implies the construction of a financial model based on theequilibrium approach.

3.3 Distortion Effects of Moral Hazard on Financial Market Prices
Misumi et al. (2015) formulated equilibrium asset price valuation whenmoral hazard is present. Moral hazard is considered to be one of the mostserious problems in finance, and the moral hazard in investment banks thatcaused the recent financial crisis reminded the world once again of its
potentially disastrous effects. A significant body of research has examinedmoral hazard in the corporate finance world (e.g., Tirole, 2006, Section 3.2).
As an example of moral hazard, if an investor is unable to observe themanagement effort made by the firm in which they invest, then the firm’s
management may neglect maximizing corporate value and instead prioritize
personal gain, causing a loss to the investor. To mitigate the threat of loss bymoral hazard, investors engage in loans/investments through contracts
meant to incentivize efforts by the firm’s management to maximize value.
Consequently, we understand that moral hazard may distort optimal risk
sharing and/or optimal allocation.
However, not all these distortions on the most micro levels of firms andinvestors in the financial world lead to possible moral hazard in the market.
If risk sharing or allocation were to be altered, then investor marginal utility(or state price [density]) would be altered as well, thus exerting influence not
only on corporate value but also on all financial asset pricing on a macrolevel. Considering the recent financial crisis, investment banks would sell off
loans via securitization, lowering oversight incentives. Moreover, hedge
funds would induce strategic insolvency through selfish investment behavior.
These and other examples of microdistortions from many different forms of
moral hazard at corporations and financial institutions accumulated acrossthe market create instability on a macro level.
Considering this, recent years have witnessed a rapid proliferation in
research analyzing the market’s unstable macroenvironment due to moral
hazard. However, moral hazard asset pricing valuation models in the past
have not been well established in the areas of asset pricing theory andfinancial engineering. How much return on investment would be demanded
in reality by investors to manage the loss from moral hazard faced bycompany management? For example, how much return would be demandedby an investor when selfish investment behavior by a hedge fund facing
moral hazard may distort the investment return? Moreover, how much wouldthat accumulate and distort the total investment return across the entire
market? Answers to these questions are yet to be revealed either

academically or in the financial field.
Moral hazard may take many forms in financial operations; recent macro
research broadly classifies moral hazard into three major categories. He andKrishnamurthy (2012, 2013) posited the existence of diversion, whereby afinancial institution neglects asset management and misappropriates
revenues for personal benefit. More specifically, their study investigated the
addition of limitations on capital holdings to curtail moral hazard anddetermined how asset pricing is distorted therein. Brunnermeier andSannikov (2014) explored the effect of financial institutions’ financial
positions on asset pricing under a similar scenario, particularly analyzing
the volatility paradox noted by Kocherlakota (2000). These bodies of researchtake continuous-time optimal restructuring contract models developed by
Biais et al. (2007), DeMarzo and Fishman (2007), and DeMarzo andSannikov (2006) and develop their premises in support of the construction ofasset pricing models.
Ou-Yang (2005) also posited that while a firm’s efforts toward on-demand
production increase (a drift item) adds cost burden to the firm, an investor
entity will not be able to directly observe the level of the firm’s efforts. Moralhazard can then be characterized by changes in drift. This applies thecontinuous-time contract models of Holmström and Milgrom (1987) and
Schättler and Sung (1993) in an asset pricing model framework and develops
a weak mathematical formulation for a company’s stochastic control
problems. Similar to Ou-Yang (2005), Nakamura (2016) also categorized
moral hazard as related to drift control but sets a strong formulation for acompany’s stochastic control problems. This study applies the study byNakamura and Takaoka (2014) in an asset pricing model framework. The
differences between these weak and strong formulations are not solely
mathematical; they have implications for economics and financial theory as
well.4Myerson (2012) posited a third scenario whereby the success probability ofa firm/financial institution’s investment project is influenced by the
management’s efforts, which then incur costs that are directly unobservableby investors. Myerson (2012) analyzed the effects of moral hazard on
4

Please see Misumi et al. (2015) and Nakamura (2016) for more on the economic and financial
implications. In addition, for definitions of strong and weak solutions in stochastic differential
equations as well as strong and weak formulations for stochastic control, see Karatzas andShreve(1991), Yong and Zhou (1999), and other related works.

macroeconomics. A significant amount of in-depth analysis has been
performed on this type of moral hazard in areas such as corporate
governance and optimal contracting theory, with everything from textbooks
to research literature analyzing this classic model of moral hazard (see Tirole,
2006, Section 3.2 and other related literature). More recently, Biais et al.
(2010) analyzed optimal contracting considering moral hazard whereby afirm may make efforts and expend funds to decrease jump probability,
although an investor cannot observe the level of effort made by the firm. This
indicated that based on shareholder limited liability systems and bankruptcy
laws, company management is less motivated to reduce jump probability for
major negative jump risks that could exceed the firm’s asset value, therefore
suggesting that the contractually stipulated threat of reducing compensation
during poor performance periods was an optimal practice. Furthermore, thestudy indicated that if the threat of reducing compensation was only
marginally effective due to extremely low performance, then the threat of
reducing the scale of investments made in poor performance situations
would also serve such a function in optimal contracting.
Myerson (2012) applied this form of moral hazard to a macro-level analysis.
Myerson (2012) indicated that without long-term financial assets and evenwith a simple, non-stochastic, constant model, granting long-term
employment incentives could curtail moral hazard. In particular, given that
financial institutions established for different numbers of years will haveaccumulated different levels of trust based on the economic conditions they
have experienced, a situation whereby multiple financial institutions coexist
with differing qualities as such will lead to variations in employment statesacross each generation in accordance with changes in economic conditions.
Myerson’s (2012) study indicated that the effect of moral hazards could
therefore induce complex cyclical variations in the economy on amacroeconomic scale.
Our study, Misumi et al. (2015), aligns itself with this third classification. It
specifically focuses on moral hazard when the stochastic distribution of
success chances has a sizable downside in a scenario where bothBrownian-based normal distributions and overall probability measures(including negative jump probability) can be modified. Although this study
simulates jump probability controls much like in the study by Biais et al.
(2010), neither shareholder limited liability systems nor corporatebankruptcy will be seen under the setting of the most appropriate contract.

This study establishes a formula for how this nature of moral hazard exerts
distortive effects on asset pricing in the macro market, indicating in its
analysis that moral hazard reduces the Sharpe ratio, which decreases theappeal of investing in risk assets. It also indicates that this moral hazard
increases risk-free interest rates as it plays a “hedge” role in shifting market
risk prices opposite to investor marginal utility. We therefore understandthat the risk-free rate puzzle, initially explored by Weil (1989), is further
exacerbated by moral hazard. Finally, we understand that the distortions in
actual resources borne of moral hazard may be alleviated by investor accessto financial markets.

4. Conclusion
This study presents new analytic trends that incorporate experience fromfinancial crises to supplant more traditional financial risk analyses. However,though we present theory, proofs, and numerical analyses of new individual
segments while specifically focusing on various identification problems
involved with financial friction, we have not yet arrived at a point ofpractical application of these concepts. In going forward, investigating actual
implications for risk management as practiced by firms and financial
institutions will be necessary.

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i[Profile: Hisashi Nakamura]
Graduate School and Faculty of Commerce and Management,
Hitotsubashi University
Naka 2-1, Kunitachi City, Tokyo
Tel：042－580－8826．Fax：042－580－8747．
Email：hisashi.nakamura@r.hit-u.ac.jp.
Dr. Nakamura obtained a Ph.D in Economics from the University of Chicago
in 2005, taking on the assistant-professor position that same year at the
University of Tokyo and holding said position until 2011. He then joined
Hitotsubashi University and has held his position there since. Dr. Nakamura
was also on the main career track at the Bank of Japan from 1994 to 2001.
Recent research fields include risk management and asset pricing underasymmetric information – more specifically, given a common real-lifescenario whereby a firm holds propriety information not available toexternal investors, theoretically and mathematically analyzing said risk
management and financial asset valuation while securitization and thefinancial derivatives market continue their rapid growth, then deriving
implications for financial system stability.