Three essays on asset pricing

In this dissertation, I investigate three related topics on asset pricing: the consumption-based asset pricing under long-run risks and fat tails, the pricing of VIX (CBOE Volatility Index) options and the market price of risk embedded in stock returns and stock options. These three topics are fully explored in Chapter II through IV. Chapter V summarizes the main conclusions. In Chapter II, I explore the effects of fat tails on the equilibrium implications of the long run risks model of asset pricing by introducing innovations with dampened power law to consumption and dividends growth processes. I estimate the structural parameters of the proposed model by maximum likelihood. I find that the stochastic volatility model with fat tails can, without resorting to high risk aversion, generate implied risk premium, expected risk free rate and their volatilities comparable to the magnitudes observed in data. In Chapter III, I examine the pricing performance of VIX option models. The contention that simpler-is-better is supported by the empirical evidence using actual VIX option market data. I find that no model has small pricing errors over the entire range of strike prices and times to expiration. In general, Whaley’s Black-like option model produces the best overall results, supporting the simpler-is-better contention. However, the Whaley model does under/overprice out-of-the-money call/put VIX options, which is contrary to the behavior of stock index option pricing models. In Chapter IV, I explore risk pricing through a model of time-changed Lvy processes based on the joint evidence from individual stock options and underlying stocks. I specify a pricing kernel that prices idiosyncratic and systematic risks. This approach to examining risk premia on stocks deviates from existing studies. The empirical results show that the market pays positive premia for idiosyncratic and market jump-diffusion risk, and idiosyncratic volatility risk. However, there is no consensus on the premium for market volatility risk. It can be positive or negative. The positive premium on idiosyncratic risk runs contrary to the implications of traditional capital asset pricing theory.

Three Essays on Asset Pricing

In this dissertation, I investigate three related topics on asset pricing: the consumption-based asset pricing under long-run risks and fat tails, the pricing of VIX (CBOE Volatility Index) options and the market price of risk embedded in stock returns and stock options. These three topics are fully explored in Chapter II through IV. Chapter V summarizes the main conclusions. In Chapter II, I explore the effects of fat tails on the equilibrium implications of the long run risks model of asset pricing by introducing innovations with dampened power law to consumption and dividends growth processes. I estimate the structural parameters of the proposed model by maximum likelihood. I find that the stochastic volatility model with fat tails can, without resorting to high risk aversion, generate implied risk premium, expected risk free rate and their volatilities comparable to the magnitudes observed in data. In Chapter III, I examine the pricing performance of VIX option models. The contention that simpler-is-better is supported by the empirical evidence using actual VIX option market data. I find that no model has small pricing errors over the entire range of strike prices and times to expiration. In general, Whaley’s Black-like option model produces the best overall results, supporting the simpler-is-better contention. However, the Whaley model does under/overprice out-of-the-money call/put VIX options, which is contrary to the behavior of stock index option pricing models. In Chapter IV, I explore risk pricing through a model of time-changed Lévy processes based on the joint evidence from individual stock options and underlying stocks. I specify a pricing kernel that prices idiosyncratic and systematic risks. This approach to examining risk premia on stocks deviates from existing studies. The empirical results show that the market pays positive premia for idiosyncratic and market jump-diffusion risk, and idiosyncratic volatility risk. However, there is no consensus on the premium for market volatility risk. It can be positive or negative. The positive premium on idiosyncratic risk runs contrary to the implications of traditional capital asset pricing theory.

Optimal Capital Requirements in Financial Networks with Fire Sales

I explore and analyze a problem of finding the socially optimal capital requirements for financial institutions considering two distinct channels of contagion: direct exposures among the institutions, as represented by a network and fire sales externalities, which reflect the negative price impact of massive liquidation of assets.These two channels amplify shocks from individual financial institutions to the financial system as a whole and thus increase the risk of joint defaults amongst the interconnected financial institutions; this is often referred to as systemic risk. In the model, there is a trade-off between reducing systemic risk and raising the capital requirements of the financial institutions. The policymaker considers this trade-off and determines the optimal capital requirements for individual financial institutions. I provide a method for finding and analyzing the optimal capital requirements that can be applied to arbitrary network structures and arbitrary distributions of investment returns.

In particular, I first consider a network model consisting only of direct exposures and show that the optimal capital requirements can be found by solving a stochastic linear programming problem. I then extend the analysis to financial networks with default costs and show the optimal capital requirements can be found by solving a stochastic mixed integer programming problem. The computational complexity of this problem poses a challenge, and I develop an iterative algorithm that can be efficiently executed. I show that the iterative algorithm leads to solutions that are nearly optimal by comparing it with lower bounds based on a dual approach. I also show that the iterative algorithm converges to the optimal solution.

Finally, I incorporate fire sales externalities into the model. In particular, I am able to extend the analysis of systemic risk and the optimal capital requirements with a single illiquid asset to a model with multiple illiquid assets. The model with multiple illiquid assets incorporates liquidation rules used by the banks. I provide an optimization formulation whose solution provides the equilibrium payments for a given liquidation rule.

I further show that the socially optimal capital problem using the ``socially optimal liquidation" and prioritized liquidation rules can be formulated as a convex and convex mixed integer problem, respectively. Finally, I illustrate the results of the methodology on numerical examples and

discuss some implications for capital regulation policy and stress testing.

Constructing good deals in discrete time arbitrage-free dynamic pricing models

Recent literature has proved that many classical pricing models (Black and Scholes, Heston, etc.) and risk measures (V aR, CV aR, etc.) may lead to “pathological meaningless situations”, since traders can build sequences of portfolios whose risk leveltends to −infinity and whose expected return tends to +infinity, i.e., (risk = −infinity, return = +infinity). Such a sequence of strategies may be called “good deal”. This paper focuses on the risk measures V aR and CV aR and analyzes this caveat in a discrete time complete pricing model. Under quite general conditions the explicit expression of a good deal is given, and its sensitivity with respect to some possible measurement errors is provided too. We point out that a critical property is the absence of short sales. In such a case we first construct a “shadow riskless asset” (SRA) without short sales and then the good deal is given by borrowing more and more money so as to invest in the SRA. It is also shown that the SRA is interested by itself, even if there are short selling restrictions.

Learning about Risk and Return: A Simple Model of Bubbles and Crashes

This paper demonstrates that an asset pricing model with least-squares learning can lead to bubbles and crashes as endogenous responses to the fundamentals driving asset prices. When agents are risk-averse they need to make forecasts of the conditional variance of a stock’s return. Recursive updating of both the conditional variance and the expected return implies several mechanisms through which learning impacts stock prices. Extended periods of excess volatility, bubbles and crashes arise with a frequency that depends on the extent to which past data is discounted. A central role is played by changes over time in agents’ estimates of risk.

Regional productivity variation and the impact of public capital stock: an analysis with spatial interaction, with reference to Spain

In this paper we examine whether variations in the level of public capital across Spain‟s Provinces affected productivity levels over the period 1996-2005. The analysis is motivated by contemporary urban economics theory, involving a production function for the competitive sector of the economy („industry‟) which includes the level of composite services derived from „service‟ firms under monopolistic competition. The outcome is potentially increasing returns to scale resulting from pecuniary externalities deriving from internal increasing returns in the monopolistic competition sector. We extend the production function by also making (log) labour efficiency a function of (log) total public capital stock and (log) human capital stock, leading to a simple and empirically tractable reduced form linking productivity level to density of employment, human capital and public capital stock. The model is further extended to include technological externalities or spillovers across provinces. Using panel data methodology, we find significant elasticities for total capital stock and for human capital stock, and a significant impact for employment density. The finding that the effect of public capital is significantly different from zero, indicating that it has a direct effect even after controlling for employment density, is contrary to some of the earlier research findings which leave the question of the impact of public capital unresolved.

Solving non-linear stochastic models by parameterizing expectations: An application to asset pricing with production

A new algorithm called the parameterized expectations approach(PEA) for solving dynamic stochastic models under rational expectationsis developed and its advantages and disadvantages are discussed. Thisalgorithm can, in principle, approximate the true equilibrium arbitrarilywell. Also, this algorithm works from the Euler equations, so that theequilibrium does not have to be cast in the form of a planner's problem.Monte--Carlo integration and the absence of grids on the state variables,cause the computation costs not to go up exponentially when the numberof state variables or the exogenous shocks in the economy increase. \\As an application we analyze an asset pricing model with endogenousproduction. We analyze its implications for time dependence of volatilityof stock returns and the term structure of interest rates. We argue thatthis model can generate hump--shaped term structures.

Competitive location and pricing on networks

In this paper we consider a location and pricing model for a retail firm that wants to enter a spatial market where a competitor firm is already operating as a monopoly with several outlets. The entering firms seeks to determine the optimal uniform mill price and its servers' locations that maximizes profits given the reaction in price of the competitor firm to its entrance. A tabu search procedure is presentedto solve the model together with computational experience.

A generalization of Hull and White formula and applications to option pricing approximation

By means of Malliavin Calculus we see that the classical Hull and White formulafor option pricing can be extended to the case where the noise driving thevolatility process is correlated with the noise driving the stock prices. Thisextension will allow us to construct option pricing approximation formulas.Numerical examples are presented.

Model for managing non-core ideas to new companies, products and services in a Finnish forest company

Suomalainen metsäteollisuus on muutoksen partaalla. Uutisissa on nähty miten metsäyrityksen sulkevat tehtaita ja paperikoneita. Suomalaisessa metsäteollisuudessa keskitytään tällä hetkellä lähinnä kulujen alentamiseen ja tuottavuuden parantamiseen. Edellytyssille, että suomalainen metsäteollisuus pysyy kilpailukykyisenä, ovat kuitenkinuudet innovaatiot ja toimialojen välinen yhteistyö. Työn tavoitteena oli luoda toimintamalli UPM-Kymmene Oyj:lle, minkä avulla ydinliiketoimintaan kuulumattomat tuote- ja palveluideat saataisiin hyödynnettyä. Aihe on erittäin ajankohtainen, mikäli halutaan pitää tuotanto jatkossakin Suomessa. Luotumalli painottaa pk-sektorin roolia ja potentiaalia kehittää UPM-Kymmeneltä peräisin olevia ja heidän ydinliiketointaan kuulumattomista tuote ja palveluideoistauusia yrityksiä, tuotteita ja palveluita. Malli edustaa uudenlaista ajattelutapaa ja sen käyttöönotto vaatii perinteisen yrityskulttuurin uudistamista UPM-Kymmenessä.

Value based pricing and marketing of marine engines

Objective of the thesis is to create a value based pricing model for marine engines and study the feasibility of implementing such model in the sales organization of a specific segment in the case company’s marine division. Different pricing strategies, concept of “value”, and how perceptions of value can be influenced through value based marketing are presented as theoretical background for the value based pricing model. Forbis and Mehta’s Economic Value to Customer (EVC) was selected as framework to create the value based pricing model for marine engines. The EVC model is based on calculating and comparing life-cycle costs of the reference product and competing products, thus showing the quantifiable value of the company’s own product compared to competition. In the applied part of the thesis, the components of the EVC model are identified for a marine diesel engine, the components are explained, and an example calculation created in Excel is presented. When examining the possibilities to implement in practice a value based pricing strategy based on the EVC model, it was found that the lack of precise information on competing products is the single biggest obstacle to use EVC exactly as presented in the literature. It was also found that sometimes necessary communication channels are missing and that there is simply a lack of interest from some clients and product end-users part to spend time on studying the life-cycle costs of the product. Information on the company’s own products is however sufficient and the sales force is capable to communicate to sufficiently high executive levels in the client organizations. Therefore it is suggested to focus on quantifying and communicating the company’s own value proposition. The dynamic nature of the business environment (variance in applications in which engines are installed, different clients, competition, end-clients etc.) means also that each project should be created its own EVC calculation. This is demanding in terms of resources needed, thus it is suggested to concentrate on selected projects and buyers, and to clients where the necessary communication channels to right levels in the customer organization are available. Finally, it should be highlighted that as literature suggests, implementing a value based pricing strategy is not possible unless the whole business approach is value based.

Modelling the simultaneous effects of intellectual capital and knowledge management on the organisational performance of Finnish companies

The aim of this study was to contribute to the current knowledge-based theory by focusing on a research gap that exists in the empirically proven determination of the simultaneous but differentiable effects of intellectual capital (IC) assets and knowledge management (KM) practices on organisational performance (OP). The analysis was built on the past research and theoreticised interactions between the latent constructs specified using the survey-based items that were measured from a sample of Finnish companies for IC and KM and the dependent construct for OP determined using information available from financial databases. Two widely used and commonly recommended measures in the literature on management science, i.e. the return on total assets (ROA) and the return on equity (ROE), were calculated for OP. Thus the investigation of the relationship between IC and KM impacting OP in relation to the hypotheses founded was possible to conduct using objectively derived performance indicators. Using financial OP measures also strengthened the dynamic features of data needed in analysing simultaneous and causal dependences between the modelled constructs specified using structural path models. The estimates were obtained for the parameters of structural path models using a partial least squares-based regression estimator. Results showed that the path dependencies between IC and OP or KM and OP were always insignificant when analysed separate to any other interactions or indirect effects caused by simultaneous modelling and regardless of the OP measure used that was either ROA or ROE. The dependency between the constructs for KM and IC appeared to be very strong and was always significant when modelled simultaneously with other possible interactions between the constructs and using either ROA or ROE to define OP. This study, however, did not find statistically unambiguous evidence for proving the hypothesised causal mediation effects suggesting, for instance, that the effects of KM practices on OP are mediated by the IC assets. Due to the fact that some indication about the fluctuations of causal effects was assessed, it was concluded that further studies are needed for verifying the fundamental and likely hidden causal effects between the constructs of interest. Therefore, it was also recommended that complementary modelling and data processing measures be conducted for elucidating whether the mediation effects occur between IC, KM and OP, the verification of which requires further investigations of measured items and can be build on the findings of this study.

How Cloud Services may Enable SMEs to Overcome International Growth Challenges: Finnish SMEs in the IT Industry

Digitalization and technology megatrends such as Cloud services have provided SMEs with a suitable atmosphere and conditions to internationalize and seek for further business growth. There is a limited amount of research on Cloud services from the business perspective and the limitations and challenges SMEs encounter when pursuing international business growth. Thus, the main research question of this study was how Cloud services may enable Finnish SMEs to overcome international growth challenges. The research question was further divided into three sub-questions dealing with matters related to features and characteristics of Cloud services, limitations and challenges Finnish SMEs experience when pursuing international growth of business, and benefits and advantages of utilizing Cloud services to mitigate and suppress international growth challenges. First, the theoretical framework of this study was constructed based on the existing literature on Cloud services, SMEs, and international growth challenges. After this, qualitative research approach and methodology were applied for this study. The data was collected through six semi-structured expert interviews in person with representatives of IBM, Exidio, Big Data Solutions, and Comptel. After analyzing the collected data by applying thematic analysis method, the results were compared with the existing theory and the original framework was modified and complemented accordingly. Resource scarcity, customer base expansion and retention, and lack of courage to try new things and take risks turned out to be major international growth challenges of Finnish SMEs. Due to a number of benefits and advantages of utilizing Cloud services including service automation, consumption-based pricing model, lack of capital expenditures (capex) and huge upfront investments, lightened organization structure, cost savings, speed, accessibility, scalability, agility, geographical expansion potential, global reaching and covering, credibility, partners, enhanced CRM, freedom, and flexibility, it can be concluded that Cloud services can help directly and indirectly Finnish SMEs to mitigate and overcome international growth challenges and enable further business growth.

Risk Aversion, Intertemporal Substitution, and Option Pricing

This paper develops a general stochastic framework and an equilibrium asset pricing model that make clear how attitudes towards intertemporal substitution and risk matter for option pricing. In particular, we show under which statistical conditions option pricing formulas are not preference-free, in other words, when preferences are not hidden in the stock and bond prices as they are in the standard Black and Scholes (BS) or Hull and White (HW) pricing formulas. The dependence of option prices on preference parameters comes from several instantaneous causality effects such as the so-called leverage effect. We also emphasize that the most standard asset pricing models (CAPM for the stock and BS or HW preference-free option pricing) are valid under the same stochastic setting (typically the absence of leverage effect), regardless of preference parameter values. Even though we propose a general non-preference-free option pricing formula, we always keep in mind that the BS formula is dominant both as a theoretical reference model and as a tool for practitioners. Another contribution of the paper is to characterize why the BS formula is such a benchmark. We show that, as soon as we are ready to accept a basic property of option prices, namely their homogeneity of degree one with respect to the pair formed by the underlying stock price and the strike price, the necessary statistical hypotheses for homogeneity provide BS-shaped option prices in equilibrium. This BS-shaped option-pricing formula allows us to derive interesting characterizations of the volatility smile, that is, the pattern of BS implicit volatilities as a function of the option moneyness. First, the asymmetry of the smile is shown to be equivalent to a particular form of asymmetry of the equivalent martingale measure. Second, this asymmetry appears precisely when there is either a premium on an instantaneous interest rate risk or on a generalized leverage effect or both, in other words, whenever the option pricing formula is not preference-free. Therefore, the main conclusion of our analysis for practitioners should be that an asymmetric smile is indicative of the relevance of preference parameters to price options.

Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-fit in Multivariate Regressions with Application to Asset Pricing Models

We study the problem of testing the error distribution in a multivariate linear regression (MLR) model. The tests are functions of appropriately standardized multivariate least squares residuals whose distribution is invariant to the unknown cross-equation error covariance matrix. Empirical multivariate skewness and kurtosis criteria are then compared to simulation-based estimate of their expected value under the hypothesized distribution. Special cases considered include testing multivariate normal, Student t; normal mixtures and stable error models. In the Gaussian case, finite-sample versions of the standard multivariate skewness and kurtosis tests are derived. To do this, we exploit simple, double and multi-stage Monte Carlo test methods. For non-Gaussian distribution families involving nuisance parameters, confidence sets are derived for the the nuisance parameters and the error distribution. The procedures considered are evaluated in a small simulation experi-ment. Finally, the tests are applied to an asset pricing model with observable risk-free rates, using monthly returns on New York Stock Exchange (NYSE) portfolios over five-year subperiods from 1926-1995.