The fair value of a token: How do markets price cryptocurrencies?

With the rise of cryptocurrency tokens as a new asset class, the question of the fair evaluation of a cryptocurrency token has become a question of increasing importance. We estimate the pricing kernel with which users price factors affecting their token holdings. We investigate how traditional risk factors such as market risk are evaluated, as well as how blockchain specific risk factors are priced in. In order to do so, we introduce an asset pricing model and modify its properties to make it applicable to cryptocurrency markets. We group the risk factors into market related and Bitcoin- and Ethereum blockchain specific risk factors. We find that blockchain specific risk factors are priced in. There is evidence that risk factors have moved from Bitcoin to Ethereum specific risk factors with an increasing importance of market factors, providing evidence for a decoupling of on-chain and off-chain trading activity.     

Pricing of the currency risk in the Canadian equity market

Based on a three-factor international capital asset pricing model, we examine whether the world market, the local market and the currency risks are priced in the Canadian equity market. The analysis presented in this paper is based on data collected from 2003 to 2010. As the dataset also includes the period of global financial crisis, we examine the issue of risk pricing in the full sample as well as in before and after global financial crisis periods. Unlike most existing studies, the empirical results presented in this paper are based on (i) the quasi maximum likelihood estimation (QMLE) based multivariate GARCH-in-Mean specification and (ii) the generalized method of moments (GMM) techniques. Our empirical analysis based on weekly data on 58 largest Canadian firms indicates that the currency as well as the local and the world market risks are priced in the Canadian equity market. This result holds for all exchange currency rates proxies and in all sample periods. We find that the price of the world market, the local market and the currency risks is time-varying and the Canadian equity market is partially segmented.     

An analysis of option pricing under systematic consumption risk using GARCH

An issue in the pricing of contingent claims is whether to account for consumption risk. This is relevant for contingent claims on stock indices, such as the FTSE 100 share price index, as investor’s desire for smooth consumption is often used to explain risk premiums on stock market portfolios, but is not used to explain risk premiums on contingent claims themselves. This paper addresses this fundamental question by allowing for consumption in an economy to be correlated with returns. Daily data on the FTSE 100 share price index are used to compare three option pricing models: the Black–Scholes option pricing model, a GARCH (1, 1) model priced under a risk-neutral framework, and a GARCH (1, 1) model priced under systematic consumption risk. The findings are that accounting for systematic consumption risk only provides improved accuracy for in-the-money call options. When the correlation between consumption and returns increases, the model that accounts for consumption risk will produce lower call option prices than observed prices for in-the-money call options. These results combined imply that the potential consumption-related premium in the market for contingent claims is constant in the case of FTSE 100 index options.     

An Equilibrium Model of Catastrophe Insurance Futures and Spreads

This article presents a valuation model of futures contracts and derivatives on such contracts, when the underlying delivery value is an insurance index, which follows a stochastic process containing jumps of random claim sizes at random time points of accident occurrence. Applications are made on insurance futures and spreads, a relatively new class of instruments for risk management launched by the Chicago Board of Trade in 1993, anticipated to start in Europe and perhaps also in other parts of the world in the future. The article treats the problem of pricing catastrophe risk, which is priced in the model and not treated as unsystematic risk. Several closed pricing formulas are derived, both for futures contracts and for futures derivatives, such as caps, call options, and spreads. The framework is that of partial equilibrium theory under uncertainty.     

Local risk factors in emerging markets: Are they separately priced?

We provide new evidence on the pricing of local risk factors in emerging stock markets. We investigate whether there is a significant local currency premium together with a domestic market risk premium in equity returns within a partial integration asset pricing model. Given previous evidence on currency risk, we conduct empirical tests in a conditional setting with time-varying prices of risk. Our main results support the hypothesis of a significant exchange risk premium related to the local currency risk. Exchange rate and domestic market risks are priced separately for our sample of seven emerging markets. The empirical evidence also suggests that although statistically significant, local currency risk is on average smaller than domestic market risk but it increases substantially during crises periods, when it can be almost as large as market risk. Disentangling these two factors is thus important in tests of international asset pricing for emerging markets.     

International asset pricing models and currency risk: Evidence from Finland 1970–2004

In this paper we investigate whether global, local and currency risks are priced in the Finnish stock market using conditional international asset pricing models. We take the view of a US investor. The estimation is conducted using a modified version of the multivariate GARCH framework of [De Santis, G., Gérard, B., 1998. How big is the premium for currency risk? Journal of Financial Economics 49, 375–412]. For a sample period from 1970 to 2004, we find the world risk to be time-varying. While local risk is not priced for the USA, the local component is significant and time-varying for Finland. Currency risk is priced in the Finnish market, but is not time-varying using the De Santis and Gérard specification. This suggests that the linear specification for the currency risk may not be adequate for non-free floating currencies.     

Asset pricing and energy consumption risk

This paper proposes energy consumption in the US as a new measure for the consumption capital asset pricing model. We find that (i) industrial energy growth produces reasonable values for the relative risk aversion coefficient and the implied risk-free rate; (ii) compared to alternative consumption measures, industrial energy performs well in explaining the cross-sectional variation in stock returns with the lowest implied risk aversion and pricing errors; (iii) the industrial energy consumption risk model performs equally well as the Fama–French three-factor model in the cross-sectional asset pricing tests; and (iv) total energy consumption risk is priced in the presence of the Fama–French factor risks.     

On the Distributional Conditions for a Consumption-oriented Three Moment CAPM

In this paper, we develop sufficient conditions on probability distributions for a three moment (mean, variance, and skewness) consumption-oriented capital asset pricing model (CAPM) to price correctly a subset of assets. The assumptions that individuals in an allocationally efficient capital market have identical probability beliefs and monotone increasing strictly concave utility functions displaying nonincreasing absolute risk aversion imply an aggregate preference function that exhibits preference for expected return, aversion to variance of return, and preference for positive skewness. For otherwise arbitrary preferences, we show that quadratic characteristic lines are sufficient for a subset of assets to be priced according to a three moment consumption-oriented CAPM.     

Two-dimensional risk-neutral valuation relationships for the pricing of options

The Black–Scholes model is based on a one-parameter pricing kernel with constant elasticity. Theoretical and empirical results suggest declining elasticity and, hence, a pricing kernel with at least two parameters. We price European-style options on assets whose probability distributions have two unknown parameters. We assume a pricing kernel which also has two unknown parameters. When certain conditions are met, a two-dimensional risk-neutral valuation relationship exists for the pricing of these options: i.e. the relationship between the price of the option and the prices of the underlying asset and one other option on the asset is the same as it would be under risk neutrality. In this class of models, the price of the underlying asset and that of one other option take the place of the unknown parameters.      

Wavelet timescales and conditional relationship between higher-order systematic co-moments and portfolio returns

This paper investigates the association between portfolio returns and higher-order systematic co-moments at different timescales obtained through wavelet multi-scaling, a technique that decomposes a given return series into timescales enabling investigation at different return intervals. In Australian industry portfolios, the relative risk positions indicated by systematic co-moments at some timescales are different from those revealed in daily returns. A strong positive (negative) linear association between beta and portfolio return and co-kurtosis and portfolio return in the up (down) market is observed in daily returns and at different timescales. The beta risk is priced in the up and down markets. Co-kurtosis is not priced when the beta is in the pricing model. Co-skewness appears to be priced at a relatively high timescale and this is observed only after the up and down separation of market returns.     

The conditional relation between dispersion and return

The main goal of this paper is to examine the conditional pricing effect of return dispersion on the cross section of returns. We observe a systematic conditional relation between dispersion and return even after controlling for market, size and book-to-market factors. However, we find that return dispersion risk is asymmetrically priced with a significantly positive premium observed during periods of large market gains only. The findings are found to be robust to alternative conditional specifications of market returns, suggesting asymmetric pricing effect of the return dispersion factor. We provide alternative explanations for the systematic risk captured by the return dispersion factor and discuss implications for portfolio management and corporate decisions.     

Liquidation equilibrium with seniority and hidden CDO

The aim of our paper is to price credit derivatives written on a single name when this name is a bank. Indeed, due to the special structure of the balance sheet of a bank and to the interconnections with other institutions of the financial system, the standard pricing formulas do not apply and their use can imply severe mispricing. The pricing of credit derivatives written on a single bank name requires a joint analysis of the risks of all banks directly or indirectly interconnected with the bank of interest. Each name cannot be priced in isolation, but the banking system must be treated as a whole. It is necessary to analyze the contagion of losses among banks, especially the equilibrium of joint defaults and recovery rates at liquidation time. We show the existence and uniqueness of such an equilibrium. Then the standard pricing formulas are modified by adding a premium to capture the contagion effects.     

The pricing of exchange rate risk and stock market segmentation: The Canadian case

Empirical evidence by Eun and Resnick (1988), among others, has demonstrated the significance of exchange rate risk in the international asset allocation and they have noted that the risk is nondiversifiable. Yet, exchange rate risk was found by Jorion (1991) to be a risk factor that is not priced in the U.S. stock market. This study reexamines such counterintuitive results using data from the Toronto Stock Exchange. The evidence here weakly supports the pricing of the exchange rate risk. Further, the sample period in this study coincides with Jorion's to ensure that both studies examine the pricing of the exchange rate risk in the same global economic environment. The significant pricing of exchange rate risk in Canada and the insignificant pricing in the U.S. imply the possibility of market segmentation.     

Option Pricing Bounds and the Elasticity of the Pricing Kernel

In this paper we use power functions as pricing kernels to derive option-pricing bounds. We derive option pricing bounds given the bounds of the elasticity of the true pricing kernel. The bounds of the elasticity of the true pricing kernel are closely related to the bounds of the representative investor's coefficient of relative risk aversion. This methodology produces a tighter upper call option bound than traditional approaches. As a special case we show how to use the Black–Scholes formula to obtain option pricing bounds under the assumption of lognormality.     

Pricing temperature derivatives with a filtered historical simulation approach

In this paper, we propose pricing temperature derivatives using a filtered historical simulation (FHS) approach that amalgamates model-based treatment of volatility and empirical innovation density. The FHS approach implicitly captures the risk premium with the entire risk-neutral model (except the innovation distribution), thereby providing significantly more flexibility than existing methods that use only one designated parameter to capture the risk premium. Additionally, instead of relying on the fitted innovation distribution, the FHS approach uses empirical innovations to capture excess skewness, excess kurtosis, and other non-standard features in the temperature data, all of which are important for the correct pricing of temperature derivatives. We apply the FHS approach to pricing derivatives written on the temperature of Chicago, and demonstrate that this approach yields better in-sample and out-of-sample pricing performance than the constant market price of risk method and the consumption-based method.     

Expected returns, risk premia, and volatility surfaces implicit in option market prices

This article presents a pure exchange economy that extends Rubinstein (1976) to show how the jump-diffusion option pricing model of Merton (1976) is altered when jumps are correlated with diffusive risks. A non-zero correlation between jumps and diffusive risks is necessary in order to resolve the positively sloped implied volatility term structure inherent in traditional jump diffusion models. Our evidence is consistent with a negative covariance, producing a non-monotonic term structure. For the proposed market structure, we present a closed form asset pricing model that depends on the factors of the traditional jump-diffusion models, and on both the covariance of the diffusive pricing kernel with price jumps and the covariance of the jumps of the pricing kernel with the diffusive price. We present statistical evidence that these covariances are positive. For our model the expected stock return, jump and diffusive risk premiums are non-linear functions of time.     

Risk evaluations with robust approximate factor models

Approximate factor models and their extensions are widely used in economic analysis and forecasting due to their ability to extracting useful information from a large number of relevant variables. In these models, candidate predictors are typically subject to some common components. In this paper we propose a new method for robustly estimating the approximate factor models and use it in risk assessments. We consider a class of approximate factor models in which the candidate predictors are additionally subject to idiosyncratic large uncommon components such as jumps or outliers. By assuming that occurrences of the uncommon components are rare, we develop an estimation procedure to simultaneously disentangle and estimate the common and uncommon components. We then use the proposed method to investigate whether risks from the latent factors are priced for expected returns of Fama and French 100 size and book-to-market ratio portfolios. We find that while the risk from the common factor is priced for the 100 portfolios, the risks from the idiosyncratic factors are not. However, we find that model uncertainty risks of the idiosyncratic factors are priced, suggesting that with effective diversifications, only the predictable idiosyncratic risks can be reduced, but the unpredictable ones may still exist. We also illustrate how the proposed method can be adopted on evaluating value at risk (VaR) and find it can delivery comparable results as the conventional methods on VaR evaluations.     

Alternate approach to unify CAPM and APT

We utilize the joint elliptical distribution to model a multi-factor return generating process and derive an equilibrium multi-beta capital asset pricing model (CAPM) in which the market portfolio and a set of nonelliptical factors are sufficient to price all financial assets. Most important, it is shown that the market portfolio, while generally nonelliptical, can proxy all elliptical factors and hence: including elliptical factors in addition to the market portfolio in the pricing equation contribute nothing to asset pricing. While the representative investor prices the exposure of aggregate wealth to various nonelliptical systematic risk factors, individual securities are priced in accordance to their contributions to different aspects of the risk of aggregate wealth. The present model collapses to the Sharpe-Lintner CAPM when either the market investor is neutral to nonelliptical risk factors or when all risk factors follow a joint spherical distribution. When residuals cancel out of the market portfolio, the present model collapses to Conner (1984) pricing model.     

Testing market efficiency with the pricing kernel

Market efficiency and the pricing kernel are closely related. A non-monotonic decreasing pricing kernel implies the existence of a trading strategy in contingent claims that stochastically dominates a direct investment in the market. Moreover, a market is assumed to be efficient only if no dominating strategies exist. Empirically, many studies of the pricing kernel find non-monotonicity, apparently ruling out market efficiency. However, these results are often unreliable, because the pricing measures of the pricing kernel are estimated using differing filtration sets. We show this effect both theoretically and empirically, and we discuss recent approaches in the literature for achieving more reliable estimates of the pricing kernel, potentially leading to better tests of market efficiency.