Min–max multi-step barrier options and their variants

This paper studies a new type of barrier option, min–max multi-step barrier options with diverse multiple up or down barrier levels placed in the sub-periods of the option’s lifetime. We develop the explicit pricing formula of this type of option under the Black–Scholes model and explore its applications and possible extensions. In particular, the min–max multi-step barrier option pricing formula can be used to approximate double barrier option prices and compute prices of complex barrier options such as discrete geometric Asian barrier options. As a practical example of directly applying the pricing formula, we introduce and evaluate a re-bouncing equity-linked security. The main theorem of this work is capable of handling the general payoff function, from which we obtain the pricing formulas of various min–max multi-step barrier options. The min–max multi-step reflection principle, the boundary-crossing probability of min–max multi-step barriers with icicles, is also derived.     

Pricing strategy in the product and service market

Existing studies have mainly focused on pricing in either primary markets or aftermarkets. However, in practice, prices in primary markets and aftermarkets are closely correlated. This study examines the joint pricing strategy in both primary markets and aftermarkets based on customer utility and establishes a pricing model for profit-maximization firms. Our results show that overpricing in the aftermarket is caused by customer myopia, while the motivation of the firm to avoid customer myopia depends on its pricing strategy. A quantity–price contract in the aftermarket is designed to raise the firm’s profit.     

Market competition and pricing strategies in retail supply chains

This study provides a better explanation for the continued prevalence of high–low (Hi–Lo) pricing strategy. We investigate the impact of market competition on adopting two different pricing strategies in the retail industry: everyday low price (EDLP) strategy and Hi–Lo strategy. We developed two analytic models using a game-theoretic modeling approach: the profit maximization model and the sales revenue maximization model. We then conducted an econometric analysis based on retail store-level dataset. The result shows that an EDLP player's equilibrium price depends highly on the cost level rather than competitor's price whereas the Hi–Lo player's equilibrium price depends mainly on the range of promotional basket as well as the cost level.     

Option Pricing under the Double Exponential Jump-Diffusion Model with Stochastic Volatility and Interest Rate

This paper proposes an efficient option pricing model that incorporates stochastic interest rate (SIR), stochastic volatility (SV), and double exponential jump into the jump-diffusion settings. The model comprehensively considers the leptokurtosis and heteroscedasticity of the underlying asset’s returns, rare events, and an SIR. Using the model, we deduce the pricing characteristic function and pricing formula of a European option. Then, we develop the Markov chain Monte Carlo method with latent variable to solve the problem of parameter estimation under the double exponential jump-diffusion model with SIR and SV. For verification purposes, we conduct time efficiency analysis, goodness of fit analysis, and jump/drift term analysis of the proposed model. In addition, we compare the pricing accuracy of the proposed model with those of the Black–Scholes and the Kou (2002) models. The empirical results show that the proposed option pricing model has high time efficiency, and the goodness of fit and pricing accuracy are significantly higher than those of the other two models.     

A unified entropic pricing framework of option: Using Cressie-Read family of divergences

The entropy valuation of option (Stutzer, 1996) provides a risk-neutral probability distribution (RND) as the pricing measure by minimizing the Kullback–Leibler (KL) divergence between the empirical probability distribution and its risk-neutral counterpart. This article establishes a unified entropic framework by developing a class of generalized entropy pricing models based upon Cressie-Read (CR) family of divergences. The main contributions of this study are: (1) this unified framework can readily incorporate a set of informative risk-neutral moments (RNMs) of underlying return extracted from the option market which accurately captures the characteristics of the underlying distribution; (2) the classical KL-based entropy pricing model is extended to a unified entropic pricing framework upon a family of CR divergences. For each of the proposed models under the unified framework, the optimal RND is derived by employing the dual method. Simulations show that, compared to the true price, each model of the proposed family can produce high accuracy for option pricing. Meanwhile, the pricing biases among the models are different, and we hence conduct theoretical analysis and experimental investigations to explore the driving causes.     

Factor pricing of cryptocurrencies

In this paper, we study the cryptocurrency pricing factors. We review the literatures which state that the cryptocurrency market is weakly efficient. We use the Fama–MacBeth method to investigate the pricing factors. The classical equity-based risk factors including size, momentum, and value to growth from the Fama–French three factor model are studied. We use crypto-unique coin-to-token as a proxy for value-to-growth. For volatility risk factor category, we investigate realized volatility, skewness and jump. We also investigate liquidity factors including bid–ask, volume growth and Roll’s measure. The macro factors are found not to be an explanatory factor. The attention factor works sometimes. The factor model constructed by the significant factors explain most of the excess return of cryptocurrencies.     

Parametric pricing of higher order moments in S&P500 options

A general parametric framework based on the generalized Student t‐distribution is developed for pricing S&P500 options. Higher order moments in stock returns as well as time‐varying volatility are priced. An important computational advantage of the proposed framework over Monte Carlo‐based pricing methods is that options can be priced using one‐dimensional quadrature integration. The empirical application is based on S&P500 options traded on select days in April 1995, a total sample of over 100,000 observations. A range of performance criteria are used to evaluate the proposed model, as well as a number of alternative models. The empirical results show that pricing higher order moments and time‐varying volatility yields improvements in the pricing of options, as well as correcting the volatility skew associated with the Black–Scholes model. Copyright © 2004 John Wiley & Sons, Ltd.     

Tests of asset pricing with time‐varying factor loads

This paper proposes an empirical asset pricing test based on the homogeneity of the factor risk premia across risky assets. Factor loadings are considered to be dynamic and estimated from data at higher frequencies. The factor risk premia are obtained as estimates from time series regressions applied to each risky asset. We propose Swamy‐type tests robust to the presence of generated regressors and dependence between the pricing errors to assess the homogeneity of the factor risk premia and the zero intercept hypothesis. An application to US industry portfolios shows overwhelming evidence rejecting the capital asset pricing model, and the three and five factor models developed by Fama and French (Journal of Financial Economics, 1993, 33, 3–56; Journal of Financial Economics, 2015, 116, 1–22). In particular, we reject the null hypotheses of a zero intercept, homogeneous factor risk premia across risky assets, and the joint test involving both hypotheses.     

Equal risk pricing under convex trading constraints

In an incomplete market model where convex trading constraints are imposed upon the underlying assets, it is no longer possible to obtain unique arbitrage-free prices for derivatives using standard replication arguments. Most existing derivative pricing approaches involve the selection of a suitable martingale measure or the optimisation of utility functions as well as risk measures from the perspective of a single trader.We propose a new and effective derivative pricing method, referred to as the equal risk pricing approach, for markets with convex trading constraints. The approach analyses the risk exposure of both the buyer and seller of the derivative, and seeks an equal risk price which evenly distributes the expected loss for both parties under optimal hedging. The existence and uniqueness of the equal risk price are established for both European and American options. Furthermore, if the trading constraints are removed, the equal risk price agrees with the standard arbitrage-free price.Finally, the equal risk pricing approach is applied to a constrained Black–Scholes market model where short-selling is banned. In particular, simple pricing formulas are derived for European calls, European puts and American puts.     

An application of nonparametric volatility estimators to option pricing

We discuss the impact of volatility estimates from high frequency data on derivative pricing. The principal purpose is to estimate the diffusion coefficient of an Itô process using a nonparametric Nadaraya–Watson kernel approach based on selective estimators of spot volatility proposed in the econometric literature, which are based on high frequency data. The accuracy of different spot volatility estimates is measured in terms of how accurately they can reproduce market option prices. To this aim, we fit a diffusion model to S&P 500 data, and successively, we use the calibrated model to price European call options written on the S&P 500 index. The estimation results are compared to well-known parametric alternatives available in the literature. Empirical results not only show that using intra-day data rather than daily provides better volatility estimates and hence smaller pricing errors, but also highlight that the choice of the spot volatility estimator has effective impact on pricing.     

Pricing by state‐owned enterprises: the case of postal services

Sappington and Sidak develop a model of state‐owned enterprise (SOE) pricing behavior in which firms maximize a weighted average of revenues and profits. The model predicts that SOEs will lower prices in more‐elastic markets and raise them in less‐elastic markets if the weight they place on profit is positive. The Postal Reorganization Act of 1970 relaxed the institutional constraints on pricing by the US Postal Service, which allows a test of the Sappington–Sidak model. The model's predictions are broadly confirmed. Congress passed the Postal Accountability and Enhancement Act in 2006, which may help address some anticompetitive concerns in this industry. Copyright © 2008 John Wiley & Sons, Ltd.     

Applications of the Likelihood Theory in Finance: Modelling and Pricing

This paper discusses the connection between mathematical finance and statistical modelling which turns out to be more than a formal mathematical correspondence. We like to figure out how common results and notions in statistics and their meaning can be translated to the world of mathematical finance and vice versa. A lot of similarities can be expressed in terms of LeCam’s theory for statistical experiments which is the theory of the behaviour of likelihood processes. For positive prices the arbitrage free financial assets fit into statistical experiments. It is shown that they are given by filtered likelihood ratio processes. From the statistical point of view, martingale measures, completeness, and pricing formulas are revisited. The pricing formulas for various options are connected with the power functions of tests. For instance the Black–Scholes price of a European option is related to Neyman–Pearson tests and it has an interpretation as Bayes risk. Under contiguity the convergence of financial experiments and option prices are obtained. In particular, the approximation of Itô type price processes by discrete models and the convergence of associated option prices is studied. The result relies on the central limit theorem for statistical experiments, which is well known in statistics in connection with local asymptotic normal (LAN) families. As application certain continuous time option prices can be approximated by related discrete time pricing formulas.     

THE ROLE OF CONDITIONAL HETEROSKEDASTICITY IN IDENTIFYING AND ESTIMATING LINEAR TRIANGULAR SYSTEMS,WITH APPLICATIONS TO ASSET PRICING MODELS THAT INCLUDE A MISMEASURED FACTOR

A new estimator is proposed for linear triangular systems, where identification results from the model errors following a bivariate and diagonal GARCH(1,1) process with potentially time‐varying error covariances. This estimator applies when traditional instruments are unavailable. I demonstrate its usefulness on asset pricing models like the capital asset pricing model and Fama–French three‐factor model. In the context of a standard two‐pass cross‐sectional regression approach, this estimator improves the pricing performance of both models. Set identification bounds and an associated estimator are also provided for cases where the conditions supporting point identification fail. Copyright © 2013 John Wiley & Sons, Ltd.     

Joint dynamic modeling and option pricing in incomplete derivative-security market

In this study, we evaluate the option prices on two assets under stochastic interest rates when the stochastic process that underlying asset prices follow is depending on a correlated bivariate Markov-modulated geometric Brownian motion model with jump risks. More specifically, we conduct the joint dynamic modeling by identifying two independent compound Poisson processes with the log-normal jump sizes to describe both individual jumps and systematic cojumps. Facilitating the cojumping behavior this way with the time-inhomogeneity of the volatility, option pricing expressions are readily obtainable since the Gerber–Siu’s approach is employed to determine a pricing kernel. The empirical results and numerical illustrations are provided to show the impact of cojumps and stochastic volatilities on option prices.     

On revenue recycling and the welfare effects of second-best congestion pricing in a monocentric city

This paper examines congestion taxes in a monocentric city with pre-existing labor taxation. When road toll revenue is used to finance labor tax cuts, 35% of the optimal road tax in our numerical model does not reflect marginal external congestion costs, but rather functions as a Ramsey–Mirrlees tax, i.e. an efficiency enhancing mechanism allowing for an indirect spatial differentiation of the labor tax. This adds a quite different motivation to road pricing, since welfare gains can be produced even in absence of congestion. We find that the optimal road tax is non-monotonic across space, reflecting the different impacts of labor supply elasticity and marginal utility of income, which both vary over space. The relative efficiencies of some archetype second-best pricing schemes (cordon toll, flat kilometer tax) are high (84% and 70% respectively). When road toll revenue is recycled lump-sum, the optimal toll lies below its Pigouvian level. Extensions in a bimodal framework show that the optimality of using road toll revenue to subsidize public transport depends on the initial inefficiency in public transport pricing.     

Financial innovation and bank behavior: Evidence from credit markets

This paper investigates whether, and through which channel, the active use of credit derivatives changes bank behavior in the credit market, and how this channel was affected by the crisis of 2007–2009. Our principal finding is that banks with larger gross positions in credit derivatives charge significantly lower corporate loan spreads, while banks׳ net positions are not consistently related to loan pricing. We argue that this is consistent with banks passing on risk management benefits to corporate borrowers but not with alternative channels through which credit derivative use may affect loan pricing. We also find that the magnitude of the risk management effect remained unchanged during the crisis period of 2007–2009. In addition, banks with larger gross positions in credit derivatives cut their lending by less than other banks during the crisis and have consistently lower loan charge-offs. In sum, our study is suggestive of significant risk management benefits from financial innovations that persist under adverse conditions – that is, when they matter most.     

Dupire’s formulas in the Piterbarg option pricing model

In this paper we derive an expression for the local volatility of an underlying asset, given the prices of liquid European call options under the Piterbarg framework. The Piterbarg framework is a multi-curve derivative pricing model which extends the well known Black–Scholes–Merton model by relaxing the assumption of a risk-free interest rate, and includes collateral payments. The expressions for the local volatility is a function of the option price surface, and is then transformed to become a function of the implied volatility surface.     

融资交易与融券交易对中国股票定价效率的影响一致吗？

分析融资交易、融券交易对标的证券定价效率影响的不一致性,可以发现,融资融券交易制度的推出显著地提高了标的证券的定价效率,但融资交易和融券交易的影响却存在不一致性。具体而言,融券交易提高了定价效率而融资交易降低了定价效率。融券交易对改善高估值股票的定价效率更加显著,融资交易的影响则没有显著差异。融资融券调控不应采取一刀切的方式,应针对不同标的采取差异化的调控。     

The pricing accuracy of alternative equity valuation models: Scandinavian evidence

In many decision contexts, there is a need for benchmark equity valuations, based on simplified modeling and publicly available information. Prior research on U.S. data however shows that the accuracy of such valuation models can be low and sensitive to the choice of model specifications and value driver predictions. In this paper, we test the applicability and pricing accuracy of three fundamental valuation (dividend discount, residual income, and abnormal earnings growth) models, all based on forecasts of company dividends, earnings, and/or equity book values. Extending prior research, we apply these models to Scandinavian firms with accounting data from the period 2005–2014, explicitly testing two approaches for the prediction of the value drivers—exogenously forecasted numbers versus projected historical numbers. Given access to the forecasted value drivers, the dividend discount model comes out as the most accurate valuation model. In particular, this holds in a comparison between the most parsimonious model specifications. The residual income valuation model generates the best pricing accuracy given the prediction of value drivers based on historical financial numbers. Notably, we observe pricing errors that in general are lower than what has been reported in prior U.S.‐based research for the dividend discount and the residual income valuation models. The pricing accuracy of the abnormal earnings growth models is surprisingly weak in the Scandinavian setting. However, these models improve somewhat after a couple of complexity adjustments, in particular with value driver predictions based on the projected history setting.