Computationally simple lattice methods for option and bond pricing

We propose new lattice-based algorithms for option and bond pricing, which rely on computationally simple trees, i.e., trees with the number of nodes that grows at most linearly in the number of time intervals. Contrary to commonly used methods, the target diffusion is approximated directly, without having to transform the original process into a constant volatility process. The discrete approximating process converges to the target continuous process, and the proposed algorithms are shown to be efficient and accurate for pricing purposes.     

An analytical approximation formula for European option pricing under a new stochastic volatility model with regime-switching

In this paper, an analytical approximation formula for pricing European options is obtained under a newly proposed hybrid model with the volatility of volatility in the Heston model following a Markov chain, the adoption of which is motivated by the empirical evidence of the existence of regime-switching in real markets. We first derive the coupled PDE (partial differential equation) system that governs the European option price, which is solved with the perturbation method. It should be noted that the newly derived formula is fast and easy to implement with only normal distribution function involved, and numerical experiments confirm that our formula could provide quite accurate option prices, especially for relatively short-tenor ones. Finally, empirical studies are carried out to show the superiority of our model based on S&P 500 returns and options with the time to expiry less than one month.     

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.     

Leverage effect on stochastic volatility for option pricing in Hong Kong: A simulation and empirical study

This paper explores the importance of incorporating the financial leverage effect in the stochastic volatility models when pricing options. For the illustrative purpose, we first conduct the simulation experiment by using the Markov Chain Monte Carlo (MCMC) sampling method. We then make an empirical analysis by applying the volatility models to the real return data of the Hang Seng index during the period from January 1, 2013 to December 31, 2017. Our results highlight the accuracy of the stochastic volatility models with leverage in option pricing when leverage is high. In addition, the leverage effect becomes more significant as the maturity of options increases. Moreover, leverage affects the pricing of in-the-money options more than that of at-the-money and out-of-money options. Our study is therefore useful for both asset pricing and portfolio investment in the Hong Kong market where volatility is an inherent nature of the economy.     

Consumer rationality and credit card pricing: An explanation based on the option value of credit lines

An option is embedded in credit cards. Since credit cards offer open credit lines, cardholders can borrow at the same terms when they become riskier. This option value raises the zero‐profit card rate. Furthermore, adverse selection occurs if cardholders are better informed about the probability of becoming riskier in the future and borrow more when they become riskier. The adverse selection can limit rate competition and keep the card rate above the zero‐profit card rate. An up‐front fee is not a good alternative because it is also vulnerable to adverse selection. A low introductory card rate is an effective way to avoid the adverse selection problem when asymmetric information is mainly about the change in the borrower's risk profile in the future, as opposed to the riskiness in the present period. Copyright © 2004 John Wiley & Sons, Ltd.     

Forecasting volatility: A reality check based on option pricing, utility function, value-at-risk, and predictive likelihood

We analyze the predictive performance of various volatility models for stock returns. To compare their performance, we choose loss functions for which volatility estimation is of paramount importance. We deal with two economic loss functions (an option pricing function and an utility function) and two statistical loss functions (a goodness-of-fit measure for a value-at-risk (VaR) calculation and a predictive likelihood function). We implement the tests for superior predictive ability of White [Econometrica 68 (5) (2000) 1097] and Hansen [Hansen, P. R. (2001). An unbiased and powerful test for superior predictive ability. Brown University]. We find that, for option pricing, simple models like the Riskmetrics exponentially weighted moving average (EWMA) or a simple moving average, which do not require estimation, perform as well as other more sophisticated specifications. For a utility-based loss function, an asymmetric quadratic GARCH seems to dominate, and this result is robust to different degrees of risk aversion. For a VaR-based loss function, a stochastic volatility model is preferred. Interestingly, the Riskmetrics EWMA model, proposed to calculate VaR, seems to be the worst performer. For the predictive likelihood-based loss function, modeling the conditional standard deviation instead of the variance seems to be a dominant modeling strategy.     

Option pricing: a yet simpler approach

Decisions in Economics and Finance - We provide a lean, non-technical exposition on the pricing of path-dependent and European-style derivatives in the Cox–Ross–Rubinstein (CRR) pricing...     

Household demand for financial assets: A life-cycle analysis

This paper examines the demand for major financial assets by householders during different stages of their lives using the life-cycle theory of consumption and saving and cross-sectional data from the Survey of Income and Program Participation (SIPP). Unlike most studies on money demand, data used in this study are microeconomic and free from the identification problem frequently encountered in the literature. Regression results show that the propensities to hold financial assets out of labor income, wealth, and net worth differ substantially among young, middle-age, and old householders. Also, the impacts of relative rates of return and demographic variables on asset demands vary among householders of different ages.     

Optimal pricing strategy for foreign market entry: a game theoretic approach

Given that pricing plays an important role in a company's international competitive strategy, researchers have long argued the need for theory building in the area of international pricing. This study develops an optimal pricing strategy for foreign market entry using a game theoretic framework. The proposed model assumes two firms, a local incumbent and a foreign entrant, competing in a market. Consumers know the quality of the incumbent's offering, but do not know how it compares to that of the foreign entrant's. Based on these assumptions, and using the theory of inference making, we propose an upward price distortion by the entrant firm as an optimal entry strategy under incomplete information. The paper presents a game theoretic derivation to establish that the game has a unique intuitive separating equilibrium where the entrant firm stands to gain by engaging in upward price distortion to signal high quality to consumers. Copyright © 2006 John Wiley & Sons, Ltd.     

Optimal strategy for a fund manager with option compensation

I consider the problem of portfolio optimization for a manager whose compensation is given by the sum of a constant and a variable term. The constant term is a fixed percentage of the managed funds that is payed to the manager independently of his performance. The variable term is a premium that is proportional to the profit earned by the manager over a benchmark at a certain evaluation date. I find the optimal strategy and the optimal portfolio value in the Black–Scholes setting when the benchmark is a linear combination of the risky asset and the money market account.     

发展都市旅游业的先决条件与战略模式

都市旅游业是城市发展的重要战略之一。发展都市旅游业当然要突破过去“就资源论开发”的传统思想误区 ,但还是要具备一定的基本的先决条件。因此应该因地制宜地采取相应的发展战略。在实际操作过程中 ,还应该注意可持续发展、投资负担合理安排以及市场营销等方面的问题。     

Formulation and implementation of a pricing policy for municipal parking

The efficient allocation of a municipally-owned resource, like automobile parking space, requires a long-term policy that recognizes the social, technical, economic and political realities of the system. This paper develops such a policy, and reviews the progress in implementing it in a medium size city over a 3 yr period. An analysis of the interim results finds a significant increase in revenue to the City, some progress toward a socially desirable allocation of space and evidence that further progress is continuing.Much of the success in implementing the recommended policy was attributed to the small number of links in the chain of decision-makers and to having essentially the same group of people involved with the project over an extended period of time. With an understandable, well-developed and logical policy to follow, rational decisionmaking could proceed in small steps, thereby building consensus by reducing uncertainty about the ultimate impact of the recommended course of action. This type of policy formulation and implementation is analogous to programmed learning.     

Privatization of businesses and flexible investment: a real option approach

In this article, we study the situation, where the opportunity is given to invest into a government-owned business by partial privatization to a private company. After payment of an initial installment cost, the private company’s investments are flexible within a range [0, k] until the business is completed. We model the problem in a real option framework, using geometric mean reversion to describe the dynamics of the business. We determine the optimal time for the private company to enter and pay the initial installment cost as well as the optimal dynamic investment strategy that it follows afterward. For the latter, analytic solution cannot be obtained. We use quadratic splines in order to solve the corresponding dynamic programming problem. Finally, we determine the optimal degree of privatization in our model from the government’s perspective.     

The Lognormal Distribution as a Model for Survival Time in Cancer, With an Emphasis on Prognostic Factors

Despite their long history, parametric survival-time models have largely been neglected in the modern biostatistical and medical literature in favour of the Cox proportional hazards model. Here, I present a case for the use of the lognormal distribution in the analysis of survival times of breast and ovarian cancer patients, specifically in modelling the effects of prognostic factors. The lognormal provides a completely specified probability distribution for the observations and a sensible estimate of the variation explained by the model, a quantity that is controversial for the Cox model. I show how imputation of censored observations under the model may be used to inspect the data using familiar graphical and other technques. Results from the Cox and lognormal models are compared and shown apparently to differ to some extent. However, it is hard to judge which model gives the more accurate estimates. It is concluded that provided the lognormal model fits the data adequately, it may be a useful approach to the analysis of censored survival data.     

Asset pricing for inefficient markets: Evidence from China and India

Over last four decades, evidence of market inefficiencies has been widely documented by several scholars for all major stock markets in the globe. Chinese and Indian markets are not exempt. Inefficiencies in these markets are described by many authors as roots of all mispricing. Mispricing might be the outcome of application of familiar asset pricing models which may mislead an investor into adopting inappropriate policies for his new investments or for reallocating his old investments. In an alternative approach, we propose a transformation on original market returns in the objective of relaxing the strong assumption of market efficiency behind application of an asset pricing model. This modification will widen the scope of rational models on asset pricing ranging from an efficient to an inefficient market.     

Multibrand pricing as a strategy for consumer search obfuscation in online markets

This paper argues that a firm with multiple brands can obfuscate consumer search by excluding the brands of other firms from a consumer's consideration set. This is examined empirically by regressing price data for a leading U.K. motor insurance price comparison site (or “shopbot”). It finds that multibrand firms own three‐quarters of brands in this market, and that allowing for other brand strategies, they post significantly lower and clustered prices relative to other firms. The firms also conceal their brand ownership, consistent with search obfuscation. The results are not otherwise explained and they have implications for market competitiveness.     

Equilibrium pricing and advertising strategies for nondurable experience products in a dynamic duopoly

The quality of many consumer nondurable goods or services is sufficiently complex or obscure that consumers cannot completely verify the true quality in a single usage. For such ‘experience’ products or services, the accumulated consumer consumption experience of a brand is an important determinant of its sales or market share. The market share of a brand is in turn directly influenced by its own and the competitive price and advertising strategies, given the different levels of quality (among other factors). In this paper, we investigate the impact of the aggregate consumption experience on the firm's dynamic pricing and advertising strategies by developing a formal game-theoretic model of a dynamic duopoly. The model of competition does not yield explicit closed-form expressions for the dynamic price and advertising paths of the two firms. Hence, we simulate the equilibrium paths using a discrete-time algorithm. Our simulation results provide interesting insights into the dynamic equilibrium price and advertising paths, under a variety of realistic competitive scenarios.     

Linear performance pricing: A collaborative tool for focused supply cost reduction

Supplier networks and the buyer/supplier relationships that comprise them are becoming increasingly important to effective supply chain management. Trust, collaboration, and efficient sharing of information are critical for true win/win relationships to surface in an environment where there is constant pressure to reduce costs and still maintain reasonable profitability. The use of across-the-board cost reduction demands and simple market clout may not always be the most effective approach in the long run. This paper describes linear performance pricing (LPP), a tool developed for a major automobile OEM in an attempt to effectively and efficiently provide more focused supply cost reductions. LPP is a data-driven methodology relying on a series of regression analyses that McKinsey and Company [2006. Automotive and assembly glossary. http://autoassembly.mckinsey.com/html/resources/glossary/1.asp (accessed 15.01.06)] describes as a “measurement tool that establishes a relationship between the value provided by a given part (performance) and its price.” We maintain that LPP facilitates a collaborative effort on the part of both the buyer and supplier and has the potential for leveraging the increased visibility of the buyer within the supplier network with respect to tier one or tier two suppliers. It helps by focusing cost reduction efforts of the tier one suppliers and provides lateral market visibility they may not have otherwise. Although widely used throughout the automotive industry in the US and Europe, little discussion of LPP is found in the literature. To promote a better understanding of LPP, we present a detailed example and discuss the managerial implications of the approach.     

Hierarchical random-effects model for the insurance pricing of vehicles belonging to a fleet

We propose a count-data model with hierarchical random effects for the posterior insurance ratemaking of vehicles belonging to a fleet, by allowing random effects for the fleet, the vehicles, and time. We derive a simple closed-form ratemaking formula based on a hierarchical random-effects specification. We estimate the corresponding econometric model and compute insurance premiums according to the past experience of both the vehicle and the fleet. Our model can be used in other count-data applications with random individual and common effects on events involving many agents having activities with a principal in a hierarchical principal–agent environment, such as in education, health care management, finance, and business firms.