Pricing

Summary

Pricing is the process whereby a business sets the price at which it will sell its products and services, and may be part of the business's marketing plan. In setting prices, the business will take into account the price at which it could acquire the goods, the manufacturing cost, the marketplace, competition, market condition, brand, and quality of product. Pricing is a fundamental aspect of product management and is one of the four Ps of the marketing mix, the other three aspects being product, promotion, and place. Price is the only revenue generating element amongst the four Ps, the rest being cost centers. However, the other Ps of marketing will contribute to decreasing price elasticity and so enable price increases to drive greater revenue and profits. Pricing can be a manual or automatic process of applying prices to purchase and sales orders, based on factors such as: a fixed amount, quantity break, promotion or sales campaign, specific vendor quote, price prevailing on ent

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https://en.wikipedia.org/wiki/Pricing

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Three Essays on Asset Pricing

Emmanuel Leclercq

In the first chapter,which is a joint work with Mathieu Cambou and Philippe H.A. Charmoy, we study the distribution of the hedging errors of a European call option for the delta and variance-minimizing strategies. Considering the setting proposed by Heston (1993), we assess the error distribution by computing its moments under the real-world probability measure. It turns out that one is better off implementing either a delta hedging or a variance-minimizing strategy, depending on the strike and maturity of the option under consideration. In the second paper, which is a joint work with Damir Filipovic and Loriano Mancini, we develop a practicable continuous-time dynamic arbitrage-free model for the pricing of European contingent claims. Using the framework introduced by Carmona and Nadtochiy (2011, 2012), the stock price is modeled as a semi-martingale process and, at each time t , the marginal distribution of the European option prices is coded by an auxiliary process that starts at t and follows an exponential additive process. The jump intensity that characterizes these auxiliary processes is then set in motion by means of stochastic dynamics of Itô's type. The model is a modification of the one proposed by Carmona and Nadtochiy, as only finitely many jump sizes are assumed. This crucial assumption implies that the jump intensities are taken values in only a finitedimensional space. In this setup, explicit necessary and sufficient consistency conditions that guarantee the absence of arbitrage are provided. A practicable dynamic model verifying them is proposed and estimated, using options on the S&P 500. Finally, the hedging of variance swap contracts is considered. It is shown that under certain conditions, a variance-minimizing hedging portfolio gives lower hedging errors on average, compared to a model-free hedging strategy. In the third and last chapter, which is a joint work with Rémy Praz, we concentrate on the commodity markets and try to understand the impact of financiers on the hedging decisions. We look at the changes in the spot price, variance, production and hedging choices of both producers and financiers, when the mass of financiers in the economy increases. We develop an equilibrium model of commodity spot and futures markets in which commodity production, consumption, and speculation are endogenously determined. Financiers facilitate hedging by the commodity suppliers. The entry of new financiers thus increases the supply of the commodity and decreases the expected spot prices, to the benefits of the end-users. However, this entry may be detrimental to the producers, as they do not internalize the price reduction due to greater aggregate supply. In the presence of asymmetric information, speculation on the futures market serves as a learning device. The futures price and open interest reveal different pieces of private information regarding the supply and demand side of the spot market, respectively. When the accuracy of private information is low, the entry of new financiers makes both production and spot prices more volatile. The entry of new financiers typically increases the correlation between financial and commodity markets.

EPFL2014

Numerical methods for option pricing: polynomial approximation and high dimensionality

Francesco Statti

Options are some of the most traded financial instruments and computing their price is a central task in financial mathematics and in practice. Consequently, the development of numerical algorithms for pricing options is an active field of research. In general, evaluating the price of a specific option relies on the properties of the stochastic model used for the underlying asset price. In this thesis we develop efficient and accurate numerical methods for option pricing in a specific class of models: polynomial models. They are a versatile tool for financial modeling and have useful properties that can be exploited for option pricing. Significant challenges arise when developing option pricing techniques. For instance, the underlying model might have a high-dimensional parameter space. Furthermore, treating multi-asset options yields high-dimensional pricing problems. Therefore, the pricing method should be able to handle high dimensionality. Another important aspect is the efficiency of the algorithm: in real-world applications, option prices need to be delivered within short periods of time, making the algorithmic complexity a potential bottleneck. In this thesis, we address these challenges by developing option pricing techniques that are able to handle low and high-dimensional problems, and we propose complexity reduction techniques. The thesis consists of four parts: First, we present a methodology for European and American option pricing. The method uses the moments of the underlying price process to produce monotone sequences of lower and upper bounds of the option price. The bounds are obtained by solving a sequence of polynomial optimization problems. As the order of the moments increases, the bounds become sharper and eventually converge to the exact price under appropriate assumptions. Second, we develop a fast algorithm for the incremental computation of nested block triangular matrix exponentials. This algorithm allows for an efficient incremental computation of the moment sequence of polynomial jump-diffusions. In other words, moments of order 0, 1, 2, 3... are computed sequentially until a dynamically evaluated criterion tells us to stop. The algorithm is based on the scaling and squaring technique and reduces the complexity of the pricing algorithms that require such an incremental moment computation. Third, we develop a complexity reduction technique for high-dimensional option pricing. To this end, we first consider the option price as a function of model and payoff parameters. Then, the tensorized Chebyshev interpolation is used on the parameter space to increase the efficiency in computing option prices, while maintaining the required accuracy. The high dimensionality of the problem is treated by expressing the tensorized interpolation in the tensor train format and by deriving an efficient way, which is based on tensor completion, to approximate the interpolation coefficients. Lastly, we propose a methodology for pricing single and multi-asset European options. The approach is a combination of Monte Carlo simulation and function approximation. We address the memory limitations that arise when treating very high-dimensional applications by combining the method with optimal sampling strategies and using a randomized algorithm to reduce the storage complexity of the approach. The obtained numerical results show the effectiveness of the algorithms developed in this thesis.

EPFL2019

Growing urban population implies many challenges for the municipalities in terms of mobility, housing, waste management or infrastructures. Public policies are thus needed to ensure a sustainable development. The main objective of this thesis is to analyze different environmental policies in the domain of mobility and waste management in order to help municipalities in designing more efficient measures.Firstly, Chapter 2 focuses on traffic congestion and in particular the acceptability of a congestion charge. We design a large survey with different plausible schemes for the Canton of Geneva, Switzerland and assess their acceptability with a discrete choice experiment (DCE). Results show that public support depends crucially on the policy design and the information provided. We find an important demand for exemptions and a preference for constant pricing. This implies a clear trade-off between efficiency and acceptability. However, the gap can be partly closed by information provision. Analyzing heterogeneity, we observe that preferences vary according to personal characteristics, especially where people live and how they commute.Chapter 3 analyzes the determinants of households' municipal waste sorting. We design a survey to investigate households' sorting motivation and use a DCE to assess households' waste sorting scheme preferences in the Canton of Geneva. We observe that households' waste sorting depends on personal characteristics such as sensitivity to the environment, guilty conscience or information level. However, it is the satisfaction with the existing sorting scheme that increases most the probability to sort waste. Our results show clear preferences for better infrastructures, but with thresholds. Interestingly, the best infrastructures and services are not always needed. By looking at heterogeneity and linking personal beliefs and characteristics with preferences, we find different groups sorting a similar number of categories, but with different underlying mechanisms like a lack of knowledge or a need for more convenient infrastructures and services.To complement our analysis on voluntary policies and in particular on the effectiveness of convenient infrastructures, Chapter 4 assesses a new voluntary environmental policy implemented in the Canton of Geneva and compares the results with a bag tax, a monetary incentive policy introduced in the neighboring canton, Vaud. The voluntary policy consists of the distribution to households of specific bins for organic waste to increase the sorting rate and decrease the amount of unsorted waste. We use a difference-in-differences methodology to assess the causal impact of the policy on organic waste as well as on overall waste generation. We find that the introduction of the voluntary policy increases significantly the proportion of households sorting organic waste. Interestingly, we observe some positive spillover effects on other waste sorted. By comparing the voluntary policy in the Canton of Geneva and the bag tax in the Canton of Vaud, we find similar effects on organic waste sorting. However, the impact of the voluntary policy is smaller on unsorted waste than the short-term effect of the bag tax.In conclusion, we show that price is not the only factor to consider in environmental policies. More stringent policies can be acceptable if well designed. Furthermore, the power of non-monetary incentives should not be underestimated.

EPFL2022