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Author: Anne Balter Publisher: ISBN: Category : Languages : en Pages : 31
Book Description
We search for a trading strategy and the associated robust price of unhedgeable assets in incomplete markets under the acknowledgement of model uncertainty. Our set-up is that we postulate an agent who wants to maximise the expected surplus by choosing an optimal investment strategy. Furthermore, we assume that the agent is concerned about model misspecification. This robust optimal control problem under model uncertainty leads to (i) risk-neutral pricing for the traded risky assets, and (ii) adjusting the drift of the nontraded risk drivers in a conservative direction. The direction depends on the agent's long or short position, and the adjustment that ensures a robust strategy leads to what is known as "actuarial" or "prudential" pricing. Our results extend to a multivariate setting. We prove existence and uniqueness of the robust price in an incomplete market via the link between the semilinear partial differential equation and backward stochastic differential equations.
Author: Anne Balter Publisher: ISBN: Category : Languages : en Pages : 31
Book Description
We search for a trading strategy and the associated robust price of unhedgeable assets in incomplete markets under the acknowledgement of model uncertainty. Our set-up is that we postulate an agent who wants to maximise the expected surplus by choosing an optimal investment strategy. Furthermore, we assume that the agent is concerned about model misspecification. This robust optimal control problem under model uncertainty leads to (i) risk-neutral pricing for the traded risky assets, and (ii) adjusting the drift of the nontraded risk drivers in a conservative direction. The direction depends on the agent's long or short position, and the adjustment that ensures a robust strategy leads to what is known as "actuarial" or "prudential" pricing. Our results extend to a multivariate setting. We prove existence and uniqueness of the robust price in an incomplete market via the link between the semilinear partial differential equation and backward stochastic differential equations.
Author: Andrea Buraschi Publisher: ISBN: Category : Languages : en Pages : 60
Book Description
This paper provides option pricing and volume implications for an incomplete market economy with heterogenous agents who face model uncertainty and disagree on the dividend growth rate. Market incompleteness makes options non-redundant while heterogeneity creates a link between differences in beliefs and option volumes. We solve for both option prices and volumes and test the joint empirical implications using SP500 index option data. We use survey data to build an Index of Dispersion in Beliefs and find that a model which takes into account information heterogeneity can explain the dynamics of option volume better than reduced-form models with stochastic volatility. Moreover, its hedging performance is superior. Finally, we find that the Index of Dispersion in Beliefs is correlated with changes in the shape of the smile and it forecasts future realized volatility even after controlling for the current implied volatility.
Author: Dan Chen Publisher: ISBN: Category : Languages : en Pages :
Book Description
The thesis focuses on valuation and hedging problems when the market is incomplete. The first essay considers the quadratic hedging strategy. We propose a generalized quadratic hedging strategy which can balance a short-term risk (additional cost) with a long-term risk (hedging errors). The traditional quadratic hedging strategies, i.e. self-financing strategy and risk-minimization strategy, can be seen as special cases of the generalized quadratic hedging strategy. This is applied to the insurance derivatives market. The second essay compares parametric and nonparametric measure-changing techniques. The essay discusses three pricing approaches: pricing via Esscher measure, via calibration and via nonparametric risk-neutral density; and empirically compares the performance of the three approaches in the metal futures markets. The last essay establishes the concept of stochastic volatility of volatility and proposes several estimation methods.
Author: Hirbod Assa Publisher: ISBN: Category : Languages : en Pages : 111
Book Description
This thesis consists of three essays in financial econometrics. In the first part of the thesis, motivated by different applications of hedging methods in the literature, we propose a general theoretical framework for hedging and pricing. First, we review briefly different strands of literature on hedging which have been developed in various fields such as finance, economics, operations research and mathematics, and then try to come up with a tractable way for hedging and pricing in this paper. By introducing different market principles, we study conditions under which the hedging problem has a solution and pricing is possible. We will conduct an in-depth theoretical analysis of hedging strategies with shortfall risks as well as the spectral risk measures, in particular those associated with Choquet expected utility. We show that asymmetric information results in incorrect risk assessment and pricing. In the second part of the thesis, we will apply our results in the first part to construct an economic risk hedge. We also introduce a general method to estimate the stochastic discount factors associated with different risk measures and different financial models. The third part of the thesis modifies the speculative storage model by embedding staggered price features into the structural model of Deaton and Laroque (1996). In an attempt to replicate the stylized facts of observed commodity price dynamics, we add an additional source of intertemporal linkage to Deaton and Laroque (1996), namely speculation in intermediate-good inventories. The introduction of this type of friction into the model is motivated by its ability to increase price stickiness which gives rise to an increased persistence in the first and higher conditional moments of commodity prices. By incorporating intermediate risk neutral speculators and a final bundler with a staggered pricing rule in the spirit of Calvo (1983) into the storage model, we are able to capture a high degree of serial correlation and conditional heteroskedasticity, which are observed in actual data. The structural parameters of both Deaton and Laroque (1996) and our modified models are estimated using actual prices for 8 agricultural commodities. Simulated data are then employed to assess the effects of our staggered price approach on the time-series properties of commodity prices. Our results lend empirical support to the possibility of staggered prices.
Author: Srdjan Stojanovic Publisher: Springer Science & Business Media ISBN: 0387714170 Category : Mathematics Languages : en Pages : 274
Book Description
This book is written for quantitative finance professionals, students, educators, and mathematically inclined individual investors. It is about some of the latest developments in pricing, hedging, and investing in incomplete markets. With regard to pricing, two frameworks are fully elaborated: neutral and indifference pricing. With regard to hedging, the most conservative and relaxed hedging formulas are derived. With regard to investing, the neutral pricing methodology is also considered as a tool for connecting market asset prices with optimal positions in such assets. Srdjan D. Stojanovic is Professor in the Department of Mathematical Sciences at University of Cincinnati (USA) and Professor in the Center for Financial Engineering at Suzhou University (China).
Author: Anne Balter
Author: Anne Balter
Author: Michael Kirch
Author: Andrea Buraschi
Author: Dimitris Bertsimas
Author: Stephanos C. Panayides
Author: Thierry Chauveau
Author: Dan Chen
Author: Hirbod Assa
Author: Zhibo Yu
Author: Srdjan Stojanovic