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Marie-claire Quenez - One of the best experts on this subject based on the ideXlab platform.
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European options in a non-linear Incomplete Market model with default
SIAM Journal on Financial Mathematics, 2020Co-Authors: Miryana Grigorova, Marie-claire Quenez, Agnès SulemAbstract:This paper studies the superhedging prices and the associated superhedging strategies for European options in a non-linear Incomplete Market model with default. We present the seller's and the buyer's point of view. The underlying Market model consists of a risk-free asset and a risky asset driven by a Brownian motion and a compensated default martingale. The portfolio processes follow non-linear dynamics with a non-linear driver f. By using a dynamic programming approach, we first provide a dual formulation of the seller's (superhedging) price for the European option as the supremum, over a suitable set of equivalent probability measures Q ∈ Q, of the f-evaluation/expectation under Q of the payoff. We also provide a characterization of the seller's (superhedging) price process as the minimal supersolution of a constrained BSDE with default and a characterization in terms of the minimal weak supersolution of a BSDE with default. By a form of symmetry, we derive corresponding results for the buyer. Our results rely on first establishing a non-linear optional and a non-linear predictable decomposition for processes which are $\mathcal{E}^f$-strong supermartingales under Q, for all Q ∈ Q.
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American options in a non-linear Incomplete Market model with default
2019Co-Authors: Miryana Grigorova, Marie-claire Quenez, Agnès SulemAbstract:We study the superhedging prices and the associated superhedging strategies for American options in a non-linear Incomplete Market model with default. The points of view of the seller and of the buyer are presented. The underlying Market model consists of a risk-free asset and a risky asset driven by a Brownian motion and a compensated default martingale. The portfolio processes follow non-linear dynamics with a non-linear driver f. We give a dual representation of the seller's (superhedging) price for the American option associated with a completely irregular payoff $(\xi_t)$ (not necessarily càdlàg) in terms of the value of a non-linear mixed control/stopping problem. The dual representation involves a suitable set of equivalent probability measures, which we call f-martingale probability measures. We also provide two infinitesimal characterizations of the seller's price process: in terms of the minimal supersolution of a constrained reflected BSDE and in terms of the minimal supersolution of an optional reflected BSDE. Under some regularity assumptions on $\xi$, we also show a duality result for the buyer's price in terms of the value of a non-linear control/stopping game problem.
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Superhedging prices of European and American options in a non-linear Incomplete Market with default
2018Co-Authors: Miryana Grigorova, Marie-claire Quenez, Agnès SulemAbstract:This paper studies the superhedging prices and the associated superhedging strategies for European and American options in a non-linear Incomplete Market with default. We present the seller's and the buyer's point of view. The underlying Market model consists of a risk-free asset and a risky asset driven by a Brownian motion and a compensated default martingale. The portfolio process follows non-linear dynamics with a non-linear driver f. By using a dynamic programming approach, we first provide a dual formulation of the seller's (superhedging) price for the European option as the supremum over a suitable set of equivalent probability measures Q ∈ Q of the f-evaluation/expectation under Q of the payoff. We also provide an infinitesimal characterization of this price as the minimal supersolution of a constrained BSDE with default. By a form of symmetry, we derive corresponding results for the buyer. We also give a dual representation of the seller's (superhedging) price for the American option associated with an irregular payoff (ξ t) (not necessarily càdlàg) in terms of the value of a non-linear mixed control/stopping problem. We also provide an infinitesimal characterization of this price in terms of a constrained reflected BSDE. When ξ is càdlàg, we show a duality result for the buyer's price. These results rely on first establishing a non-linear optional decomposition for processes which are E f-strong supermartingales under Q, for all Q ∈ Q.
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Portfolio optimization in a default model under full/partial information
Probability in the Engineering and Informational Sciences, 2015Co-Authors: Marie-claire QuenezAbstract:In this paper, we consider a financial Market with assets exposed to some risks inducing jumps in the asset prices, and which can still be traded after default times. We use a default-intensity modeling approach, and address in this Incomplete Market context the problem of maximization of expected utility from terminal wealth for logarithmic, power and exponential utility functions. We study this problem as a stochastic control problem both under full and partial information. Our contribution consists in showing that the optimal strategy can be obtained by a direct approach for the logarithmic utility function, and the value function for the power utility function can be determined as the minimal solution of a backward stochastic differential equation. For the partial information case, we show how the problem can be divided into two problems: a filtering problem and an optimization problem. We also study the indifference pricing approach to evaluate the price of a contingent claim in an Incomplete Market and the information price for an agent with insider information.
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PORTFOLIO OPTIMIZATION IN A DEFAULT MODEL UNDER FULL/PARTIAL INFORMATION
Probability in the Engineering and Informational Sciences, 2015Co-Authors: Marie-claire QuenezAbstract:In this paper, we consider a financial Market with an asset exposed to a risk inducing a jump in the asset price, and which can still be traded after the default time. We use a default-intensity modeling approach, and address in this Incomplete Market context the problem of maximization of expected utility from terminal wealth for logarithmic, power and exponential utility functions. We study this problem as a stochastic control problem both under full and partial information. Our contribution consists of showing that the optimal strategy can be obtained by a direct approach for the logarithmic utility function, and the value function for the power (resp. exponential) utility function can be determined as the minimal (resp. maximal) solution of a backward stochastic differential equation. For the partial information case, we show how the problem can be divided into two problems: a filtering problem and an optimization problem. We also study the indifference pricing approach to evaluate the price of a contingent claim in an Incomplete Market and the information price for an agent with insider information.
Robert A Jarrow - One of the best experts on this subject based on the ideXlab platform.
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volatility uncertainty time decay and option bid ask spreads in an Incomplete Market
Management Science, 2017Co-Authors: Peilin Hsieh, Robert A JarrowAbstract:This paper documents the fact that in options Markets, the (percentage) implied volatility bid-ask spread increases at an increasing rate as the option’s maturity date approaches. To explain this stylized fact, this paper provides a Market microstructure model for the bid-ask spread in options Markets. We first construct a static equilibrium model to illustrate the aforementioned phenomenon where risk averse and competitive option Market makers quote bid and ask prices to minimize their inventory risk in an Incomplete Market with both directional and volatility risk. We extend this model to multiperiods and show that the same phenomenon occurs there as well. Two new implications are generated: a volatility level effect and a volatility variance effect. These implications are empirically tested, and the empirical results confirm the model’s validity. Finally, we document the importance of detrending the maturity effect by showing that the detrended percentage volatility spread explains future jump intensit...
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volatility uncertainty time decay and option bid ask spreads in an Incomplete Market
2017Co-Authors: Peilin Hsieh, Robert A JarrowAbstract:This paper documents the fact that in option Markets, the percentage implied volatility bid-ask spread increases at an increasing rate as the option’s maturity date approaches. We construct an equilibrium model to explain this phenomena. The equilibrium model has risk averse and competitive option Market makers quoting bid and ask prices to minimize their inventory risk in an Incomplete Market with both directional and volatility risk. Two additional testable implications of the model are generated. These are that: (1) an increase in the level of the underlying’s volatility decreases an option’s percentage implied volatility bid-ask spread, and (2) holding the level of the volatility constant, an increase in the volatility’s variance also increases an option’s percentage implied volatility bid-ask spread. These additional implications are empirically tested using index options on the Taiwan stock price index over the time period 2007-2010. The empirical results confirm the model’s validity.
Hildegard Dierker - One of the best experts on this subject based on the ideXlab platform.
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ownership structure and control in Incomplete Market economies with transferable utility
Economic Theory, 2012Co-Authors: Egbert Dierker, Hildegard DierkerAbstract:We consider an economy with Incomplete Markets and a single firm and assume that utility can be freely transferred in the form of the initially available good 0 (quasilinearity). In this particularly simple and transparent framework, the objective of a firm can be defined as the maximization of the total utility of its control group $${\fancyscript C}$$ measured in units of good 0. We analyze how the size and the composition of $${\fancyscript C}$$ influence the firm’s Market behavior and state conditions under which the firm sells its output at prices which are at, above, or below marginal costs, respectively. We discuss the assumption of competitive price perceptions and point out important differences between the concepts of a Dreze and of a Grossman-Hart equilibrium that occur in spite of the close similarity of the formulas which define them. Copyright Springer-Verlag 2012
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ownership structure and control in Incomplete Market economies with transferable utility
Vienna Economics Papers, 2011Co-Authors: Egbert Dierker, Hildegard DierkerAbstract:We consider an economy with Incomplete Markets and a single ¯rm and assume that utility can be freely transferred in the form of the ini- tially available good 0 (quasilinearity). In this particularly simple and transparent framework, the objective of a firm can be defined as the max- imization of the total utility of its control group C measured in units of good 0. We analyze how the size and the composition of C influences the rm's Market behavior and state conditions under which the firm sells its output at prices which are at, above, or below marginal costs, respectively. We discuss the assumption of competitive price perceptions and point out important differences between the concepts of a Dreze and of a Grossman- Hart equilibrium that occur in spite of the close similarity of the formulas which define them.
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welfare and efficiency in Incomplete Market economies with a single firm
Journal of Mathematical Economics, 2010Co-Authors: Egbert Dierker, Hildegard DierkerAbstract:Abstract In the quasilinear case, surplus maximization leads to constrained efficient Dreze equilibria. We investigate the question of whether surplus maximization can be useful beyond the quasilinear case. We use two different surplus concepts, the equivalent and the compensating surplus. The first one is a utilitarian social welfare function and the second one a measure of inefficiency. We show that social welfare maximization can be at odds with constrained efficiency. In particular, a unique Dreze equilibrium can maximize welfare although it is not minimally constrained efficient. The Dreze equilibrium can also minimize welfare although it entails no efficiency losses. We argue that the two surplus concepts should be used together and that they can help to distinguish between different Dreze equilibria on welfare and efficiency grounds.
Peilin Hsieh - One of the best experts on this subject based on the ideXlab platform.
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volatility uncertainty time decay and option bid ask spreads in an Incomplete Market
Management Science, 2017Co-Authors: Peilin Hsieh, Robert A JarrowAbstract:This paper documents the fact that in options Markets, the (percentage) implied volatility bid-ask spread increases at an increasing rate as the option’s maturity date approaches. To explain this stylized fact, this paper provides a Market microstructure model for the bid-ask spread in options Markets. We first construct a static equilibrium model to illustrate the aforementioned phenomenon where risk averse and competitive option Market makers quote bid and ask prices to minimize their inventory risk in an Incomplete Market with both directional and volatility risk. We extend this model to multiperiods and show that the same phenomenon occurs there as well. Two new implications are generated: a volatility level effect and a volatility variance effect. These implications are empirically tested, and the empirical results confirm the model’s validity. Finally, we document the importance of detrending the maturity effect by showing that the detrended percentage volatility spread explains future jump intensit...
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volatility uncertainty time decay and option bid ask spreads in an Incomplete Market
2017Co-Authors: Peilin Hsieh, Robert A JarrowAbstract:This paper documents the fact that in option Markets, the percentage implied volatility bid-ask spread increases at an increasing rate as the option’s maturity date approaches. We construct an equilibrium model to explain this phenomena. The equilibrium model has risk averse and competitive option Market makers quoting bid and ask prices to minimize their inventory risk in an Incomplete Market with both directional and volatility risk. Two additional testable implications of the model are generated. These are that: (1) an increase in the level of the underlying’s volatility decreases an option’s percentage implied volatility bid-ask spread, and (2) holding the level of the volatility constant, an increase in the volatility’s variance also increases an option’s percentage implied volatility bid-ask spread. These additional implications are empirically tested using index options on the Taiwan stock price index over the time period 2007-2010. The empirical results confirm the model’s validity.
Lane P. Hughston - One of the best experts on this subject based on the ideXlab platform.
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Optimal Hedging in Incomplete Markets
Applied Mathematical Finance, 2020Co-Authors: George Bouzianis, Lane P. HughstonAbstract:We consider the problem of optimal hedging in an Incomplete Market with an established pricing kernel. In such a Market, prices are uniquely determined, but perfect hedges are usually not available...
