Forward indifference valuation of American options

Leung, Tim; Sircar, Ronnie; Zariphopoulou, Thaleia

doi:10.1080/17442508.2012.694438

Cited by 20 publications

(19 citation statements)

References 34 publications

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“…If we were to allow the agents to trade other securities, one could envisage adding risk aversion by considering utility-based valuation and hedging, yielding combined optimal stopping and control problems. Such ESO problems have been considered for constant drift models by Leung and Sircar [35,36] and Grasselli and Henderson [27] using classical utility, and by Leung, Sircar and Zariphopoulou [37] using forward utility. These works take the required regularity of value functions as given.…”

Section: 1mentioning

confidence: 99%

Executive Stock Option Exercise with Full and Partial Information on a Drift Change Point

Henderson¹,

Kladívko²,

Monoyios³

et al. 2020

SIAM J. Finan. Math.

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We analyse the optimal exercise of an American call executive stock option (ESO) written on a stock whose drift parameter falls to a lower value at a change point, an exponentially distributed random time independent of the Brownian motion driving the stock. Two agents, who do not trade the stock, have differing information on the change point, and seek to optimally exercise the option by maximising its discounted payoff under the physical measure. The first agent has full information, and observes the change point. The second agent has partial information and filters the change point from price observations. This scenario is designed to mimic the positions of two employees of varying seniority, a fully informed executive and a partially informed less senior employee, each of whom receives an ESO. The partial information scenario yields a model under the observation filtration F in which the stock drift becomes a diffusion driven by the innovations process, an F-Brownian motion also driving the stock under F, and the partial information optimal stopping value function has two spatial dimensions. We rigorously characterise the free boundary PDEs for both agents, establish shape and regularity properties of the associated optimal exercise boundaries, and prove the smooth pasting property in both information scenarios, exploiting some stochastic flow ideas to do so in the partial information case. We develop finite difference algorithms to numerically solve both agents' exercise and valuation problems and illustrate that the additional information of the fully informed agent can result in exercise patterns which exploit the information on the change point, lending credence to empirical studies which suggest that privileged information of bad news is a factor leading to early exercise of ESOs prior to poor stock price performance.

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Section: 1mentioning

confidence: 99%

Executive Stock Option Exercise with Full and Partial Information on a Drift Change Point

Henderson¹,

Kladívko²,

Monoyios³

et al. 2020

SIAM J. Finan. Math.

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“…The aim of this paper is to study optimal investment evaluated by a forward performance criterion in a stochastic factor market model, in which the probability measure that models future stock price evolutions is ambiguous. The forward performance process, as an adapted stochastic dynamic utility evolving forward in time, has been introduced and developed in [41]- [45] (see also [24] and [55], and more recently [2], [3], [6], [12], [23], [28], [33], [37], [39] and [51]). This new concept differs from the classical expected utility function, in which the objective is to solve a stochastic control problem in a backward way via dynamic programming principle.…”

Section: Introductionmentioning

confidence: 99%

A Game Theoretical Approach to Homothetic Robust Forward Investment Performance Processes in Stochastic Factor Models

Li¹,

Liang

2020

SSRN Journal

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This paper studies an optimal forward investment problem in an incomplete market with model uncertainty, in which the underlying stocks depend on the correlated stochastic factors. The uncertainty stems from the probability measure chosen by an investor to evaluate the performance. We obtain directly the representation of the homothetic robust forward performance processes in factor-form by combining the zero-sum stochastic differential game and ergodic BSDE approach. We also establish the connections with the risk-sensitive zero-sum stochastic differential games over an infinite horizon with ergodic payoff criteria, as well as with the classical robust expected utilities for long time horizons. Finally, we give an example to illustrate that our approach can be applied to address a type of robust forward investment performance processes with negative realization processes.

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“…The aim of this paper is to study optimal investment evaluated by a forward performance criterion in a stochastic factor market model, in which the probability measure that models future stock price evolutions is ambiguous. The forward performance process, as an adapted stochastic utility function with respect to wealth and evolving forward in time, has been introduced and developed in [31]- [35] (see also [19], [29], and [44] and more recently [1], [18], and [23]). This new concept differs from the classical expected utility function, in which the problem is to solve a stochastic control problem in a backward way via dynamic programming principle.…”

Section: Introductionmentioning

confidence: 99%

A game theoretical approach to homothetic robust forward investment performance processes in stochastic factor models

Li¹,

Li²,

Liang³

2020

Preprint

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This paper studies an optimal forward investment problem in an incomplete market with model uncertainty, in which the dynamics of the underlying stocks depends on the correlated stochastic factors. The uncertainty stems from the probability measure chosen by an investor to evaluate the performance. We obtain directly the representation of the power robust forward performance process in factor-form by combining the zero-sum stochastic differential game and ergodic BSDE approach. We also establish the connections with the risk-sensitive zero-sum stochastic differential games over an infinite horizon with ergodic payoff criteria, as well as with the classical power robust expected utility for long time horizons.

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Forward indifference valuation of American options

Cited by 20 publications

References 34 publications

Executive Stock Option Exercise with Full and Partial Information on a Drift Change Point

Executive Stock Option Exercise with Full and Partial Information on a Drift Change Point

A Game Theoretical Approach to Homothetic Robust Forward Investment Performance Processes in Stochastic Factor Models

A game theoretical approach to homothetic robust forward investment performance processes in stochastic factor models

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