On the Pricing of Perpetual American Compound Options

Gapeev, Pavel V.; Rodosthenous, Neofytos

doi:10.1007/978-3-319-02069-3_13

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…Carmona and Dayanik (2008) then obtained a closed form solution of a multiple (multi-step) optimal stopping problem for a general linear regular diffusion process and a general payoff function among others. The problem of pricing of American compound standard put and call options in the classical Black-Merton-Scholes model was explicitly solved in Gapeev and Rodosthenous (2014a). The same problem in the more general stochastic volatility framework was studied by Chiarella and Kang (2009), where the associated two-step free-boundary problems for partial differential equations were solved numerically, by means of a modified sparse grid approach.…”

Section: Formulation Of the Problemsmentioning

confidence: 99%

Optimal Double Stopping Problems for Maxima and Minima of Geometric Brownian Motions

Gapeev

Kort

Lavrutich

et al. 2022

Methodol Comput Appl Probab

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We present closed-form solutions to some double optimal stopping problems with payoffs representing linear functions of the running maxima and minima of a geometric Brownian motion. It is shown that the optimal stopping times are th first times at which the underlying process reaches some lower or upper stochastic boundaries depending on the current values of its running maximum or minimum. The proof is based on the reduction of the original double optimal stopping problems to sequences of single optimal stopping problems for the resulting three-dimensional continuous Markov process. The latter problems are solved as the equivalent free-boundary problems by means of the smooth-fit and normal-reflection conditions for the value functions at the optimal stopping boundaries and the edges of the three-dimensional state space. We show that the optimal stopping boundaries are determined as the extremal solutions of the associated first-order nonlinear ordinary differential equations. The obtained results are related to the valuation of perpetual real double lookback options with floating sunk costs in the Black-Merton-Scholes model.

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Section: Formulation Of the Problemsmentioning

confidence: 99%

Optimal Double Stopping Problems for Maxima and Minima of Geometric Brownian Motions

Gapeev

Kort

Lavrutich

et al. 2022

Methodol Comput Appl Probab

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“…Some distributional characteristics including the probability of a drawdown of a given size occurring before a drawup of a fixed size were computed by Pospisil et al (2009) in several one-dimensional diffusion models (see also Zhang (2018) for an extensive survey of models with stochastic drawdowns). The problem of pricing of American compound standard put and call options in the classical Black-Merton-Scholes model was explicitly solved in Gapeev and Rodosthenous (2014a). The same problem in the more general stochastic volatility framework was studied by Chiarella and Kang (2009), where the associated two-step free-boundary problems for partial differential equations were solved numerically, by means of a modified sparse grid approach.…”

Section: Introductionmentioning

confidence: 99%

Perpetual American Double Lookback Options on Drawdowns and Drawups with Floating Strikes

Gapeev

2022

Methodol Comput Appl Probab

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We present closed-form solutions to the problems of pricing of the perpetual American double lookback put and call options on the maximum drawdown and the maximum drawup with floating strikes in the Black-Merton-Scholes model. It is shown that the optimal exercise times are the first times at which the underlying risky asset price process reaches some lower or upper stochastic boundaries depending on the current values of its running maximum or minimum as well as the maximum drawdown or maximum drawup. The proof is based on the reduction of the original double optimal stopping problems to the appropriate sequences of single optimal stopping problems for the three-dimensional continuous Markov processes. The latter problems are solved as the equivalent free-boundary problems by means of the smooth-fit and normal-reflection conditions for the value functions at the optimal stopping boundaries and the edges of the three-dimensional state spaces. We show that the optimal exercise boundaries are determined as either the unique solutions of the associated systems of arithmetic equations or the minimal and maximal solutions of the appropriate first-order nonlinear ordinary differential equations.

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Pricing Perpetual American Compound Options under a Matrix-Exponential Jump-Diffusion Model

Chang

Sheu

Tsai

2015

Applied Mathematical Finance

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On the Pricing of Perpetual American Compound Options

Cited by 3 publications

References 14 publications

Optimal Double Stopping Problems for Maxima and Minima of Geometric Brownian Motions

Optimal Double Stopping Problems for Maxima and Minima of Geometric Brownian Motions

Perpetual American Double Lookback Options on Drawdowns and Drawups with Floating Strikes

Pricing Perpetual American Compound Options under a Matrix-Exponential Jump-Diffusion Model

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