Rank Process, Stochastic Corridor and Applications to Finance

Miura, Ryozo

doi:10.1142/9789812708298_0026

Cited by 2 publications

(3 citation statements)

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“…Corridor options such as the α-quantile option have been studied in [19], [20]. Below we consider pricing of α-quantile options on the drawdown process.…”

Section: Option Pricing For the Drawdown Processmentioning

confidence: 99%

Occupation Times, Drawdowns, and Drawups for One-Dimensional Regular Diffusions

Zhang

2015

Adv. Appl. Probab.

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The drawdown process of a one-dimensional regular diffusion process X is given by X reflected at its running maximum. The drawup process is given by X reflected at its running minimum. We calculate the probability that a drawdown precedes a drawup in an exponential time-horizon. We then study the law of the occupation times of the drawdown process and the drawup process. These results are applied to address problems in risk analysis and for option pricing of the drawdown process. Finally, we present examples of Brownian motion with drift and three-dimensional Bessel processes, where we prove an identity in law.

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“…Corridor options such as the α-quantile option have been studied in [19], [20]. Below we consider pricing of α-quantile options on the drawdown process.…”

Section: Option Pricing For the Drawdown Processmentioning

confidence: 99%

Occupation Times, Drawdowns, and Drawups for One-Dimensional Regular Diffusions

Zhang

2015

Adv. Appl. Probab.

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“…It can be, for example, the logarithm of an asset price process.) The Laplace transform in (20) is readily available in Theorem 5. Hence, the price (19) can be computed via double Laplace inversion:…”

Section: Option Pricing For the Drawdown Processmentioning

confidence: 99%

“…where p and q are Laplace inversion operators. Corridor options such as the α-quantile option have been studied in [19], [20]. Below we consider pricing of α-quantile options on the drawdown process.…”

Section: Option Pricing For the Drawdown Processmentioning

confidence: 99%

Occupation Times, Drawdowns, and Drawups for One-Dimensional Regular Diffusions

Zhang

2015

Advances in Applied Probability

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The drawdown process of an one-dimensional regular diffusion process X is given by X reflected at its running maximum. The drawup process is given by X reflected at its running minimum. We calculate the probability that a drawdown proceeds a drawup in an exponential time-horizon. We then study the law of the occupation times of the drawdown process and the drawup process. These results are applied to address problems in risk analysis and for option pricing of the drawdown process. Finally, we present examples of Brownian motion with drift and three-dimensional Bessel processes, where we prove an identity in law.

show abstract

Rank Process, Stochastic Corridor and Applications to Finance

Cited by 2 publications

References 0 publications

Occupation Times, Drawdowns, and Drawups for One-Dimensional Regular Diffusions

Occupation Times, Drawdowns, and Drawups for One-Dimensional Regular Diffusions

Occupation Times, Drawdowns, and Drawups for One-Dimensional Regular Diffusions

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