Actuarial approach in a mixed fractional Brownian motion with jumps environment for pricing currency option

Shokrollahi, Foad; Kılıçman, Adem

doi:10.1186/s13662-015-0590-8

Cited by 24 publications

(16 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, due to the absence of actual market transaction data, the market price of risk cannot be calculated. Since Bladt and Rydberg [44] proposed the use of actuarial pricing, this method has been widely used in options pricing [45]. As an important classical tool in actuarial pricing, the Esscher transform is widely used in options pricing and has a wide range of applications [46].…”

Section: Literature Reviewmentioning

confidence: 99%

An Actuarial Pricing Method for Air Quality Index Options

Liu

Zhao

Wang

et al. 2019

IJERPH

View full text Add to dashboard Cite

Poor air quality has a negative impact on social life and economic production activities. Using financial derivatives to hedge risks is one of the important methods. Air quality index (AQI) options are designed to help enterprises cope with the operational risk caused by air pollution. First, the expanded Ornstein–Uhlenbeck model is established using an autoregressive-generalized autoregressive conditional heteroscedasticity (AR-GARCH) method to predict AQI for a city. Next, the average AQI is constructed to be as the underlying index for the AQI options. We then priced AQI options using an actuarial method with an Esscher transform. Meanwhile payoff functions for the options are established to let enterprises hedge against the operational risk caused by air pollution. Finally, we determined the price of AQI options using data from Xi’an, China, and the example of a tourism enterprise as a case study of how AQI options can be applied to hedge against operational risk for enterprises. With AQI options trading, enterprises can hedge against operational risks caused by air pollution. The applicability of AQI options is wide, it can also be applied in other cities or regions.

show abstract

Section: Literature Reviewmentioning

confidence: 99%

An Actuarial Pricing Method for Air Quality Index Options

Liu

Zhao

Wang

et al. 2019

IJERPH

View full text Add to dashboard Cite

show abstract

“…Falkowski [59] proposed a fractional Black-Scholes pricing model with time-dependent volatility for options and derived the analytic formulae via an actuarial method. Shokrollahi and Klllçman [60] studied the strategy of fair insurance premium actuarial approach for pricing foreign currency option under the jump mixed fractional Brownian motion environment. A lot of the literature on options pricing using the actuarial approach could be found in [61][62][63][64].…”

Section: Introductionmentioning

confidence: 99%

Pricing Vulnerable Options in the Bifractional Brownian Environment with Jumps

Cheng

2021

Journal of Mathematics

View full text Add to dashboard Cite

In this paper, we study the valuation of European vulnerable options where the underlying asset price and the firm value of the counterparty both follow the bifractional Brownian motion with jumps, respectively. We assume that default event occurs when the firm value of the counterparty is less than the default boundary. By using the actuarial approach, analytic formulae for pricing the European vulnerable options are derived. The proposed pricing model contains many existing models such as Black–Scholes model (1973), Merton jump-diffusion model (1976), Klein model (1996), and Tian et al. model (2014).

show abstract

“…However, continuous assumptions on the dynamics of assets ignore sudden shocks to asset returns due to the arrival of important information, since the financial crisis and significant business always result in sudden changes in firm values, which cannot be captured by continuous sample paths. To get around this problem and to take into account the long memory property, it is reasonable to use the mfBm with jumps model to capture fluctuations of the financial asset (see [27,30,31,33,36]).…”

Section: Introductionmentioning

confidence: 99%

A New Stopping Problem and the Critical Exercise Price for American Fractional Lookback Option in a Special Mixed Jump-Diffusion Model

Yang

2018

Prob. Eng. Inf. Sci.

View full text Add to dashboard Cite

A new stopping problem and the critical exercise price of American fractional lookback option are developed in the case where the stock price follows a special mixed jump diffusion fractional Brownian motion. By using Itô formula and Wick-Itô-Skorohod integral a new market pricing model is built, and the fundamental solutions of stochastic parabolic partial differential equations are deduced under the condition of Merton assumptions. With an optimal stopping problem and the exercise boundary, the explicit integral representation of early exercise premium and the critical exercise price are also derived. Numerical simulation illustrates the asymptotic behavior of this critical boundary.

show abstract

Actuarial approach in a mixed fractional Brownian motion with jumps environment for pricing currency option

Cited by 24 publications

References 20 publications

An Actuarial Pricing Method for Air Quality Index Options

An Actuarial Pricing Method for Air Quality Index Options

Pricing Vulnerable Options in the Bifractional Brownian Environment with Jumps

A New Stopping Problem and the Critical Exercise Price for American Fractional Lookback Option in a Special Mixed Jump-Diffusion Model

Contact Info

Product

Resources

About