Analytically pricing volatility swaps and volatility options with discrete sampling: Nonlinear payoff volatility derivatives

Rujivan, Sanae; Rakwongwan, Udomsak

doi:10.1016/j.cnsns.2021.105849

Cited by 12 publications

(6 citation statements)

References 26 publications

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“…In addition, the outcomes presented in [11] , [12] and Rujivan and Rakwongwan [12] show that the method proposed in [10] can be used for pricing variance swaps and volatility swaps. Thamrongrat and Rujivan [17] used the outcomes proposed in [13] to the pricing of interest rate swaps in terms of bond prices when the interest rate process follows the ECIR model (1.2) .…”

Section: Introductionmentioning

confidence: 99%

A closed-form expansion for the conditional expectations of the extended CIR process

Rujivan

Thamrongrat

2022

Heliyon

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Section: Introductionmentioning

confidence: 99%

A closed-form expansion for the conditional expectations of the extended CIR process

Rujivan

Thamrongrat

2022

Heliyon

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“…In hypothesis testing, several test statistics converge in distribution toward a conic combination of independent noncentral chi-square random variables (see, e.g., [2][3][4][5]). Moreover, f Y n (y) and E[Y γ n ] play an interesting role in financial applications; see, e.g., [6][7][8][9][10][11]. Very recently, Rujivan and Rakwongwan [11], Chumpong et al [6], and Rujivan [10] showed that the log-return realized variance when the underlying asset follows the extended Black-Scholes model can be expressed in terms of a conic combination of independent noncentral chi-square random variables.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, f Y n (y) and E[Y γ n ] play an interesting role in financial applications; see, e.g., [6][7][8][9][10][11]. Very recently, Rujivan and Rakwongwan [11], Chumpong et al [6], and Rujivan [10] showed that the log-return realized variance when the underlying asset follows the extended Black-Scholes model can be expressed in terms of a conic combination of independent noncentral chi-square random variables. As a result, they derived the exact PDF of the log-return realized variance as well as an explicit formula for the γ th moment of the log-return realized variance for γ = 1 2 , 1, yielding the first explicit pricing formulas for volatility swaps, volatility options, variance swaps, and variance options, respectively.…”

Section: Introductionmentioning

confidence: 99%

Analytically Computing the Moments of a Conic Combination of Independent Noncentral Chi-Square Random Variables and Its Application for the Extended Cox–Ingersoll–Ross Process with Time-Varying Dimension

et al. 2023

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This paper focuses mainly on the problem of computing the γth, γ>0, moment of a random variable Yn:=∑i=1nαiXi in which the αi’s are positive real numbers and the Xi’s are independent and distributed according to noncentral chi-square distributions. Finding an analytical approach for solving such a problem has remained a challenge due to the lack of understanding of the probability distribution of Yn, especially when not all αi’s are equal. We analytically solve this problem by showing that the γth moment of Yn can be expressed in terms of generalized hypergeometric functions. Additionally, we extend our result to computing the γth moment of Yn when Xi is a combination of statistically independent Zi2 and Gi in which the Zi’s are distributed according to normal or Maxwell–Boltzmann distributions and the Gi’s are distributed according to gamma, Erlang, or exponential distributions. Our paper has an immediate application in interest rate modeling, where we can explicitly provide the exact transition probability density function of the extended Cox–Ingersoll–Ross (ECIR) process with time-varying dimension as well as the corresponding γth conditional moment. Finally, we conduct Monte Carlo simulations to demonstrate the accuracy and efficiency of our explicit formulas through several numerical tests.

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“…For the American option (on stocks), the reader can consult Kim [13], Underwood and Wang [23], and Carr et al [5] for more details. Moreover, the PDE approach based on the Feynman-Kac theorem [15] was applied to price volatility derivatives as proposed in [7,[16][17][18][19][20]24].…”

Section: Introductionmentioning

confidence: 99%

An Analytical Option Pricing Formula for Mean-Reverting Asset With Time-Dependent Parameter

2021

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We present an analytical option pricing formula for the European options, in which the price dynamics of a risky asset follows a mean-reverting process with a time-dependent parameter. The process can be adapted to describe a seasonal variation in price such as in agricultural commodity markets. An analytical solution is derived based on the solution of a partial differential equation, which shows that a European option price can be decomposed into two terms: the payoff of the option at the initial time and the time-integral over the lifetime of the option driven by a time-dependent parameter. Finally, results obtained from the formula have been compared with Monte Carlo simulations and a Black–Scholes-type formula under various kinds of long-run mean functions, and some examples of option price behaviours have been provided.

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Analytically pricing volatility swaps and volatility options with discrete sampling: Nonlinear payoff volatility derivatives

Cited by 12 publications

References 26 publications

A closed-form expansion for the conditional expectations of the extended CIR process

A closed-form expansion for the conditional expectations of the extended CIR process

Analytically Computing the Moments of a Conic Combination of Independent Noncentral Chi-Square Random Variables and Its Application for the Extended Cox–Ingersoll–Ross Process with Time-Varying Dimension

An Analytical Option Pricing Formula for Mean-Reverting Asset With Time-Dependent Parameter

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