Applications of Hilfer-Prabhakar operator to option pricing financial model

2020 ◽  
Vol 23 (4) ◽  
pp. 996-1012 ◽  
Author(s):  
Živorad Tomovski ◽  
Johan L. A. Dubbeldam ◽  
Jan Korbel
Keyword(s):  
Option Pricing ◽  
Fractional Diffusion ◽  
Pricing Models ◽  
Financial Model ◽  
Series Representations ◽  
Risk Neutral

AbstractIn this paper, we focus on option pricing models based on time-fractional diffusion with generalized Hilfer-Prabhakar derivative. It is demonstrated how the option is priced for fractional cases of European vanilla option pricing models. Series representations of the pricing formulas and the risk-neutral parameter under the time-fractional diffusion are also derived.

scholarly journals Risk‐neutral moment‐based estimation of affine option pricing models

2018 ◽  
Vol 33 (7) ◽  
pp. 1007-1025 ◽  
Author(s):  
Bruno Feunou ◽  
Cédric Okou
Keyword(s):  
Option Pricing ◽  
Pricing Models ◽  
Risk Neutral

scholarly journals GARCH Option Pricing Models and the Variance Risk Premium

2020 ◽  
Vol 13 (3) ◽  
pp. 51
Author(s):  
Wenjun Zhang ◽  
Jin E. Zhang
Keyword(s):  
Option Pricing ◽  
Risk Premium ◽  
Empirical Estimation ◽  
Pricing Models ◽  
Variance Risk Premium ◽  
Pricing Options ◽  
Volatility Index ◽  
Risk Neutral ◽  
Local Risk ◽  
Variance Risk

In this paper, we modify Duan’s (1995) local risk-neutral valuation relationship (mLRNVR) for the GARCH option-pricing models. In our mLRNVR, the conditional variances under two measures are designed to be different and the variance process is more persistent in the risk-neutral measure than in the physical one, so that one is able to capture the variance risk premium. Empirical estimation exercises show that the GARCH option-pricing models under our mLRNVR are able to price the SPX one-month variance swap rate, i.e., the CBOE Volatility Index (VIX) accurately. Our research suggests that one should use our mLRNVR when pricing options with GARCH models.

scholarly journals Fractional Partial Differential Equations associated with L$\hat{e}$vy Stable Process

2020 ◽  
Author(s):  
Reem Abdullah Aljedhi ◽  
Adem Kilicman
Keyword(s):  
Diffusion Equation ◽  
Option Pricing ◽  
Stable Process ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
European Option ◽  
Fractional Partial Differential Equations ◽  
European Option Pricing ◽  
Risk Neutral ◽  
Time Fractional Diffusion Equation

In this study, we first present a time-fractional L$\hat{e}$vy diffusion equation of the exponential option pricing models of European option pricing and the risk-neutral parameter. Then, we modify a particular L$\hat{e}$vy-time fractional diffusion equation of European-style options. Introduce a more general model from the models based on the L$\hat{e}$vy-time fractional diffusion equation and review some recent findings regarding of the Europe option pricing of risk-neutral free.

scholarly journals Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 796 ◽  
Author(s):  
Jean-Philippe Aguilar ◽  
Jan Korbel ◽  
Yuri Luchko
Keyword(s):  
Diffusion Equation ◽  
Option Pricing ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Model Parameters ◽  
Exotic Options ◽  
European Option ◽  
European Option Pricing ◽  
Space Fractional Diffusion Equation ◽  
Risk Neutral

In this article, we first provide a survey of the exponential option pricing models and show that in the framework of the risk-neutral approach, they are governed by the space-fractional diffusion equation. Then, we introduce a more general class of models based on the space-time-fractional diffusion equation and recall some recent results in this field concerning the European option pricing and the risk-neutral parameter. We proceed with an extension of these results to the class of exotic options. In particular, we show that the call and put prices can be expressed in the form of simple power series in terms of the log-forward moneyness and the risk-neutral parameter. Finally, we provide the closed-form formulas for the first and second order risk sensitivities and study the dependencies of the portfolio hedging and profit-and-loss calculations upon the model parameters.

scholarly journals Fractional Partial Differential Equations Associated with Lêvy Stable Process

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 508
Author(s):  
Reem Abdullah Aljedhi ◽  
Adem Kılıçman
Keyword(s):  
Diffusion Equation ◽  
Option Pricing ◽  
Stable Process ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
European Option ◽  
Fractional Partial Differential Equations ◽  
European Option Pricing ◽  
Risk Neutral ◽  
Time Fractional Diffusion Equation

In this study, we first present a time-fractional L e ^ vy diffusion equation of the exponential option pricing models of European option pricing and the risk-neutral parameter. Then, we modify a particular L e ^ vy-time fractional diffusion equation of European-style options. Further, we introduce a more general model based on the L e ^ vy-time fractional diffusion equation and review some recent findings associated with risk-neutral free European option pricing.

scholarly journals Additive logistic processes in option pricing

2021 ◽  
Author(s):  
Peter Carr ◽  
Lorenzo Torricelli
Keyword(s):  
Option Pricing ◽  
Pricing Models ◽  
Underlying Asset ◽  
Formula One ◽  
Additive Type ◽  
Black Scholes ◽  
Minimum Price ◽  
Risk Neutral ◽  
Risk Neutral Probabilities ◽  
Security Price

AbstractIn option pricing, it is customary to first specify a stochastic underlying model and then extract valuation equations from it. However, it is possible to reverse this paradigm: starting from an arbitrage-free option valuation formula, one could derive a family of risk-neutral probabilities and a corresponding risk-neutral underlying asset process. In this paper, we start from two simple arbitrage-free valuation equations, inspired by the log-sum-exponential function and an $\ell ^{p}$ ℓ p vector norm. Such expressions lead respectively to logistic and Dagum (or “log-skew-logistic”) risk-neutral distributions for the underlying security price. We proceed to exhibit supporting martingale processes of additive type for underlying securities having as time marginals two such distributions. By construction, these processes produce closed-form valuation equations which are even simpler than those of the Bachelier and Samuelson–Black–Scholes models. Additive logistic processes provide parsimonious and simple option pricing models capturing various important stylised facts at the minimum price of a single market observable input.

Risk-Neutral and Physical Jumps in Option Pricing

2007 ◽  
Author(s):  
Jian Chen ◽  
Xiaoquan Liu ◽  
Chenghu Ma
Keyword(s):  
Option Pricing ◽  
Risk Neutral

Joint Calibration of Option Pricing Models via Particle Methods

2005 ◽  
Author(s):  
Billy Amzal ◽  
Yonathan Ebguy ◽  
Sebastien Roland
Keyword(s):  
Option Pricing ◽  
Particle Methods ◽  
Pricing Models
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