scholarly journals Option Pricing Formulas Based on a Non-Gaussian Stock Price Model

2002 ◽  
Vol 89 (9) ◽  
Author(s):  
Lisa Borland
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Price Model ◽  
Non Gaussian

Learning for infinitely divisible GARCH models in option pricing

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Fumin Zhu ◽  
Michele Leonardo Bianchi ◽  
Young Shin Kim ◽  
Frank J. Fabozzi ◽  
Hengyu Wu
Keyword(s):  
Option Pricing ◽  
Stock Returns ◽  
Bayesian Learning ◽  
Space Structure ◽  
Estimation Methods ◽  
Garch Models ◽  
Learning Approaches ◽  
Infinitely Divisible ◽  
Asymmetric Garch ◽  
Non Gaussian

AbstractThis paper studies the option valuation problem of non-Gaussian and asymmetric GARCH models from a state-space structure perspective. Assuming innovations following an infinitely divisible distribution, we apply different estimation methods including filtering and learning approaches. We then investigate the performance in pricing S&P 500 index short-term options after obtaining a proper change of measure. We find that the sequential Bayesian learning approach (SBLA) significantly and robustly decreases the option pricing errors. Our theoretical and empirical findings also suggest that, when stock returns are non-Gaussian distributed, their innovations under the risk-neutral measure may present more non-normality, exhibit higher volatility, and have a stronger leverage effect than under the physical measure.

scholarly journals Optimal feedback control of stock prices under credit risk dynamics

2021 ◽  
Author(s):  
Jinghai Shao ◽  
Sovan Mitra ◽  
Andreas Karathanasopoulos
Keyword(s):  
Credit Risk ◽  
Stock Prices ◽  
Stock Price ◽  
Global Financial Crisis ◽  
Optimal Feedback Control ◽  
Dynamic Programming Principle ◽  
Price Model ◽  
Managerial Control ◽  
Optimal Feedback ◽  
The Impact

AbstractIn this paper we provide a stock price model that explicitly incorporates credit risk, under a stochastic optimal control system. The stock price model also incorporates the managerial control of credit risk through a control policy in the stochastic system. We provide explicit conditions on the existence of optimal feedback controls for the stock price model with credit risk. We prove the continuity of the value function, and then prove the dynamic programming principle for our system. Finally, we prove the Viscosity Solution of the Hamilton–Jacobi–Bellman equation. This paper is particularly relevant to industry, as the impact of credit risk upon stock prices has been prominent since the commencement of the Global Financial Crisis.

scholarly journals Good Volatility, Bad Volatility, and Option Pricing

2018 ◽  
Vol 54 (2) ◽  
pp. 695-727 ◽  
Author(s):  
Bruno Feunou ◽  
Cédric Okou
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Asset Price ◽  
Jump Diffusion ◽  
Quadratic Variation ◽  
Pricing Model ◽  
Economic Gain ◽  
Underlying Asset ◽  
Model Free ◽  
Option Pricing Model

Advances in variance analysis permit the splitting of the total quadratic variation of a jump-diffusion process into upside and downside components. Recent studies establish that this decomposition enhances volatility predictions and highlight the upside/downside variance spread as a driver of the asymmetry in stock price distributions. To appraise the economic gain of this decomposition, we design a new and flexible option pricing model in which the underlying asset price exhibits distinct upside and downside semivariance dynamics driven by the model-free proxies of the variances. The new model outperforms common benchmarks, especially the alternative that splits the quadratic variation into diffusive and jump components.

scholarly journals OPTION PRICING IN MARKETS WITH INFORMED TRADERS

2020 ◽  
Vol 23 (06) ◽  
pp. 2050037 ◽  
Author(s):  
Yuan Hu ◽  
Abootaleb Shirvani ◽  
Stoyan Stoyanov ◽  
Young Shin Kim ◽  
Frank J. Fabozzi ◽  
...  
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Stock Return ◽  
Asset Pricing Theory ◽  
Black Scholes ◽  
Informed Traders ◽  
Pricing Theory ◽  
Option Pricing Theory ◽  
Information Intensity ◽  
Dynamic Asset Pricing

The objective of this paper is to introduce the theory of option pricing for markets with informed traders within the framework of dynamic asset pricing theory. We introduce new models for option pricing for informed traders in complete markets, where we consider traders with information on the stock price direction and stock return mean. The Black–Scholes–Merton option pricing theory is extended for markets with informed traders, where price processes are following continuous-diffusions. By doing so, the discontinuity puzzle in option pricing is resolved. Using market option data, we estimate the implied surface of the probability for a stock upturn, the implied mean stock return surface, and implied trader information intensity surface.

Predicting the stock price of frontier markets using machine learning and modified Black–Scholes Option pricing model

2020 ◽  
Vol 555 ◽  
pp. 124444 ◽  
Author(s):  
Reaz Chowdhury ◽  
M.R.C. Mahdy ◽  
Tanisha Nourin Alam ◽  
Golam Dastegir Al Quaderi ◽  
M. Arifur Rahman
Keyword(s):  
Machine Learning ◽  
Option Pricing ◽  
Stock Price ◽  
Pricing Model ◽  
Black Scholes ◽  
Option Pricing Model

Dynamic Pricing Model of Power Options in a Fractional Market

2011 ◽  
Vol 225-226 ◽  
pp. 338-341
Author(s):  
Hui Zhang ◽  
Wen Yu Meng
Keyword(s):  
Option Pricing ◽  
Dynamic Pricing ◽  
Stock Price ◽  
Risk Preference ◽  
Conditional Density ◽  
Hurst Parameter ◽  
Pricing Model ◽  
Conditional Density Function ◽  
Price Process ◽  
Random Events

In this paper, we study the new method of option pricing based on the risk preference. We define the equivalent classes of random events based on the historical information and the risk preference. The dynamic pricing model of power options has been studied. Applying the conditional density function of the stock price process, we have given the explicit solution of the model. And we analyze the influence of Hurst parameter on pricing formula.

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