A Mean-Reverting Stochastic Volatility Option-Pricing Model With An Analytic Solution

2002 ◽  
Author(s):  
Henrik Andersson
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Analytic Solution ◽  
Pricing Model ◽  
Option Pricing Model

THE BRITTEN-JONES AND NEUBERGER SMILE-CONSISTENT WITH STOCHASTIC VOLATILITY OPTION PRICING MODEL: A FURTHER ANALYSIS

2002 ◽  
Vol 05 (01) ◽  
pp. 1-31 ◽  
Author(s):  
ALESSANDRO ROSSI
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Pricing Model ◽  
Pricing Models ◽  
No Arbitrage ◽  
Option Pricing Model ◽  
Exotic Option ◽  
Exotic Option Pricing ◽  
Insight Into

In part of the recent financial literature, exotic option pricing models have been built by establishing a link with European-style options. All these models share the characteristic of being consistent with the observed market smile. They differ respect to the specification of the volatility process. This paper provides a deeper insight into the Britten-Jones and Neuberger (1999) smile-consistent no arbitrage with stochastic volatility option pricing model. Their approach is similar, in spirit, to that one of Derman and Kani (1997), but the implementation is simpler and faster. We explain the main features of the model by performing a set of exercises. In addition we propose some extensions of the model, which make it more flexible.

OPTION PRICING AND EXECUTIVE STOCK OPTION INCENTIVES: AN EMPIRICAL INVESTIGATION UNDER GENERAL ERROR DISTRIBUTION STOCHASTIC VOLATILITY MODEL

2011 ◽  
Vol 28 (01) ◽  
pp. 81-93 ◽  
Author(s):  
MIN PAN ◽  
SHENGQIAO TANG
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Stock Option ◽  
Error Distribution ◽  
Stochastic Volatility Model ◽  
Pricing Model ◽  
Executive Stock Option ◽  
Volatility Model ◽  
Option Pricing Model ◽  
General Error

This article investigates the valuation of executive stock options when the stock return volatility is governed by the general error distribution stochastic volatility model, involving both the features of the stock return volatility and the abnormal fluctuations of the stock price at the expiration date. We estimate the parameters in the general error distribution stochastic volatility model using the Markov Chain Monte Carlo method with Shanghai & Shenzhen 300 Index in China as a sample, and compare the executive stock option values calculated by Black-Scholes option pricing model and the option pricing model under general error distribution stochastic volatility model. The results show that the general error distribution stochastic volatility model has greater veracity in describing the volatility of stock market returns, and there is divergence between the two values estimated by Black-Scholes option pricing model and the option pricing model under general error distribution stochastic volatility model. The divergence varies with the discrepancy between the price of underlying stock at the granting date and the strike price of the option.

Empirical study based on the model of rough fractional stochastic volatility (RFSV)

2021 ◽  
Author(s):  
Songyan Zhang ◽  
Chaoyong Hu
Keyword(s):  
Monte Carlo Simulation ◽  
Option Pricing ◽  
Stochastic Volatility ◽  
Option Price ◽  
Pricing Model ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Research Findings ◽  
S Model ◽  
The Empirical Analysis

To estimate the parameters of the model of option pricing based on the model of rough fractional stochastic volatility (RFSV), we have carried out the empirical analysis during our study on the pricing of SSE 50ETF options in China. First, we have estimated the parameters of option pricing model by adopting the Monte Carlo simulation. Subsequently, we have empirically examined the pricing performance of the RFSV model by adopting the SSE 50ETF option price from January 2019 to December 2020. Our research findings indicate that by leveraging the RFSV model, we are able to attain a more accurate and stable level of option pricing than the conventional Black–Scholes (B-S) model on constant volatility. The errors of option pricing incurred by the B-S model proved to be larger and exhibited higher volatility, revealing the significant impact imposed by stochastic volatility on option pricing.

scholarly journals EFFECTS OF RETURN PREDICTABILITY ON OPTION PRICES WITH STOCHASTIC VOLATILITY FOR THE MARKET PORTFOLIO

2005 ◽  
Vol 01 (01) ◽  
pp. 0550005
Author(s):  
MELANIE CAO
Keyword(s):  
Option Pricing ◽  
Interest Rates ◽  
Stochastic Volatility ◽  
Return Predictability ◽  
Option Prices ◽  
Pricing Model ◽  
Stochastic Interest Rates ◽  
Market Portfolio ◽  
Stochastic Interest ◽  
Option Pricing Model

I examine the effects of return predictability on option prices for the market portfolio in the presence of stochastic volatility and/or stochastic interest rates. The analysis is implemented in an equilibrium framework where a consistent option pricing model is derived with the return predictability and stochastic volatility and the precise link between the actual and the risk neutral measures is endogenized. The equilibrium analysis indicates that the return predictability is induced by the mean-reverting and heteroskedastic features of aggregate dividends. It is shown that risk-neutral option pricing model with the stochastic volatility and/or stochastic interest rates can be consistent with return predictability. Numerical results suggest that (i) models with either perfect predictability or no predictability will significantly overprice long-term options across different strike prices when the return of the underlying exhibits modest predictability; (ii) the stochastic volatility does not affect option prices in a significant way when asset return predictability is properly reflected in the actual stock price process; (iii) when return predictability is correctly specified, the effects of stochastic interest rates are not uniform.

Empirical Performance of the Constant Elasticity Variance Option Pricing Model

2009 ◽  
Vol 12 (02) ◽  
pp. 177-217 ◽  
Author(s):  
Ren-Raw Chen ◽  
Cheng-Few Lee ◽  
Han-Hsing Lee
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Pricing Model ◽  
Implementation Cost ◽  
Pricing Models ◽  
Cev Model ◽  
Constant Elasticity ◽  
Volatility Model ◽  
Option Pricing Model

In this essay, we empirically test the Constant–Elasticity-of-Variance (CEV) option pricing model by Cox (1975, 1996 ) and Cox and Ross (1976), and compare the performances of the CEV and alternative option pricing models, mainly the stochastic volatility model, in terms of European option pricing and cost-accuracy based analysis of their numerical procedures. In European-style option pricing, we have tested the empirical pricing performance of the CEV model and compared the results with those by Bakshi et al. (1997). The CEV model, introducing only one more parameter compared with Black-Scholes formula, improves the performance notably in all of the tests of in-sample, out-of-sample and the stability of implied volatility. Furthermore, with a much simpler model, the CEV model can still perform better than the stochastic volatility model in short term and out-of-the-money categories. When applied to American option pricing, high-dimensional lattice models are prohibitively expensive. Our numerical experiments clearly show that the CEV model performs much better in terms of the speed of convergence to its closed form solution, while the implementation cost of the stochastic volatility model is too high and practically infeasible for empirical work. In summary, with a much less implementation cost and faster computational speed, the CEV option pricing model could be a better candidate than more complex option pricing models, especially when one wants to apply the CEV process for pricing more complicated path-dependent options or credit risk models.

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