Noise trading and stock market bubbles: what the derivatives market is telling us

2020 ◽  
Vol 46 (9) ◽  
pp. 1165-1182
Author(s):  
Scott B. Beyer ◽  
J. Christopher Hughen ◽  
Robert A. Kunkel
Keyword(s):  
Stochastic Volatility ◽  
Noise Level ◽  
Implied Volatility ◽  
Mean Reversion ◽  
Jump Diffusion ◽  
Futures Prices ◽  
Noise Traders ◽  
Content Type ◽  
Noise Trading ◽  
Technology Bubble

PurposeThe authors examine the relation between noise trading in equity markets and stochastic volatility by estimating a two-factor jump diffusion model. Their analysis shows that contemporaneous price deviations in the derivatives market are statistically significant in explaining movements in index futures prices and option-market volatility measures.Design/methodology/approachTo understand the impact noise may have in the S&P 500 derivatives market, the authors first measure and evaluate the influence noise exerts on futures prices and then investigate its influence on option volatility.FindingsIn the period from 1996 to 2003, this study finds significant changes in the volatility and mean reversion in the noise level and a significant increase in its relation to implied volatility in option prices. The results are consistent with a bubble in technology stocks that occurred with significant increases in noise trading.Research limitations/implicationsThis study provides estimates for this model during the periods preceding and during the technology bubble. The study analysis shows that the volatility and mean reversion in the noise level are much stronger during the bubble period. Furthermore, the relation between noise trading and implied volatility in the futures market was of a significantly larger magnitude during this period. The study results support the importance of noise trading in market bubbles.Practical implicationsBloomfield, O'Hara and Saar (2009) find that noise traders lower bid–ask spreads and improve liquidity through increases in trading volume and market depth. Such improved market conditions could have positive effects on market quality, and this impact could be evidenced by lower implied volatility when noise traders are more active. Indeed, the results in this study indicate that the level and characteristics of noise trading are fundamentally different during the technology bubble, and this noise trading activity has a larger impact during this period on implied volatility in the options market.Originality/valueThis paper uniquely analyzes derivatives on the S&P 500 Index in order to detect the presence and influence of noise traders. The authors derive and implement a two-factor jump diffusion noise model. In their model, noise rectifies the difference of analysts' opinions, market information and beliefs among traders. By incorporating a reduced-form temporal expression of heterogeneities among traders, the model is rich enough to capture salient time-series characteristics of equity prices (i.e. stochastic volatility and jumps). A singular feature of the authors’ model is that stochastic volatility represents the random movements in asset prices that are attributed to nonmarket fundamentals.

A theoretical model of jump diffusion-mean reversion

2017 ◽  
Vol 23 (3) ◽  
pp. 537-554
Author(s):  
Anindya Chakrabarty ◽  
Zongwei Luo ◽  
Rameshwar Dubey ◽  
Shan Jiang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Theoretical Model ◽  
Interest Rate ◽  
Mean Reversion ◽  
Jump Diffusion ◽  
Fixed Income ◽  
Short Term ◽  
Content Type ◽  
Better Than

Purpose The purpose of this paper is to develop a theoretical model of a jump diffusion-mean reversion constant proportion portfolio insurance strategy under the presence of transaction cost and stochastic floor as opposed to the deterministic floor used in the previous literatures. Design/methodology/approach The paper adopts Merton’s jump diffusion (JD) model to simulate the price path followed by risky assets and the CIR mean reversion model to simulate the path followed by the short-term interest rate. The floor of the CPPI strategy is linked to the stochastic process driving the value of a fixed income instrument whose yield follows the CIR mean reversion model. The developed model is benchmarked against CNX-NIFTY 50 and is back tested during the extreme regimes in the Indian market using the scenario-based Monte Carlo simulation technique. Findings Back testing the algorithm using Monte Carlo simulation across the crisis and recovery phases of the 2008 recession regime revealed that the portfolio performs better than the risky markets during the crisis by hedging the downside risk effectively and performs better than the fixed income instruments during the growth phase by leveraging on the upside potential. This makes it a value-enhancing proposition for the risk-averse investors. Originality/value The study modifies the CPPI algorithm by re-defining the floor of the algorithm to be a stochastic mean reverting process which is guided by the movement of the short-term interest rate in the economy. This development is more relevant for two reasons: first, the short-term interest rate changes with time, and hence the constant yield during each rebalancing steps is not practically feasible; second, the historical literatures have revealed that the short-term interest rate tends to move opposite to that of the equity market. Thereby, during the bear run the floor will increase at a higher rate, whereas the growth of the floor will stagnate during the bull phase which aids the model to capitalize on the upward potential during the growth phase and to cut down on the exposure during the crisis phase.

STOCHASTIC VOLATILITY AND JUMP-DIFFUSION — IMPLICATIONS ON OPTION PRICING

1999 ◽  
Vol 02 (04) ◽  
pp. 409-440 ◽  
Author(s):  
GEORGE J. JIANG
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Implied Volatility ◽  
Dynamic Properties ◽  
Jump Diffusion ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
Pricing Errors ◽  
Volatility Model ◽  
Random Jump

This paper conducts a thorough and detailed investigation on the implications of stochastic volatility and random jump on option prices. Both stochastic volatility and jump-diffusion processes admit asymmetric and fat-tailed distribution of asset returns and thus have similar impact on option prices compared to the Black–Scholes model. While the dynamic properties of stochastic volatility model are shown to have more impact on long-term options, the random jump is shown to have relatively larger impact on short-term near-the-money options. The misspecification risk of stochastic volatility as jump is minimal in terms of option pricing errors only when both the level of kurtosis of the underlying asset return distribution and the level of volatility persistence are low. While both asymmetric volatility and asymmetric jump can induce distortion of option pricing errors, the skewness of jump offers better explanations to empirical findings on implied volatility curves.

scholarly journals Option Pricing under the Jump Diffusion and Multifactor Stochastic Processes

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Shican Liu ◽  
Yanli Zhou ◽  
Yonghong Wu ◽  
Xiangyu Ge
Keyword(s):  
Diffusion Process ◽  
Option Pricing ◽  
Stochastic Volatility ◽  
Term Structure ◽  
Implied Volatility ◽  
Jump Diffusion ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Volatility Model ◽  
Jump Diffusion Process

In financial markets, there exists long-observed feature of the implied volatility surface such as volatility smile and skew. Stochastic volatility models are commonly used to model this financial phenomenon more accurately compared with the conventional Black-Scholes pricing models. However, one factor stochastic volatility model is not good enough to capture the term structure phenomenon of volatility smirk. In our paper, we extend the Heston model to be a hybrid option pricing model driven by multiscale stochastic volatility and jump diffusion process. In our model the correlation effects have been taken into consideration. For the reason that the combination of multiscale volatility processes and jump diffusion process results in a high dimensional differential equation (PIDE), an efficient finite element method is proposed and the integral term arising from the jump term is absorbed to simplify the problem. The numerical results show an efficient explanation for volatility smirks when we incorporate jumps into both the stock process and the volatility process.

scholarly journals A Hull and White Formula for a General Stochastic Volatility Jump-Diffusion Model with Applications to the Study of the Short-Time Behavior of the Implied Volatility

2008 ◽  
Vol 2008 ◽  
pp. 1-17 ◽  
Author(s):  
Elisa Alòs ◽  
Jorge A. León ◽  
Monique Pontier ◽  
Josep Vives
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Asset Price ◽  
Jump Diffusion ◽  
Stochastic Volatility Model ◽  
Time Behavior ◽  
Volatility Model ◽  
Jump Diffusion Model ◽  
White Type ◽  
Short Time

We obtain a Hull and White type formula for a general jump-diffusion stochastic volatility model, where the involved stochastic volatility process is correlated not only with the Brownian motion driving the asset price but also with the asset price jumps. Towards this end, we establish an anticipative Itô's formula, using Malliavin calculus techniques for Lévy processes on the canonical space. As an application, we show that the dependence of the volatility process on the asset price jumps has no effect on the short-time behavior of the at-the-money implied volatility skew.

scholarly journals Option Pricing under Two-Factor Stochastic Volatility Jump-Diffusion Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Guohe Deng
Keyword(s):  
Stochastic Volatility ◽  
Diffusion Model ◽  
Implied Volatility ◽  
Empirical Work ◽  
Jump Diffusion ◽  
Model Parameters ◽  
Single Factor ◽  
Proposed Model ◽  
Volatility Model ◽  
Jump Diffusion Model

Empirical evidence shows that single-factor stochastic volatility models are not flexible enough to account for the stochastic behavior of the skew, and certain financial assets may exhibit jumps in returns and volatility. This paper introduces a two-factor stochastic volatility jump-diffusion model in which two variance processes with jumps drive the underlying stock price and then considers the valuation on European style option. We derive a semianalytical formula for European vanilla option and develop a fast and accurate numerical algorithm for the computation of the option prices using the fast Fourier transform (FFT) technique. We compare the volatility smile and probability density of the proposed model with those of alternative models, including the normal jump diffusion model and single-factor stochastic volatility model with jumps, respectively. Finally, we provide some sensitivity analysis of the model parameters to the options and several calibration tests using option market data. Numerical examples show that the proposed model has more flexibility to capture the implied volatility term structure and is suitable for empirical work in practice.

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