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How are options actually priced?

How are options actually priced?

Unlocking the Secrets of Option Pricing: A Novel Framework for Analyzing Volatility Risk and Risk Premium

Analyzing Volatility Risk and Risk Premium in Option Contracts: A New Theory[1]

by Peter Carr and Liuren Wu

The paper presents a novel framework for understanding and analyzing the volatility risk and risk premium embedded in option contracts. The paper provides empirical evidence to support the proposed theory, which is based on a stochastic volatility model that accounts for the time-varying nature of volatility.

Firstly, the authors highlighted the importance of understanding volatility risk and risk premium in option contracts.

Traditional option pricing models, such as the BS model, assume that the volatility of the underlying asset is constant over time. 

However, this assumption is not consistent with empirical observations, which indicate that volatility is a time-varying process. To solve this problem, the authors proposed a new model that incorporates stochastic volatility and time-varying risk.

The model is a stochastic volatility model that assumes the volatility of the underlying asset is a function of a latent variable that is subject to random shocks. It`s consistent with a variety of empirical observations, including the volatility smile and skewness in option prices.

The paper then introduced a new measure of volatility risk, the “implied volatility risk premium”.

The measure captures the additional compensation required by option sellers to bear the risk of changes in implied volatility. 

The authors proved that this measure is a significant determinant of option prices, after accounting for other factors that may influence option prices.

For the experiment part, the authors conducted an empirical analysis using S&P 500 index options.

To test the validity of the proposed model, the results of the analysis provide strong support for the new theory, showing that the implied volatility risk premium has a significant impact on option prices. 

The empirical analysis shows that the model outperforms traditional option pricing models in accuracy and predictive power.

The paper also discussed the implications of the new theory for risk management and option trading strategies. 

According to the authors, the proposed model and measure of volatility risk can assist market participants in comprehending and managing their exposure to volatility risk. 

The paper also suggests that the new theory can help create more effective trading strategies that leverage the time-varying nature of volatility.

Overall, the paper presented a novel framework for understanding and analyzing the time-varying nature of the volatility and the impact of volatility on option pricing. 

The empirical analysis provides strong support for the theory proposed in the paper!

Additionally, the paper gives insightful discussion of the implications of its theory for risk management and option trading strategies.

However, there are some limitations.

Since the model assumes that the volatility follows a mean reverting process. Although this assumption is consistent with some empirical observations, it may not be valid in all situations. 

Also, when the market is stressed and uncertain, the option prices may not be efficient and reflect all believable information, so the implied volatility risk premium may not be accurately measured.

It’s worth noting that this paper is intended for readers who are already familiar with option pricing models and want to delve deeper into the subject. 

As such, the paper might not be suitable for beginners or general readers without a background in finance or economics. The authors use complex mathematical and statistical techniques to develop and test their model, which may be challenging for readers without a strong foundation in these areas. 

Nevertheless, for readers who are familiar with option pricing models and have a strong interest in understanding the time-varying nature of volatility, this is a valuable paper.

In conclusion, this is a well-written and insightful paper that presents a novel framework for understanding and analyzing the time-varying nature of volatility and its impact on option pricing.

Through empirical analysis, the paper offers evidence to support the proposed theory and highlights the implications for risk management and option trading strategies. 

However, it’s worth noting that the model and measure of volatility risk have some limitations, as with any financial model. 

Nonetheless, this paper makes a valuable contribution to the literature on option pricing and risk management. Offering a fresh perspective on the time-varying nature of volatility which could be beneficial to practitioners and researchers.

Analyzing volatility risk and risk premium in option contracts: A new theory – ScienceDirect

Reference:

[1] Carra, P., & Wu, L. (2022). Analyzing volatility risk and risk premium in option contracts: A new theory. Journal of Financial Economics. 140(1), 44-64.

How are options actually priced? Written by Albert Zhang

Peter Carr NYU Tandon Finance Chair : Remembering A Quant Hero

Peter Carr | NYU Tandon School of Engineering