In the realm of finance, the risk-neutral measure takes precedence in pricing financial derivatives. However, the real-world measure remains significantly valuable and indispensable across various domains. It plays a pivotal role in risk management and asset/liability applications, facilitating comprehensive evaluation and mitigation of risks.
Real-world measures are useful for simulation-based analyses of trading and investment strategies, offering insights into the practical implications of decisions in complex market environments. Moreover, real-world measures are important in investment-based pricing and the assessment of asset price behavior, fostering a more realistic understanding of market dynamics.
Reference [1] undertakes the calibration of stochastic volatility models as a means to estimate the real-world measure. Employing the efficient method of moments (EMM), the authors perform calibration on the Heston and Bates SVJ models. Subsequently, the calibrated models are used to explore and analyze the risk and returns associated with volatility-target strategies. The authors pointed out,
Our results indicate that the volatility target strategy serves to reduce the likelihood of extreme returns and reduces the volatility of volatility.
For all investment horizons, the risk and return of the portfolio increases as the volatility target increases. The 10% volatility target has the lowest risk when viewing the mean of volatility and volatility of volatility estimates, but also the lowest return. On the other hand, an equity only-holding strategy has the highest risk but also the highest expected return. Volatility targeting, therefore, gives investors an effective way of managing the downside risk of a portfolio, but limits the upside potential as shown by the minimum and maximum statistics.
This article serves to exemplify the practical utility of the real-world measure by demonstrating its application in assessing investment strategies. Specifically, the study underscores the effectiveness of volatility targeting as a strategic approach that empowers investors to effectively manage and mitigate the downside risk inherent in portfolio management.
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References
[1] Alexis Levendis and Eben Mare, On the calibration of stochastic volatility models to estimate the real-world measure used in option pricing, Orion, Volume 39(1), pp. 65 – 91
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