Inversion of Option Prices for Implied Risk Neutral Probability Density Functions: General Theory and its Applications to the Natural Gas Market

2008 ◽  
Author(s):  
Chen Wang ◽  
Yijun Du
Keyword(s):  
Natural Gas ◽  
General Theory ◽  
Probability Density ◽  
Probability Density Functions ◽  
Density Functions ◽  
Option Prices ◽  
Natural Gas Market ◽  
Risk Neutral ◽  
Gas Market

Estimating Option-implied Risk Aversion for Indian Markets

2017 ◽  
Vol 6 (1) ◽  
pp. 90-97
Author(s):  
Sonalika Sinha ◽  
Bandi Kamaiah
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Probability Density ◽  
Implied Volatility ◽  
Probability Density Functions ◽  
Density Functions ◽  
Relative Risk Aversion ◽  
Option Prices ◽  
Theoretical Assumption ◽  
Investor Expectations

What do nearly 1.5 lakh observations of options data say about risk preferences of Indian investors? This paper explores a nonparametric technique to compute probability density functions (PDFs) directly from NIFTY 50 option prices in India, based on the utility preferences of the representative investor. Use of probability density functions to estimate investor expectations of the distribution of future levels of the underlying assets has gained tremendous popularity over the last decade. Studying option prices provides information about the market participants’ probability assessment of the future outcome of the underlying asset. We compare the forecast ability of the risk-neutral PDF and risk-adjusted density functions to arrive at a unique index of relative risk aversion for Indian markets. Results indicate that risk-adjusted PDFs are reasonably better forecasts of investor expectations of future levels of the underlying assets. We find that Indian investors are not neutral to risk, contrary to the theoretical assumption of risk-neutrality among investors. The computed time-series of relative risk aversion overcomes the limitations of the VIX (implied volatility index) to yield a more reliable index, particularly useful for the Indian markets. Validity of the computed index is established by comparing with existing measures of risk and the relationships are found to be consistent with market expectations.

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