Subjective Probability Density Functions from FX Option Prices: Predictive Power and Performance on a Carry Trade Strategy

2017 ◽  
Vol 18 (2) ◽  
pp. 253-286
Author(s):  
André Santos ◽  
João Guerra ◽  
Tiago Neves
Keyword(s):  
Probability Density ◽  
Subjective Probability ◽  
Predictive Power ◽  
Probability Density Functions ◽  
Density Functions ◽  
Option Prices ◽  
Carry Trade ◽  
And Performance

scholarly journals Iterative Algorithm for Parameterization of Two-Region Piecewise Uniform Quantizer for the Laplacian Source

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3091
Author(s):  
Jelena Nikolić ◽  
Danijela Aleksić ◽  
Zoran Perić ◽  
Milan Dinčić
Keyword(s):  
Neural Networks ◽  
Performance Assessment ◽  
Probability Density ◽  
Probability Density Functions ◽  
Density Functions ◽  
Uniform Quantization ◽  
Memory Footprint ◽  
High Bit Rates ◽  
And Performance ◽  
Laplacian Distribution

Motivated by the fact that uniform quantization is not suitable for signals having non-uniform probability density functions (pdfs), as the Laplacian pdf is, in this paper we have divided the support region of the quantizer into two disjunctive regions and utilized the simplest uniform quantization with equal bit-rates within both regions. In particular, we assumed a narrow central granular region (CGR) covering the peak of the Laplacian pdf and a wider peripheral granular region (PGR) where the pdf is predominantly tailed. We performed optimization of the widths of CGR and PGR via distortion optimization per border–clipping threshold scaling ratio which resulted in an iterative formula enabling the parametrization of our piecewise uniform quantizer (PWUQ). For medium and high bit-rates, we demonstrated the convenience of our PWUQ over the uniform quantizer, paying special attention to the case where 99.99% of the signal amplitudes belong to the support region or clipping region. We believe that the resulting formulas for PWUQ design and performance assessment are greatly beneficial in neural networks where weights and activations are typically modelled by the Laplacian distribution, and where uniform quantization is commonly used to decrease memory footprint.

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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