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Go through the research paper by Tripathi & Bhandari(2015). In this paper, authors compared the performance of various funds using various risk adjusted measure like Sharpe Ratio, Treynor ratio, Jensen's Alpha, and information ratio. Authors have carefully examined the limitation of each and every ratio and also suggested for an alternatives measures. ...


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If you're using greeks for your past trading session's analysis , you should use historical Vol If you intend to make trading decisions in future and want to have a future outlook of greeks, you should use implied Vol.


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You should take a look at this paper: "A Sharper Ratio: A General Measure for Correctly Ranking Non-Normal Investment Risks". The authors prove closed form solution to rank alternative investments even when the underlying is not normally distributed under a very general utility specification. In their own words, they derive a generalized ranking measure ...


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According to literature ADEH(1999) standard deviation (& VaR aswell) do not respect "properties" for coherent risk measures. (Sub-additivity etc.) An appropriate and easy risk measure could be the Expected Shortfall (CVaR) which instead do respect these properties. An alternative could be using the so called Spectral risk measures, which similarly to ...


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They expire 30 days before the expiration of the S&P monthly options. The latter usually expire on the third Friday of the month (however, in rare cases the S&P opts. expire on Thursday because the Friday is a holiday; the last time it happened was April 17, 2014 since April 18 2014 was a NYSE holiday). Neglecting the holiday thing, the expiration ...


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There is an easy method to calculate volatility if you have a historic time series of price data. First, obtain the standard deviation of the log returns. Imagine you have these observed prices, {30.00, 31.70, 27.38, 27.50, 23.96, 23.30, 30.63, 24.04} Calculate the log return, ln(31.70/30.00), ln(27.38/31.70), . . . ln(24.04/30.63). Calculate ...


2

What is risk? If one defines risk heuristically as deviation from expectation, then (assuming returns have finite variance) standard deviation can be considered a first approximation for risk. For most distributions the mean and variance do not fully parameterize the distribution. Some standard measures of risk for general distributions include Value at ...


4

Since the volatility is not changing, we can assume that the only change is the underlying asset price $S$. Then \begin{align*} C(S+\Delta) &\approx C(S) + Delta \times\Delta +\frac{1}{2} Gamma \times \Delta^2 \\ &=11.50 + 0.58 \times 0.5 + \frac{1}{2}\times 2 \times (0.5)^2\\ &=12.04. \end{align*}


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Depending of $\lambda$, pasts observations will be weighted differently, if you compute the volatility at time $t$ , the $t-1$ observation will be weighted by $(1-\lambda)*\lambda^{0}$, the $t-2$ observation by $(1-\lambda)*\lambda^{1}$ and so on so forth. For $\lambda= 0.94 $ : The first observation is weighted by = $(1-0.94) * 0.94^0 =0.06%$ The second ...


3

In a standard approach you would think about the evolution of a return process in the following form: $$dr_t=\mu dt+\sigma dW_t,$$ where for the sake of simplicity I assumed constant volatility and drift ($\mu$ and $\sigma$ can also depend on the time parameter $t$). Often you will be interested into the variance of your stock returns (for example to hedge ...


0

What I would do : Step 1. Calculate $V=\sum_i \frac{\Delta P_i^2}{dt_i}$ Step 2. Annualize V. $V_a=\frac{V}{T}$ Step 3. Find $\sigma = \sqrt{V_a}$


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Ideally you'd want to use daily returns and just annualise it, but if you only have monthly returns then calculating the weighted variance in the following way might do it: $$ Var = \frac{\sum_{i=0}^{24}(R_i - \mu)^2}{24 + \frac{21}{31}} + \frac{\frac{21}{31} (R_{25}' - \mu)^2}{24 + \frac{21}{31}} $$ $$ Vol = \sqrt{Var} $$ Where $R_i$ is the returns of ...


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If you want to know what Greeks the market assigns to an option, i.e. the market implied Greeks, then you would use the implied volatility. And that is what traders like to look at.


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For the first question there are two approaches, the first is you can simply backfill and use the last minutes tick if it exists. If there is no liquidity, the second way is you can try cubic or other interpolations to see if it creates a better curve.


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Welcome to quant.SE! I do not have specific experience with the CARR Model, however, I had a short look in the paper you mentioned: As far as I understand the model specification you just implement a GARCH(p,q) estimation for the range $R_t:=\max{P_\tau}-\min{P_\tau}$ where $\tau=t-1,t-1+\frac{1}{n},\dots,t$ where $n$ is the number of intervals used in ...



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