# Tag Info

5

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.

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*}

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 ...

2

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 ...

2

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 ...

1

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 ...

1

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 ...

1

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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