New answers tagged volatility
5
I have heard the following argument- barring transaction fees, if my estimation of future realized vol is 30% and 1-month ATM implied vol is 20%, then I could potentially buy a 1-month ATM call/put and delta hedge it; as time passes and my vol estimate comes true I will make a profit.
You are not guaranteed to make a profit even in this case since delta ...
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Because of differing underlying factor risks. These might include such things as policy risk (eg. tax, capital controls), central bank intervention risk (eg. a currency peg at one extreme), economic factors (eg. sensitivity to outlook for GDP growth and inflation), and financial market risk dependencies (eg. interest rate differentials, equity market risk).
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You should always use the biggest volatility to minimise the risk and hedge the option correctly. Don't forget to multiply daily volatility by square(252) to annualize it.
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You should come up with some relationship you want to explore. For example maybe you think that the t+1 observation depends linearly in some way on the last (t) observation. Then you would regress the t+1 observation on the t observation and examine the fit. Maybe you think that the sum of the last 5 observations has a relationship to the t+1 observation. ...
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You should review the difference between implied volatility and realised volatility. Historical volatility is the realised volatility that happen in the past but an option price will have to be determined by the view of the market about volatility in the future for a given period. Normally you do the inverse, ie the option price is given by the market but ...
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The Heston model can have that property. If you make the correlation negative between the Brownian motions in the $dS_{t}$ process and the $d\nu_{t}$ process you imply that price is negatively correlated with variance.
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Yeah this is often called Spot-Vol correlation and is well known. Most people take this into account. I think if you just google spot-vol correlation you will come up with many example/models.
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Apologies for the delay on the hedging of non-forward-starting volatility swaps, but it's only since this week that I have an answer for this.
So, for plain volswaps, I can give you a nonparametric hedge in terms of varswaps only. That's not as cheap as using a single option (which I believe is not possibe anyway), but certainly better than trading an ...
1
Portfolio beta is a function of market vol, portfolio
vol and correlation between market and portfolio; so
correlation is indeed the only free variable. (But if you have complete control over the portfolio-construction process, you might as well target beta and then scale the weights so that you meet your volatility target.)
To control correlation,
you'll ...
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The 'burst' in the first figure is just due to overnight returns, so nothing fancy (the unit if you read the axis is T/5 min so 84 corresponds to 84 x 5 min= 7 hours = 1 trading day). There is always a peak at 1-day lag due to overnight returns.
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In quant environments, there are many different things that we call volatility (this is one thing I am quite unhappy, and think we should do better):
The statistical definition, as the standard deviation of the returns (usually logarithmic returns) of a stochastic process
The number you have to put in the Black Scholes formula to get the price you get in ...
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Yes, because GARCH is taking in account for characteristics of exchange rate volatility such as dynamics of conditional heteroscedasticity.
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I assume you work in the Black Scholes framework. Then,
\begin{align*}
P(S_0,K,T) = Ke^{-rT}\Phi(-d_2)-S_0\Phi(-d_1),
\end{align*}
where
\begin{align*}
d_1 &= \frac{\ln\left(\frac{S_0}{K}\right)+\left(r+\frac{1}{2}\sigma^2\right)T}{\sigma\sqrt{T}}, \\
d_2 &= \frac{\ln\left(\frac{S_0}{K}\right)+\left(r-\frac{1}{2}\sigma^2\right)T}{\sigma\sqrt{T}}= ...
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Nevermind, i'm just confusing myself. Now I understand what I misunderstood.
The implied volatility surface of a prices of calls generated by a stochastic volatility model will not be constant since the implied volatility is found using the Black-Scholes model. The Black-Scholes model and a stochastic volatility model of course disagree on prices, and hence ...
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