New answers tagged volatility
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The formula looks like the square-root-of-$t$ rule for scaling
return-variance, but for simple multi-period returns, not log-returns. That is, the formula shows you how to compute
$$\mbox{var}\bigg(1+R^{(\tau)}\bigg) = \mbox{var}\bigg(\prod_{t=1}^{\tau} 1+R_t\bigg)$$ starting from the expectation and variance of $R_t$.
In which case $r^d$ would be a ...
0
Such a question really invites me to recommend my own book Applied Quantitative Finance for Equity Derivatives, which you can buy on Amazon.
The book devotes 200 pages to the subject of volatility. It covers the Dupire local volatility model, along with tricks that are required to apply it in practice. It also covers stochastic volatility models, and local ...
2
The stock specific volatility (also known as idiosyncratic volatility) is the volatility that remains after controlling for beta. I suppose you have $$R_i = R_f + \beta_i \cdot \big(R_m-R_f\big) + \varepsilon_i.$$ Then, the standard deviation of epsilon is your stock specific volatility. One frequently assumes $\varepsilon_i\sim N(0,\sigma^2_{\varepsilon_i})$...
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A standard book in the volatility literature is Gatheral (2006). The book begins with stochastic volatility, llocal volatility and the Heston model. Then he adds jumps and default risks. He concludes with barrier options, exotic options and volatility derivatives. He includes many tables and graphs and writes rather well. The only downside is that he does ...
1
To trade forward starting volatility swaps, see this paper (actually more a practitioner's scribble than a paper) and all references therein: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3354408
Just to let you know, I think there may be a small error term in the paper that needs to be included still, but based on some simple numerical tests I was ...
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On the Equity side the Skew introduces correlation between volatility and future prices because of:
leverage effect: when Equity prices go down the leverage debt/equity increases making the underlying more and more risky
crashophobia/behavioural finance: due to disposition effect, investors are more concerned/afraid about losses than optimistic for gains
...
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There is no single best way of modeling time series. Taking or not taking logs is a modeling question. The answer in general depends on either your belief about the structure of the data set or some model selection method (the one that you believe in) or maybe something else.
That being said, the usual way to go is to take logs and apply (G)ARCH on the log-...
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The use of forwards is just another method to look at the underlying. The Black-Scholes options model utilizes Spot and handles the carry as an interest rate in the model. On the other hand the Black Model uses forwards instead. Since the forward price would take into account the carry, both models should yield the same result if one is accounting for all ...
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Your question is using some terminology incorrectly. Forward volatility refers to the volatility realized from t1 to t2 given that it's currently t0 and t0 < t1 < t2. What you are talking about is whether the moneyness of an option is expressed in relative to the spot or relative to the forward.
Which parametrization to pick is a choice; as long as ...
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