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Question 1 (how to set asset level risk budgets as well as portfolio level target volatility) is discussed in Modern Portfolio Optimization by Bernd Scherer and Douglas Martin in section 3.1.1 on risk budgeting constraints. They set upper and lower bounds for their risk budget constraints in a mean variance optimization. The recent work by James Sefton, ...


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Very interesting question. I am not an expert on the subject, however, I was able to find a collection of papers on the subject that should get you started. Here is a good and very informative paper that walks you through several tick by tick volatility estimators that seek to reduce the volatility imposed by market micro-structure: Efficient estimation of ...


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As I don't really understand your question except for the volatility smile: Here is a presentation about how the volatility smile flattens as computational precision increases: http://www.rinfinance.com/agenda/2013/talk/Chance+Hanson+etal.pdf the intuition there is that the smile may be the result of computational error. I would look at agent based ...


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You can pass in the parameters are you estimating with EWMA or GARCH using the mu (mean), sigma (co/variance) m3 (co/skewness) and m4(co/kurtosis) arguments. e.g. blahblah = EWMA(my_time_series) VaR(my_time_series,mu=blahblah)


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I think there is a slight misconception into the purpose of an economic theory. The market is a complex entity to be modeled and yes, it is neither efficient nor arbitrage free but it is trading and there is a price process that corresponds to the market one. You could say that classical economic theory has failed, but I would argue the idea of a theory is ...


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I would argue that indeed none of the so-called stylized facts you mentioned can be explained by classical economic theory. That there was a gross delta between the predictions of classical economic theory and empirical data was foremost found out by Benoit Mandelbrot as far back as 1963 in his seminal paper: The Variation of Certain Speculative Prices In ...


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Classical economics cannot "explain" volatility smiles, but neither does it preclude their existence. Economics is far more abstract than financial "quant"modeling and answers very different questions. In the more abstract framework of economics, volatility skew, mean reverting volatility, bubbles, and crashes are all conceivable scenarios. ...


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We use Derman and Kani's notations. Arrow-Debreu prices The Arrow-Debreu price $\lambda_i$ is the price of the security $\Lambda_i$ paying \$1 in node $(n, i)$, and \$0 in all other states $(n, j)$, for $j \neq i$. Let $\mathbb{P}_{n,j}$ be the risk-neutral probability of getting to state $(n,j)$, from state $(1,1)$. The price of $\Lambda_i$ is the ...


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If you call "classical" what is usually tagged as "neoclassical mainstream", then perhaps the answer is no. From the other hand behavioral finance is long time ago became widely accepted and taught, together with cascades stories a-la Hirshleifer. So in wider sense, economics has long ago explained observed deviations from standard theory.


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Actually BS model is still applicable in the market where the upwards/downwards move is much more probable than move in the opposite direction. The Black-Scholes price process model has the form: $\frac{dS}{S} = \mu dt + \sigma dW$ And with significantly non-zero $\mu$ (called drift) it will capture just what you are talking about. Quite surprisingly, the ...


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Well if you think that this model represents reality more accurately than the Black-Scholes assumptions. A lot of people do indeed think so. But I wouldn't say you're "tweaking" Black-Scholes... you're just assuming another model altogether and you will use risk-neutral pricing to compute the fair value of the option at time $t$, just like BS. Frankly, I'm ...


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Let's first rewrite the tow processes and let $X_t = 1/S_t$ Then we have $$ dX_t/X_t = (\sigma^2-r)dt + \sigma dW_t, $$ with the solution (apply Ito) $$ X_t = X_0 \exp((\sigma^2/2-r) t + \sigma W_t), $$ and $$ dS_t/S_t = r dt + \sigma dW_t, $$ with the solution (apply Ito) $$ S_t = S_0 \exp((r-\sigma^2/2) t + \sigma W_t). $$ If we look at the two processes ...


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We need to start from $(2)$. We start from Ito's Lemma which stipulates for the single variable case that: $$ \\ df(S_t) = f'(S_t)dS_t + \frac{1}{2}df''(S_t)Var[dS_t] $$ Setting $f=1/S_t$ yields: $$ \\ d\bigg(\frac{1}{S_t}\bigg) = -\frac{1}{(S_t)^2}dS_t+\frac{1}{2}\frac{2}{(S_t)^3}\sigma^2(S_t)^2Var[dW_t] \Rightarrow $$ $$\\d\bigg(\frac{1}{S_t}\bigg) = ...


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In the case of application in finance, usually, GARCH is used in estimating realized volatility of returns based on the weight we would like to give to each past observation. Ultimately after estimating (calibrating) the parameters of the model to an existing time-series, GARCH is used for forecasting multi-step ahead return (future) volatility. Different ...


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From my understanding I believe you will calculate conditional variance with GARCH. You would then need to take the square root of the variance to calculate the standard deviation/ volatility. One key aspect in GARCH is that you can calculate the "persistence" , I.e. How likely is the asset to "persist" to its long run variance


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Intuitively put you can say that volatility is the within variation and beta is the between variation. Within means the variation that A has within its own time-series, whereas between means between A and the index.


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Calculus, differential equations, linear algebra, and probability. That will be enough to understand popular textbooks on the subject intended for upper-level undergraduates or first-year graduate students. To understand the research literature you will also need stochastic processes, stochastic calculus, real analysis, and potentially PDE. Many other ...



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