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2

I assume $\alpha>0$. Let $V^\lambda$ be the solution of : \begin{equation*} \begin{cases} \frac{\partial V^\lambda}{\partial t} + \Bigl [ \alpha \Bigl(\mu - \frac{\lambda}{\alpha} - \log (S) \Bigr) S \Bigr ] \frac{\partial V^\lambda}{\partial S} + \frac{1}{2} \sigma^2 S^2 \frac{\partial^2 V^\lambda}{\partial S^2} - rV^\lambda = 0, \\ V^\lambda(S,T) = (S -...

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The formulae are on p17 of the document attached to the link you included. http://www.bis.org/bcbs/publ/d352.pdf It's just the profit or loss due to a specified shock in the underlying, which is not explained by the local delta of the position.

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What you're looking for looks to be more in the realm of a mathematical model (specific to the company's size, available liquidity, and industry). Credit Risk Pricing Models may provide a decent overview of how to build such a model. Unfortunately duration/convexity will only help you capture the interest rate risk on your bonds, and not any of the ...

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Risk Transfer simply involves transferring "only" risk to another person for price. For example, downside risk of stock can be transferred by purchasing a call option. In this way, the buyer of call option transfer its risk to writer of call option. Another example is insurance, wherein, the buyer transfer its risk to insurance company. Risk Sharing is ...

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I have studied unsystematic risk [USR] for more than two decades. In fact, I wrote a book (which is here) whose central focus is how to deal with USR in the valuation of non-public companies. It is a multifaceted, complex, and difficult issue. Modern Portfolio Theory did professionals in my line of work no favors when it assumed away the existence of USR ...

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Yes, it is correct. Underestimation: you under-estimate the risk, so you have more VaR violations than what your model predicts. Ex: With 100 observations, and a 99% VaR, you expect 1 violation but you observe 5 violations. Overestimation: you over-estimate the risk, i.e the risk is less important that you expect. You observe less VaR violations that you ...

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I think this paper gives a really good overview about risk parity link. As it points out, risk parity is a alternative to traditional mean variance portfolio construction.

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Volatility (often defined in terms of standard deviation of returns, or in terms of implied volatility from option markets) is indeed one measure of risk, but like any single measure of risk, it is incomplete. Part of the reason for this is that in financial markets, the returns are not normally distributed but rather have "fat tails." This means that ...

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