# Tagged Questions

The possibility that a negative event (such as a loss) will happen.

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### Stationarity in first differences of CoVar

I'm currently in the middle of my master thesis and I can't get my head around a specific problem. I have the following process: where the $\Delta CoVar$ measure is calculated in two ways. First, ...
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### Interpretation of Risk Premium for Schwartz one-factor model

I have to deal with this one-factor model: \begin{equation*} \begin{cases} dS_t = \alpha \bigl(\mu - \log(S_t) \bigr)S_t \, dt + \sigma S_{t} \, dW_t \, , t \geq 0,\\ S|_{t=0} = S_0 > 0, \end{...
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### What is curvature risk?

The BCBS has presented a new standard approach for measuring risk for a portfolio, which is based on sensitivities, that is “delta”, “vega” and “curvature” risks. Delta risk measures the change in ...
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### How do you quantify credit risk?

I am trying to figure out how to quantify the change in price on a bond for a change in credit risk. I'm not even sure how to quantify a change in credit risk, but I'm thinking possibly something ...
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### Difference between Risk Transfer and Risk Sharing

There seems to be a thin line between risk transfer and risk sharing. Can someone explain with example how can this be differentiated?
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### The name conventions such as ATM, Risk reversal and Butterflies to construct volatility surface

Why people call (vol call - vol put) risk reversal when risk reversal actually is (call 25 delta -put detlta +25)? when constructing volatility surface? The vol of risk revesal should not be vol call -...
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### Overestimating or underesitmating risk?

This question might be silly, but I want to be sure of myself. If one has Value-at-Risk forecasts and there are zero VaR breaches (i.e. no return value is smaller than or equal to the VaR value) then ...
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### help with p&L vectors historical simulation

My question is about the calculation of the Value at Risk based on historical simulation. I have a table which contains the P&L-vectors of each day of one year. But I don't know what is contained ...
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### How is possible to relate volatility with risk?

I read that equallying voliatility with risk is one of the hardest critics on Quantitative Finance and that this is -indeed- the fundamental base of Quant. This question is analogous considering that ...
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### Mathematical Derivation of Residual Risk

I understand the difference between Excess, Residual and Active Returns. I also understand what Active Risk; defined as: $\sigma_{r_P-r_B}$ (i.e. standard deviation of the difference in returns ...
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### Estimate the risk of swaptions

I would like to model OTM Swaptions. I can use some implementation of the Bachelier model (not B76 due to negative rates) and implied volatilities from Bloomberg. For 10Y X 10Y (10 years option ...
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### What is Estimation Risk - VAR Backtest

Simple Question. Can someone explain please: What is Estimation Risk in Value at Risk Backtesting
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### How to Calculate Minimun total Risk?

Is it possible to calculate Minimum Total Risk mathematically for below problem. ...
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### Factor sensitivities for EURUSD swap

Trying to understand various risk factors for a EURUSD swap. While I understand why a EURUSD swap would have USD LIBOR, EURIBOR, EURUSD currency as risk factors, why is it that it would also have EUR ...
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### subadditivity of VaR

It is known that the VaR (Value at risk) doesn't fulfill subadditivity, i.e. $VaR(X)+VaR(Y) \le VaR(X+Y)$ But for elliptical distributions subadditivity is true. Questions: (1) Which ...
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### Coherent Risk Measures and VaR

I am working on a problem that is worded exactly as follows: Consider the functions $\rho_{1}$ and $\rho_{2}$, defined on the space of random variables with finite expected value in the following way ...
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### Calculating ex ante returns & probability of a negative return over some horizon

One way to go on about this is to parametrically calculate the returns, i.e. hold the exposure constant and backtest against the factor changes over that horizon. This is not forward looking per se ...
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### Where to find good notations to teach investment portfolio maths?

I don't know whether this question is in order here. I do a bit of teaching and I am preparing my own notes but I thought that his should not be necessary. In which book/pdf on the web can we find a ...
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### How to determine portion of portfolio's risks from components?

Say I have a portfolio of 3 stocks $A,B,C$ with $\mu_A = 5%$, $\mu_B = 10%$, $\mu_C = 15%$ and volatility $\sigma_A = 10%$, $\sigma_B = 15%$, and $\sigma_C = 25%$. Let us also say that correlations ...
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### Option analysis

Assume zero dividend and that the strike price for a European call option on a stock at a fixed maturity T and strike price K is given by C(K).Suppose that $C(K)=e^{-k}$ for all $K\geq 0$ ,then, I ...
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### Calculate VaR for a liabilty taking a exponential distribution?

An insurance company faces the liability loss off $L = \begin{cases} 0, & \mbox{with probability } 0.75 \\ Z, & \mbox{with probability } 0.25\end{cases}$ where $Z\sim Exp(\mu)$. I want to ...
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### Convex risk measure and a coherent risk measure?

A coherent risk measure is: $\rho(\lambda X_1+(1-\lambda X_2))$ How can it be shown that everey convex risk measure is indeed a coherent risk measure? I assume that it is enough to show that a ...
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### What risks is an exchange exposed to?

Putting aside operational/reputational/business risks for a minute, a financial institution is concerned with the risk of losing money on their positions. What about an exchange ? I can only think of ...
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### efficient portfolio with given risk

Is there a formula to derive an efficient portfolio to maximise the return, x'mu, for a given risk, x'S x (where x are the portfolio coefficients, mu is the mean return for each asset and S is the var-...
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### CVA using difference between 2 counterparty's spreads

The approximation to calculate CVA as a spread is $CVA = Spread * Expected$ $Exposure$. I assume this means the counterparty's spread over a proxy for the risk free rate such as LIBOR or OIS. Is this ...