Questions tagged [value-at-risk]

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89 views

Intraday Value at Risk approximations

We use full valuation of derivatives portfolios using scenarios from historical data. For simple contracts, this is relatively fast. For contracts requiring monte carlo simulation, this becomes ...
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1answer
186 views

Analytical portfolio optimization for VaR under multivariate normality

Given a set of assets with returns following a multivariate normal distribution with a known mean vector and a known covariance matrix, $$ r \sim N(\mu,\Sigma), $$ I want to find optimal portfolio ...
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1answer
166 views

Stop-Loss strategies

Does anyone know some bibliography about the problems or limitations of using Stop-Loss strategies in a portfolio? Let me explain better: for example you can have a portfolio of 30 stocks from ...
2
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0answers
31 views

Estimator for Conditional value at risk (average value at risk)

I am following a book: Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization by Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi I'm learning about average value at risk. ...
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1answer
170 views

PCA on a portfolio of spot and forward contracts

I have a portfolio of spot and FX forwards on various currencies all based to AUD. I need to able to quantify how the changes in amount, tilt and curvature of the AUD curve would impact my p/l. ...
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2answers
136 views

Modified Sharpe ratio

I would like to model different type of investors, hence I need to find some kind of utility functions to optimize. Apart from very abstract exponential utility function, I couldn't find any proper ...
2
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0answers
117 views

Methods for calculating Expected shortfall

Let B1, B2 be two defaultable zero-coupon bonds maturing in 1 year, each with a face value of $100. Assume: each bond is priced at 90 dollars each bond has a 4% probability to default within 1 year ...
2
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0answers
42 views

VaR of ARCH model

Consider the following: $r_t = \theta r_{t-1}+u_t$ $u_t=\sigma_t\epsilon_t$ $\sigma^2_t=\omega+\alpha u^2_{t-1}$ $-1<\theta<1,\omega>0,\alpha \in(0,1)$ What is the 99% 2-day VaR of a ...
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0answers
57 views

Pricing default risk in cryptos

I'm looking to figure out how to price "insurance" against a counter-party defaulting in an OTC cryptocurrency transaction. I think the first measure would be to calculate VaR? I'm planning on ...
2
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0answers
59 views

VaR decomposition of non-normal portfolio by g-and-h distribution

According to Doowoo Nam (2013), VaR of non-normal portfolio returns approximated by g-and-h distribution can be decomposed pretty much in the same way as the VaR of a portfolio with normal returns. ...
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0answers
290 views

Problems in computing VaR with GARCH-GPD-copula approach

I use a time-varying Gaussian copula (with GARCH-filtered standardized residuals modeled semiparametrically with Gaussian kernel interior and GPD tails, i.e. generalized pareto distributed) to ...
2
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0answers
76 views

Value-at-Risk Calculation with respect to the Capital Requirements

I want to calculate the Value-at-Risk at date $t$ in such a way that I minimize the capital requirements given as \begin{align} \text{CR}_{\,t+1\,:\,t+250} = \sum_{h=0}^{249}\max\left( -(3+k_{t})\...
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0answers
176 views

Beta distribution - Holding period

Let's say I have a risk factor that is defined between [0,1], such as recovery rates. Assuming I have daily data, I can estimate the "daily VaR", i.e. the tails over 1 day period, since the data is ...
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0answers
381 views

Comparing Backtests of Value-at-Risk and Expected Shortfall

My goal is to test if ES (CVaR) empirically is a better risk measure than VaR for a set of given variables (assumed underlying distribution, confidence level, sample size) for different asset classes. ...
2
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1answer
149 views

Energy Risk Quant--Any discussion boards for energy related quant topics?

Any discussion boards for energy related quant topics? Like VaR in energy portfolio, and pipeline option pricing.. just want to know where is the best discussion board for such energy specific topics. ...
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20 views

Lognormal asymmetry implication on Value at Risk

To examine the Value at Risk implications for a portfolio consisting of a spot and futures time series I have generated a 1-day monte carlo simulation. I was long in the spot and short in the future (...
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0answers
39 views

Can value at risk be computed using downside deviation?

Value at risk is usually computed with a regular standard deviation. But can it be computed using downside deviation (semi-deviation) instead? Particularly if I want to consider a Var that includes ...
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0answers
32 views

How to measure specific risk charge?

IFRS requires banks to compute different risks including market risk based on Basel iii. To do so, the capital requirement is defined as follows: $$max(VaR_{t−1},m_c × VaR_{avg}) + SRC$$ $SRC$ is ...
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69 views

Opposite of Value-at-Risk. Criteria for Optimization

I'm trying to optimize portfolio of undervalued and portfolio of overvalued stocks. I have simulated scenarios of stock returns, and based on them I would like to find optimal weights. One criteria is ...
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44 views

Risk Measure-identication

Let X be a variable with existing moment generating function $M_x(z)=E[e^{zX}]$. Define the following risk measure: $\rho_{\alpha}(X)=inf_{z>0}(z^{-1}ln(\frac{M_x(z)}{1-\alpha}))$ Does anyone know ...
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0answers
50 views

Does it make sense to subtract VaR from spot shocks?

I have a model to compute the Event Risk (in dollars) from a shock to the spot price of an asset. I also have the 10-day VaR PnL for the same assets returns. These two numbers are then aggregated to ...
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0answers
142 views

Monte Carlo VAR with differente asset classes

I have found a very useful post regarding the use of Monte Carlo simulaton to obtain portfolio Value at risk, based on Cholesky decomposition, random variates, etc. This post I'm talking about is: Is ...
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0answers
30 views

Hedger's utility function associated with minimizing value at risk

What must be the general shape of a hedger's utility function if the hedger is minimizing value at risk? What is a simple example of such a utility function?
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66 views

How can I find what Loss Given Default to use

I want to come up with the appropriate loss given default for a commodity derivative in my CVA calculation. would anyone know where I can find this information?
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0answers
78 views

Calculate VaR using the extreme value theory

I am trying to calculate the Value at Risk for different models. But I am now confused for some reason. Could you please help me? I calculate the 1% and 5% VaR (so negative numbers) and I am also ...
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1k views

How to backtest Value at Risk Models using Conditional and Unconditional tests?

I am trying to carry out backtesting on a number of Value at Risk figures i obtained using var/covar, historical, and monte carlo simulation. The two methods im using are the Kupiec test (...
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562 views

Simulating Option Positions VaR with Monte Carlo in Python

I'm trying to calculate VaR for overall option positions. Currently I do a MC simulation for the underlying, and derive the theoretical value of the option from those theoretically. Then I calculate ...
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0answers
20 views

Decomposition of Contribution to Variance

$C$ is a $N\times N$ covariance matrix of stock returns. Assuming $w$ is a vector of positions in each asset, the total variance of the portfolio is $$w^TCw$$ The contribution to total variance of the ...
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15 views

How to prove the following relation of Conditional Value-at-Risk and Value-at-Risk and Conditional Tail Expectation?

How to prove the following relation of Conditional Value-at-Risk and Value-at-Risk and Conditional Tail Expectation????
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47 views

What is the differential Value-at-Risk?

I am currently working on a Machine Learning Project, implementing portfolio optimization algorithms according to different risk measures. I have found sufficient information on Sharpe Ratio ...
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0answers
24 views

Univariate Portfolio Analysis

We want to form 10 portfolios based on the level of VAR (99%) for equity data over a 30 year period. Portfolio 1 is the portfolio of stocks with the lowest value-at-risk and Portfolio 10 is the ...
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0answers
29 views

Backtesting conditional VaR

I'm writing a thesis about conditional VaR of Standard & Poor's 500 index. I have fitted my log-returns with GARCH(1,1)-proces and then made some conditional VaR-forecast (500 observations) with ...
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16 views

Variance minimization vs. Value at risk

When computing Minimum Variance Hedge Ratios as explained f.e. in Hull (2012) the goal is to select a hedge ratio such that the variance of the portfolio is minimized. My question is now what are the ...
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56 views

portfolio return, sharpe ratio and value at risk

Can you please help me to confirm if my calculations are correct or need improvement, or (too simplistic...) : - portfolio return, - portfolio standard deviation, - portfolio sharpe ratio - ...
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25 views

Correlation in GARCH model

I don't think I have ever come across the concept of stochastic correlation so I imagine it's not very widespread, but I had the idea to implement a Monte Carlo VaR model for a portfolio of stocks by ...
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0answers
26 views

Interpretation of $\alpha$ (confidence level) in mean CVaR optimization

How are an investors risk preferences related to $\alpha \in (0,1)$ in a mean CVaR optimization? Would a risk averse investor choose a higher value of $\alpha$, and if so why? My understanding is, ...
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77 views

Approximation of portfolio VaR (after mapping) when Delta and Gamma both equal zero

As titled, I am having trouble estimating the VaR of a portfolio mapped as a function of a single risk factor $S$, in the form : $$V(S) = S^3 - 30S^2 + 300S + 150$$ with current value $S = 10$. $S$...
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1answer
220 views

Historical Simulation of Bond, Stock and Option Portfolio

If I have a portfolio consisting of 1-one stock of unit price equal to S, 2-one 9% coupon American bond with 20 years to maturity and a par value of $1000, 3-and one European call option on the ...
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45 views

Does it make sense to simulate from the multidimensional GBM?

Suppose I have times series data on 3 assets and I do $N$ simulations (GBM) first for each of assets individually and then from a multidimensional GBM since their log-returns are correlated (I use ...
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338 views

Large deviations theory and extreme value theory

I'll enter into details of both, sooner or later, but for the moment I'm concerned about the differences (and relationships, if any) between these two theories. Can someone give me a brief, but still ...
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1answer
92 views

Backtesting a stock scoring model

I'm working on a simple stock scoring model consisiting of 3 factors: 1.market cap 2.liquidity of the stock 3.the value at risk we defined 3 intervals for each factor and we assigned the ...