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11

I'm sure this falls short of proper philosophical precision, but here goes. Hark back to a slightly modified rehash of Donald Rumsfeld's infamous: Reports that say that something hasn't happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we ...


4

It helps to get some intuition on all the terms. Point-in-Time (PiT) Probability of Default (PD) is a probability that the counterparty will default in a specific time-interval. I will denote the event of default between $t_1$ and $t_2$ as $A(t_1,t_2)$ for any arbitrary time interval. If we think about it logically, given today's state of the world (i.e. ...


3

See the graph below. Let's define the PNL as the position's payoff at expiry plus accrued initial investment, i.e. collected / paid option premia. Assuming $K_1=95,K_2=100,K_3=105$ (i.e. $\lambda=0.5$), the orange payoff diagram below belongs to a setup where $C_2<\lambda C_1 + (1-\lambda) C_3$: You paid some net fee initially, and you obtain a position ...


3

The conditional notation is indeed a bit confusing for those who do not spend a lot of time with mathematics. Downside beta is computed simply by taking only those data rows for which we see underperformance, and then doing the regular beta calculation. So, for example, if you have percent returns like Asset Benchmark 5 4 -2 2 8 -1 4 6 3 1 3 5 Then ...


3

Just to add to the above answer, if $\tau$ is the default time of an entity, we have $$P(\tau>t-1) =: SP_{t-1}$$ as the definition of survival probability beyond time $t-1$ (where $t$ and $t-1$ are some fixed period appart, say one quarter), and conditional probability of default over period $(t-1,t]$ $$ P(\tau \leq t | \tau > t-1) =: PD_t$$ as the ...


3

A more risky investment doesn't necessarily need to have a downside as in loss, just the possibility of earning less than a less risky asset. Let's walk through a simplified example - please tell me which parts are not clear. Suppose we have a choice of two investments. The "riskless" investment costs $1 now, and is certain to be worth \$2.50 in 1 ...


2

@DimitriVulis explained it well. The dynamic that is the source of your uncertainty here is that "risk premium" can mean slightly different things, when seen from slightly different perspectives. Much of the confusion around this subject stems from inconsistency in the use of these close and related but distinct concepts. Start with the basic ...


2

Risk-free assets refer to assets with a definite rate of return and no risk of default.   From the perspective of mathematical statistics, risk-free assets refer to assets with zero variance or standard deviation of investment returns. Of course, the covariance and correlation coefficient between the rate of return of risk-free assets and the rate of return ...


2

Actually, the issue is fundamental to quantitative finance, even though most people never go deep enough to notice. It has to do with the axiomatic foundations of Frequentist and Bayesian statistics. The Black Swan is a different thing and is not related to Knightian uncertainty. Frequentist methods are founded on aleatory risk, while Bayesian methods are ...


2

The TLDR; to your question: How can one use realized volatility as a volatility model to do out-of-sample prediction? You extended known models to incorporate additional information procured from high-frequency data. Going from the vanilla GARCH to a realized GARCH model can be done by adding an auxiliary model as an external regressor that captures ...


2

(I didn't quite understand where exactly you are going with your questions, but I inserted a few statements below that might be useful.) Jorion's table shows: $$ \begin{bmatrix} P(A\cap B) & P(A\cap B^c) & : & P(A)\\ P(A^c\cap B) & P(A^c\cap B^c) & : & P(A^c)\\ .. & .. & & \\ P(B) & P(B^c) & & \end{bmatrix} $$ ...


2

I would disagree more with the initial premise (ie the intellectual "straw man" you then kill) than with any of your perfectly cogent arguments that follow. I trust we both accept that stdev and var are monotonic in nature, each being the square (root) of the other?!?! The basic premise of Markowitz is thus indeed gloriously indifferent to which ...


2

As a ball park figure, your value would be around 5k (=10M x 0.01% x 5). If your swap in in EUR or JPY that have very low rates, you won't be too far off. However, this will give you the PV01, i.e., the discounted value of 1 bps, which is the same (or very very close) as the sensitivity of the market value to a change in 1bp (DV01) if the swap is at fair ...


2

Commonly, the definition of credit risk is the risk that, over a given time horizon, at a certain confidence level, names in our credit portfolio deteriorate or even default, leading to a (present value) loss. Commonly, this risk is not marked-to-market (most of our credit is not tradeable) and the risk horizon is 1 year. As you already noted, the risk is $...


2

the estimated forward curve actually predicts the amount of future cash flows of floating leg while the discount curve is used to compute the PV of those cash flows based on a supposedly risk free rate or OIS rate which is deemed to be lower thus, the IRS is more sensitive to estimation curve


2

Calculating correlation under the Basel II accords: Your second equation is almost in line with the international regulatory framework of the Basel II accords for calculating a banks minimum capital requirement, which is a framework telling you how to model PD, LGD and EAD following (at minimum) the foundational IRB approach. Any country that is a Basel ...


2

Below, I describe three cases: The standard $$\beta=Cov(r_p,r_m)/Var(r_m)$$ The case of a (up-)sided beta with arbitrary market return threshold $\theta$, $$\beta^+_m+(\theta)= Cov(r_p,r_m|r_m>\theta)/Var(r_m|r_m>\theta)$$ The case where we condition on your portfolio instead of the market, $$\beta^+_p(\theta)=Cov(r_p,r_m|r_p>\theta)/Var(r_m|r_p>...


1

There are several aspects: The holding period that you want to measure: Usually, you want to calculate VaR for a specified holding period. For USCITS funds it is e.g. 20 days for bank pillar 2 regulations it is an annual holding period. What is your holding period? Returns over periods If you have daily returns for certain assets, then you can aggregate them ...


1

Market risk limits are part of a risk appetite framework, which includes appetite for othe risk stripes, like non-financial (operational), reputational, and model risk. A good paper on setting up a risk appetite framework is The Financial Stability Board (FSB) Principles for an Effective Risk Appetite Framework (November 18, 2013). The general principles in $...


1

Let us consider separately the interest rate sensitivities of the fixed leg and the floating leg. Let us assume notional exchange ge, so each leg looks like a bond. If the mark ro market of the swap is zero, then the mrm's of the legs are the same,with opposite sign, but their cash flows and risks are not the same. All the coupons of the fixed leg are known ...


1

Thank you Dimitri, that is indeed who I was thinking of! Kudos for closing this search off so quickly.


1

It sounds like your professor is asking you to code the formulas in the Duffie-Singleton paper https://web.stanford.edu/~duffie/ds.pdf . (Also found in excellent papers by Bielecki and other sources.) A few technical details to keep in mind: In case of default, bond's accrued coupon is wiped out, and you have recovery only on the remaining principal ...


1

Credit spread risk is a risk-neutral probability of default. That is, it includes the expected loss plus a systemic risk premium if one ignores factors like liquidity, counterparty risk, and tax effects. Other posts in this page show how one can calculate a risk-neutral probability of default given CDS spreads. CDS Spread = EL + RP Credit risk is a real-...


1

it's me again... So i find out what a negative shape parameter in Generalized Pareto Distribuition means and why it's not possible to calculate EVT with it. negative shape parameter means that the distribuition has a limit, not quite what you are looking for when fitting an extreme value theory model.


1

There are two kinds of factors. Named or defined factors are related to observable economic or financial variables, such as FamaFrench HMB, or the market factor or an oil price factor. Unnamed or statistically identified factors are the result of a PCA using only stock prices. Although the first PCA factor is usually close the Market factor mentioned above (...


1

I understand that you want to derive some form of risk preference parameter from portfolios that you can observe 'in the wild', and I will discuss that accordingly. As a side note, there is a whole thread in the literature that discusses elicitability of risk preferences using cleverly designed choice experiments -- and the form of the utility function. The ...


1

It depends. If you believe in (fractional) stochastic volatility then the delta, in the strict sense of the word, is zero, since the VIX future is a volatility derivative. A simple linear regression is probably not such a bad idea to estimate the "delta" of the VIX future wrt to SPX if you do not believe in / assume any particular model. It is more ...


1

In general, the P&L of options is non-linear with respect to the underlying. Unless the options are very far in or out of the money, the delta alone does not accurately tell you what the value of the option will be if the underlying exchange rate moves 2.33 standard deviations. Even if you were told the gamma, estimating the change in value of the ...


1

There is a significant amount of literature on this topic ("risk integration") and a number of different approaches have been proposed. A relatively accessible introduction to this topic (See Chapter 7 in particular) can be found here: Stress Testing and Risk Integration in Banks. At a high level, adding the risk measures involves estimating the ...


1

I am actually more interested in it from the other perspective. If we have a price shock what is the likely IV change that will affect the options pricing? If you're using Python, I would recommend the Mibian library (http://code.mibian.net/). You can simulate a price shock by increasing the volatility parameter (which is HISTORICAL volatility in this case) ...


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