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We want the duration $D$ to satisfy $$\mathrm{d}P=-PD\mathrm{d}y,$$ i.e. it tells us the proportional change in the bond price if the interest rate (yield) changes. The minus is due to the inverse relationship between bond yield and bond price. Thus, $$D=-\frac{1}{P}\frac{\mathrm{d} P}{\mathrm{d} y}.$$ Duration can be seen as a linear approximation to the ...


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You would need to provide more details for an accurate PnL attribution. However, here are some additional points to consider that might help. When you sold protection, you effectively became long the 5Yr synthetic debt of the reference entity at a credit spread of 190bps. Since the coupon is 5%, this would imply a 5Yr (at the coupon frequency of the ...


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To keep notations uncluttered assume zero funding costs and consider a European contingent claim priced as $$ V = \Bbb{E}_0 \left[ h(S_N) \right] $$ Suppose you would like to make the dependence of your pricing on a specific model parameter $\theta$ appear. You then usually have the following representation choices \begin{align} V &= \int_0^\infty h(S) q(...


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There is no contradiction and basically no ambiguity. Furthermore, the kind of product (linear or non-linear) has no bearing on the question. It is really only a question of basic calculus. Let us call the three FX rates $x, y, z$ which satisfy the relation (or constraint) $z=xy$ and your product $P$, which is a function of $z$ only. You can interpret $P$ ...


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We set out a general scheme for doing this sort of thing in our paper http://ssrn.com/abstract=1401094 and its sequel http://ssrn.com/abstract=1437847 Whilst the case studied is different, the techniques are the same. I also discuss in detail the whole process in a chapter of More Mathematical Finance. The adjoint method when it applies is generally ...


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When you long a 5y CDS and the spreads <5y increase and the 5y spread remains constant, the premium leg value is decreased. It appears that the CDS value should increase, and you should have a positive sensitivity. However, depending on the shape of the survival probability curve, the protection leg value may also decreased, and then the CDS value, which ...


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Market sensitivity is beta of your portfolio returns to market return, momentum sensitivity is beta against your momentum returns. You'd likely want to run a multiple regression of your portfolio returns against market returns and momentum returns to get those betas/sensitivities.


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Use the swap uploader on SWPM to save the deals and "CUSIP" them (starts with "S" and has a Corp tail). I believe you can then reference them through the Excel add-in by the "CUSIP" Another way using Excel is if you have an Anywhere subscription, you can make use of the Derivatives toolkit and structure/price/analyze your swaps all in the sheet.


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Here is some historical context. Macaulay introduced the duration concept as in the ‘duration of cash flows’ sense, in a way to measure the effective term of the loan. For the weights, he considered (or more like debated) alternatives, but then concluded to use present value. So Duration as per Macaulay is a present value weighted average of cash flows ...


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The raw Greeks so to speak $-$ e.g. from Wiki - European Option Greeks $-$ usually represent (broadly speaking) the $ amount lost per +1 absolute move in the respective risk-factor. So for example, if your Spot-Delta is $$\text{Delta} = \Delta \approx O(S+1, K, T, V) - O(S, K, T, V)$$ and spot moves relatively by $x$ (say 1%) then your PnL is $$\text{...


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Please see below: Copied from Quantitative Methods in Derivative Pricing by Tavella.


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I learned that I can contact Bloomberg Help Desk and got an answer from there: YAS_RISK is DV01/100, where DV01 is the dollar price change resulting from a one-basis-point change in yield. YAS_RISK is given in the currency of the bond, because DV01/100 is a percentage of the face value, and the face value is given in the currency of the bond. Please ...


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I think it might be helpful to give an example here. So lets say you would want to estimate your PnL for a bond using the yield change and use YAS_RISK to retrieve your DV01 for a specific nominal. Assuming nominal of 1,000,000 Yield change: Lets use a realtime field for yield change RT_YLD_CHG_NET_1D This is in percentage To get the DV01 for your nominal ...


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We note $A$ the annuity, so that $V^{swap} = A(s - K)$ so that $\frac{\partial V^{swap}}{\partial s} = A$. As the chain rule gives $$\frac{\partial V^{swap}}{\partial r} = \frac{\partial s}{\partial r} \frac{\partial V^{swap}}{\partial s}$$ we get that $$\frac{\partial s}{\partial r} = \frac{1}{A} \frac{\partial V^{swap}}{\partial r}$$ and as the chain rule ...


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@AlRacoon was completely right by suspecting convexity for this issue. The Chart below shows the impact of the convexity in this trade very well.


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First and foremost I do not agree with you Closed Form value. I get $\Theta=-8.963$. There are various of BS calculator you can use the check your results and in general you should do that. Here is one: https://goodcalculators.com/black-scholes-calculator/ Have in mind that maturity T is fixed then your forward FD problem should look like this: $$ \Theta(T-...


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If you want a simple example which you can easily reproduce in a spreadsheet, look at section 3 of the paper "Adjoints and automatic (algorithmic) differentiation in computational finance by Christian Homescu. Table 1 is wrong though but you should be able to generate the same numbers using all 4 methods 1) Finite Difference 2) Complex Step 3) Tangent ...


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This is a common confusion, and it comes down to the difference between forward rates and swap rates. Swap rates are essentially the integral of forward rates (just like zero coupon rates). The behaviour you're seeing is easy to understand if you think about the effect on the forward rates of bumping a swap rate. Here's a sketch of some implied forward ...


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The assumption of 100% delta for an option would give a good upper estimate for the exposure due only to the part of the option exposure that comes from the movements in the underlying price. But for example, imagine you had a portfolio which is long a long dated call and long a long dated put, such that the portfolio is overall delta neutral over a ...


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Based on the UCITS directives: E = n * c * UL * delta where E denotes Exposure, n = contract size, c= contract sie, UL= underlying price. As you're probably aware from BSmodel, call has >0 delta vs <0 for puts. Hope the explanation merely helps you to grasp the direct correlation between E and delta in a UCITS framework.


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Yes, you are right. It appears to be a trivial typographical error in the book. I checked the formulas on Wikipedia https://en.wikipedia.org/wiki/Greeks_%28finance%29 and they agree with yours. The signs are obvious also since N(.) is between 0 and 1, i.e. non-negative. Now, about the reasoning starting with "from a logical point of view". Are you familiar ...


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