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8

$$ \frac{1}{2} \frac{\partial^2 f}{\partial S^2} dS^2 \approx \frac{1}{2} \sigma^2 S^2\frac{\partial^2 f}{\partial S^2} dt$$ (for small $dt$, ignoring $(dt)^2$ terms ) $\sigma$ is embedded in $dS = \mu S dt + \sigma S dW$ and $$ dS^2 = \mu^2 S^2 dt^2 + 2\mu \sigma S^2 dt dW + \sigma^2 S^2 dt \approx \sigma^2 S^2 dt$$ You picked up $1/2\Gamma \sigma^2$ from ...


4

There are a number of ways you might consider it: 1) As an investor (speculator) you may be required to post collateral that permits the holding of the position. What is your return relative to the invested collateral (and/or possibly expected collateral if the trade moves adversely) 2) This is one of the performance metrics measured in an investment bank. ...


4

If you have a covariance matrix, $Q$ the VaR is a measure of the standard deviation of the portfolio, ie. $$VaR, V \propto \sqrt{S^T Q S}$$ and, $$ \frac{\partial V}{\partial S} = \frac{QS}{V} $$ Suppose you had 3 assets, with large positions in the first two assets, and small position in the third, AND that the first two were perfectly negatively correlated,...


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I'm not aware of any great reference. However Peter Nash Effective product control: controlling for trading desks. Wiley (2018) chapter 10 Review of Mark-to-Market P&L is a good start. I wrote some notes here that I hope may help. You should have risk-theoretical P&L (RTPL - Taylor sereis approximation of the P&L) for all positions. For the ...


3

Most banks use mid market to compute daily MTM p/l whilst maintaining a reserve to account for liquidation costs. The latter is usually recalculated periodically and is indeed a function of market bid-offers. Market participants may use different methods because the definition of MTM pnl may differ depending on jurisdiction, accounting standards etc.


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References https://www.bis.org/publ/bcbs265.pdf This one is directly used by banks for programs such as FRTB. https://assets.kpmg/content/dam/kpmg/xx/pdf/2018/10/frtb-white-paper-july-2018.pdf. This one describes it from a P&L variance ratio point of view. https://en.wikipedia.org/wiki/PnL_Explained. Basic summary of P&L attribution. Summary The ...


3

It sounds like the P&L's you are given are not really the historical P&L's. Rather, you have some portfolio and market data currently; you have 260 days of historical market data changes; and you calculate what the P&L of the present portfolio would have been if the market moved as it did on that historical date from the current market data. You'...


3

One way to look at answering this question is VAR Contribution. Evaluate VAR of the Portfolio, and then evaluate VAR of the Portfolio without the asset. The largest difference of VAR with the asset - VAR of the portfolio without the asset would be the asset which is contributing the most to VAR. You may want to correct the size of the portfolio for each ...


3

There is more than one way to approach this. Given your comment that this is a small strategy in a larger account, I assume that you are testing it and, if it bears enough fruit, you may want to scale it up. You should assume some starting value. I'm going to assume a number that's equal to your initial nominal value (as you requested in your comment). ...


3

Good question! The answer to this is no. Let us work through a simple example to see why. Assume that the Gamma is $10$ and that the break-even move is $1$. For simplicity, also assume that, these are unchanged by price moves in the underlying (this is reasonably accurate for small price moves), so: $\Gamma = 10$ $\delta S_{Break-Even} = 1$ Note that we ...


3

Delta is the partial derivative of Call price C with respect to Stock price S, i.e $\frac{\partial C}{\partial S}$. In the BSM model implied vol $\sigma$ is constant, in particular it does not depend on $S$ so there is nothing further to discuss. When we allow for skew (but still compute IV according to the BSM model) the effect of a change in S is more ...


3

The fundamental underlying PnL you have is PnL on a bond and PnL on a swap, but you can choose to arbitrarily allocate this in different perspectives. Say you have the following DV01s: Bond +102, Swap -99, and say the market movements are: Bond +2bp, Swap: +1.7bp. The corresponding PnLs are: Bond +204, Swap -168, Total: +36. Your question thus becomes how do ...


3

Lots of ways to do this. Below is a pretty simple example: Side Position (Shares) Entry Price Current Price Open PnL Long 1000 100 90 -10,000 Short -1000 100 90 10,000 You don't need the Side and Position if you are going to use -ve values for Short positions. I just put ...


3

This document may be helpful Understanding Eurodollar futures The value of a 1 point price change (for example from 98 to 99) is equal to 2500 USD per contract (this is $1000000\frac{90}{360}1\%$ since the nominal amount for the loan is one million and interest is paid every 3 month on 30/360 convention). Equivalently the value of a 1 bp change (from 98 to ...


3

This is an excellent philosophical question. Recall that the goal of mark to market is to predict the P&L if we unwound this position in an orderly market. Suppose that you're in a very convinient world, where for every asset you know at all times the bid and offer (ask) prices, at which you can sell or buy these assets. Suppose you're just long some ...


2

First, I would say that it is realized PnL because with futures, you always have to settle up at the end of the day in the margin accounts. If you bought the futures at 98.51, then you only post margin since the futures contract has zero value. If the contract settled at 98.505, then you lost 0.005 on the contract. Each Eurodollar contract is on 1MM ...


2

The result you're referring to is actually $$ P\&L_{[0,T]} = \int_0^T \frac{1}{2} \Gamma(t,S_t,\sigma) S_t^2 \left( (\sigma_t^r)^2 - \sigma^2\right) dt $$ which is the total P&L of a continuously delta hedged long option portfolio, where $(\sigma_t^r)^2$ is the realised quadratic variation of log-prices over $[t, t+dt[$ and $\sigma^2$ is the hedging ...


2

Adding to Attack68 answer- you can do a few things: calculate total and average pnl over a given time. calculate skew, kurtosis etc. as suggested above. calculate hit rate. calculate max drawdown. SR using daily pnl is fine but ideally the returns should be in %.


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If the actual dynamics are those of Black Scholes and if the vol used in the delta hedge is the actual vol, then the P&L will be 10 cents i.e. not random and not dependent on the path.


2

You are right that the Total P&L (or as you call it the Net P&L) must be the same for the two methods, so something went wrong. In addition, by a strange coincidence, the realized P&L's although different (9,21 versus 6,24) add up to the same amount at the end (30), which does not usually happen. Here are my calculations First let's use FIFO: ==...


2

Hope this answers your qs, Denote $C_{model}(S,t)=e^{-rT}E_{{model}}[(S_T-K)^+]$ We model the spot dynamics $S$ with different models, e.g. In BS, $$\frac{dS}{S}=rdt+\sigma dW$$ $dC_{BS}(S,t)=\frac{\partial C_{BS}}{\partial t}dt+\frac{\partial C_{BS}}{\partial S}dS+\frac{1}{2}\frac{\partial^2 C_{BS}}{\partial S^2}dS^2$ $dC_{BS}(S,t)=\frac{\partial C_{BS}}...


2

I'll try to give some views on this, I hope it helps bringing some closure to your question. You seem to relate consensus to "theoretical prices". I think this is a bit misleading. I view consensus as nothing more than the average view across the street for market factors, e.g. the correlation between the Korean KOSPI and the Spanish IBEX, the ...


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Assuming your are modeling a product that is not linear in the underlying risk factor (not the FX rate per se), and assuming you are using logarithmic FX returns, you may arrive at the following: Let $f$ denote the value of your FX-product, $X_0$ denote today's exchange rate, and $r$ denote the log return (change) of your FX rate. Linearising around $r=0$ ...


1

VaR is a loss function calculated from what's available in step 1, whose value is a magnitude, and whose sign indicates whether there is a portfolio loss, or a negative loss (which is actually a gain, given that VaR, as a loss, is ordinarily reported as a negative number). So to ask which asset, whose returns are available in step 2, is driving this loss ...


1

By definition, a Taylor expansion is a local approximation, so you shouldn't use using it for large moves. Also you always have for options a 'gamma ladder', as gamma is a function of the underlying. One thing you could try maybe is to fit a curve to you gamma profile, then use a numerical method to calculate the derivative at your current point. This will ...


1

PnL = Profit - Funding Costs PnL = (Exit - Entry) - (50 * Capital - Capital) * Funding Rate % Gain = PnL / Capital Capital is how much you are investing (inclusive of margin). Your funding costs is 49 * Capital as that is how much you are borrowing to get to 50x leverage.


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There is no need to use the following confusing formula: PNL = quantity * multiplier * (1 / Entry Price - 1 / Exit Price) For all asset classes the following formula is sufficient: PNL = quantity * (ExitPrice - EntryPrice) The "multiplier" is only used when converting from one bucket (e.g. currency) to another. Looking at the following example: ...


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"Swimming delta" is another name for "floating delta" (as opposed to sticky delta). books.google.com/books?id=LnLgAgAAQBAJ&pg=PA170 Glen Swindle's excellent book "Valuation and Risk Management in Energy Markets" happens to be in Google books and explains it well on page 170. I'm just going to quote from his book here (see the book for formulas). ...


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Your total pnl is the mark-to-market pnl of your option position and its hedge .


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Usually when you invest in a CDS you rarely pay zero as the CDS coupons, unlike textbooks CDS and rates swaps, are standardized to 25bp, 100bp or 500bp. To compensate for the difference with the quoted spread, you receive/pay an upfront. So in practice you invest the upfront. Also in practice, if you are running a mutual fund, you will never find a bank to ...


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