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9 votes
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Gamma PnL from Itô's Lemma derivation

$$ \frac{1}{2} \frac{\partial^2 f}{\partial S^2} dS^2 \approx \frac{1}{2} \sigma^2 S^2\frac{\partial^2 f}{\partial S^2} dt$$ (for small $dt$, ignoring $(dt)^2$ terms ) $\sigma$ is embedded in $dS = \...
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  • 4,963
6 votes

Good references on PNL explain?

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. Andrew ...
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4 votes

Return on a CDS portfolio

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 ...
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  • 7,997
4 votes

How to determine what's driving the VaR?

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, $$ \frac{\partial V}{\partial S} = \frac{QS}{V} $$ ...
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  • 7,997
3 votes

Why using mid price to compute mark-to-market P&L if it is less accurate than using bid/offer price?

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 ...
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3 votes

Good references on PNL explain?

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 ...
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3 votes

How to determine what's driving the VaR?

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 ...
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3 votes

How to determine what's driving the VaR?

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 - ...
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  • 5,010
3 votes
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Continuous Percentage Profit and Loss calculation

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 ...
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  • 3,475
3 votes

Gamma PnL Formula and Break-Even volatility

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 ...
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3 votes
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PnL with FIFO and LIFO

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 ...
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  • 9,347
3 votes

What is "swimming delta" as a risk attribute in pnl explain?

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 ...
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  • 9,347
3 votes
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Calculating PnL on Swap Spread Trade

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 ...
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  • 7,997
3 votes
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How does a Short position impact the PnL?

Lots of ways to do this. Below is a pretty simple example: ...
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  • 3,475
3 votes

Calculating PnL on Eurodollar futures trading

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 $1000000\frac{90}{360}1\%$ ...
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  • 9,347
3 votes
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Why using mid price to compute mark-to-market P&L if it is less accurate than using bid/offer price?

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 ...
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3 votes
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Explain daily P&L by risk factor for a portfolio of bonds and FX forwards

It makes sense to calculate P&L due to passage of time, and to try to separate it into carry and rolldown. What would the P&L be if all the rates today were the same as they were yesterday, ...
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2 votes
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Calculating PnL on Eurodollar futures trading

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 ...
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2 votes
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Can we rewrite the pnl of a continuous hedge option as the time average of the volatility weighted by the square gamma?

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 ...
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  • 13.9k
2 votes
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performance measure using pnl series

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. ...
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  • 111
2 votes
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Delta Hedged PnL on Call Spread

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.
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  • 173
2 votes
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Question about using Ito's lemma in Gamma PnL

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{...
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  • 356
2 votes

Structured Trade / Hedge consistency

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 ...
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2 votes
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compute Expected Shortfall / Conditional VaR from distribution

Generally, VaR and ES can been seen from two different points of view: $R_t$ are portfolio returns. Then VaR is left quantile (e.g. 0.05) and ES is expected return below this quantile. $L_t = -R_t$ ...
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1 vote

Using Taylor formula with logarithmic returns

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 $...
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  • 5,333
1 vote

How to determine what's driving the VaR?

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, ...
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  • 2,815
1 vote

Historical PNL using Taylor Expansion for Gamma Ladders

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. ...
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1 vote
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realized/unrealized PnL with leverage

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 ...
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  • 5,010
1 vote

realized/unrealized PnL with multiplier

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 ...
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  • 145
1 vote

What is "swimming delta" as a risk attribute in pnl explain?

"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 ...
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