Newest Questions
23,553 questions
2
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The use of L2 Regularization in portfolio optimization
In portfolio optimization, the goal is to calibrate the weights of assets in a portfolio according to a stated objective (mean-variance, minimum-variance, risk parity etc.). Often, mean-variance or ...
- 2,862
1
vote
0
answers
66
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Realistic understanding of YTM and reinvestment [duplicate]
Studying for CFA level 1 right now and there are a couple questions I have about YTM and reinvestment rates. It states the following: There are three sources of returns from investing in a fixed-rate ...
- 11
1
vote
1
answer
53
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How to calculate basis risk for a floating rate bond?
Right now the bank, I work in, calculates basis risk (BR01) for floating rate bonds (FRNs) in the following way.
In the post below Dimitri Vulis and Kermittfrog suggested using Jacobian matrices for ...
- 85
-1
votes
0
answers
52
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two ways to calculate bond carry
there are two ways to calculate bond carry
forward yield minus spot yield, where forward yield is the bond forward's yield solved on the forward settlement date;
the coupon income minus funding cost
...
- 793
2
votes
1
answer
102
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EURIBOR Fixing Risk
So this is really about EURIBOR as we are in a RFR framework in other major currencies. I'm interested in understanding the exact EURIBOR fixing risk a swap trader really faces if he manages a large ...
- 963
0
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2
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94
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Constrained Optimization Problem Applied to a Portfolio
Can someone explain, how do i find the weights $ w_A, w_B, w_C $ that minimize the variance of the portfolio? And also what are the first-order conditions? (FOC)
$\sigma_{A}^{2}$ $\sigma_{B}^{2}$ and $...
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0
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1
answer
86
views
Practically pricing index futures using cost to carry
I am trying to compute a rough approximation for the theoretical price of a Nikkei 225 index future with a far-away expiry. I don't need much accuracy, just a very rough but reasonable upper and lower ...
2
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1
answer
111
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Can a swaption be priced when the underlying swap has already started before the option’s exercise date?
I would like to confirm whether a swaption is still well-defined and how it should be priced when the underlying swap starts before the swaption’s exercise date.
Typically, a European swaption assumes ...
- 21
1
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0
answers
73
views
Market impact models for vanilla options
What are the common ways of modelling slippage (bid/ask spreads + market impact) of vanilla options?
E.g. in linear instruments it is common to model the costs as a term proportional to bid/ask spread ...
- 386
0
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0
answers
70
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Simulating stock returns GARCH-copula approach
I am currently in need of simulating stock returns from 2025 until 2100 for scenario analysis purpose. I used a GARCH-copula approach : mean = ARX for GARCH, student t residuals and student t copula. ...
- 31
1
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1
answer
118
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Discounting future cash flow for credit risk calculation
In calculation of the expected credit loss (ECL) for a loan portfolio, regulatory frameworks like IFRS and CECL require that all loan cash flows are discounted based on the effective interest rate (...
- 231
2
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1
answer
218
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Modelling energy derivatives from a purist perspective
I continue to attempt wrap my head around the mathematical foundations of modelling in energy trading, but I get stuck, or rather, cannot find any definitive references.
From a purist perspective, I ...
- 21
0
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1
answer
102
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Single Callable Bond - from Option Price to Z-Spread
The pricing software I use requires the specification of a z-spread for the valuation of a single callable bond. According to many sources, however, the Z-spread is determined based on the bond price, ...
0
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0
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72
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Beginner question about Option pricing, Risk and Rational portfolios
I'm a physics student currently reading "Econophysics and Physical Economics by Peter Richmond, J¨urgen Mimkes, and Stefan Hutzler" for the first time and this is my first touch with the ...
- 101
0
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1
answer
60
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NPV function sensitivity to FX rates, when those rates are not in the variables of the function
How do I calculate a sensitivity of NPV function to FX rate to the reporting (base) currency, when that FX rate is not in the variables of the said function?
For example,
$$f(C_1, C_2, DF_1, DF_2, [...
- 85
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2
answers
85
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Why does the forward-price formula compound discrete dividends using cost-of-carry-rate 𝑐 rather than interest rate 𝑟?
In Wikipedia, the formula for the forward price of a tradable underlying that pays discrete dividends is given as:
My confusion is this: once a dividend $D_i$is paid at time $t_i$, it becomes cash ...
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1
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53
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QuantLib issue with creating a FixedRateBond
When trying to construct a simple bond object using QuantLib using the example from the docs, I get the following error:
...
0
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1
answer
66
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CDS upfront fee in CDSW
I want to understand how the upfront fee that is paid/received at the start of a CDS is calculated. My understanding is that it should equal the difference between the present values of the two legs ...
- 11
0
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0
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39
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using AMC across the board (for all trade types) for calculating CVA
I know that some banks use AMC (american monte-carlo) to calculate exposure simulation (for CVA) across the board (for all trade types, not just american style option trade types) instead of ...
- 101
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0
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54
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Are there two versions of Avellaneda & Stoikov (2008) “High-frequency trading in a limit order book”?
I’ve noticed that there seem to be at least two versions of the well-known paper High-frequency trading in a limit order book by Marco Avellaneda and Sasha Stoikov.
The original version, often dated ...
1
vote
1
answer
141
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Clarification on compounding logic in Chapter 23 of Pricing and Trading Interest Rate Derivatives by Darbyshire
I'm working through Chapter 23 (page 396) of Pricing and Trading Interest Rate Derivatives: A Practical Guide to Swaps by J.H.M. Darbyshire, and I’m having trouble understanding a specific statement ...
- 11
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1
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100
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Interest rates swap P&L
I heard about different ways of estimating the PnL of an IRS. Say I receive through a 10y swap where fixed is 5%, I hold the position for 1 year time.
you pay float and receive fixed so estimate PnL =...
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47
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Finding an invariant/stationary quantity in prediction markets?
I am looking at trade data for specific outcome of an event on a prediction market (Kalshi, but this could apply to others) and trying to model market microstructure effects such as inferring mid ...
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2
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1
answer
165
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ICVS 490 curve date vs swap settlement date
The more I look into curve construction the more questions I have. For example, the ICVS 490 curve (USD OIS SOFR vs Fixed):
The calibration/input instruments are USOSFR* instruments, i.e. OIS SOFR ...
- 3,813
2
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97
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Using SOFR 1M futures for curve construction/bootstrapping
Using continuous time notation, the 1M SOFR futures rate R (price is 1-R) is
$$
R = \frac1T E^Q_t \left[\int_0^T r_u du \right]
$$
where $[0,T]$ is the reference month.
So I initially thought that the ...
- 3,813
0
votes
2
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229
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Why do recruiters ask you to solve lots of basic, yet not simple, probability problems?
Why do recruiters in Quant Research ask you to solve lots of basic probability problems that have to do with uniform discrete random variables and cumbersome conditioning (cards, dices, coins)? Wouldn’...
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1
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53
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Convergence of Numerical Methods on Lookback Options in R
I have been practicing using R code for my Quant course and I came across an issue when testing the convergence of numerical methods for lookback options to the analytical solutions provided by Hull ...
0
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0
answers
82
views
Orthogonalizing returns or signal
Say you want to test the performance of a signal, you can multiply it by forward returns. And do these each time the signal changes.
One can orthogonalize either the return or the signal with the ...
- 171
0
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1
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84
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Calculating swap npv 1 day in the futures with rateslib
I’m trying to evaluate a SOFR IRS at two different dates using RatesLib.
At date t, I build a curve using market data and use it to price an IRS.
At date t+1, I revalue the same swap using the updated ...
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0
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71
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Exercise 30.2 on Hull's OFOD
In Hull's Options, Futures, and Other Derivatives, there is the following exercise in Chapter 30:
Explain whether any convexity or timing adjustments are necessary when:
(a) We wish to value a spread ...
- 101
2
votes
1
answer
210
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Compounding vs. Averaging Swaps Convexity
Suppose first that we are concerned with a standard ARR compounding swap, where the floating coupons are semi-annual and are computed as the overnight realized ARR, compounded every six months. The ...
- 137
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44
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Which mean, standard deviation and beta should I use in a cointegration pairs trading strategy?
I'm running a cointegration pairs trading strategy.
In sample, the implementation is very straightforward:
run a Engle y Granger two-step procedure and reject $H_0$
Calculate de hedge coefficient $\...
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0
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49
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Why do market-makers use the delta on the a-axis of the IV-plot? [duplicate]
I've been accepted as junior at an top MM-firm at the skin of my teeth mainly due to mistakes in simulated trading with pricing with an IV-plot I just failed to understand it. The plot is made of the ...
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0
answers
27
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Understand fit results from a t distribution
I'm trying to understand the results of fitting a t distribution to a sample of data. For some reason the obtained parameters are decimal. Could somebody explain me what does decimal degrees of ...
0
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0
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95
views
Hypothetical question on the value of "inside" institutional info
I have a hypothetical scenario I can't get my head around and wanted to see what people with real-world knowledge think.
Let's say someone hypothetically gained access to an internal investment ...
2
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0
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41
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Is that simplest impossible to get price-level aggregated L2 data using IBKR reqMktDepth()?
Hi all — I’m logging IBKR SMART (cross-venue) raw L2 updates via reqMktDepth(..., isSmartDepth=True) and trying to aggregate them into a price-level order book (sum ...
- 21
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1
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93
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How to design an effective reward function for RL-based FX hedging strategy?
I'm working on an Reinforcement learning (RL) algorithm for optimizing a foreign exchange (FX) hedging strategy, specifically for the USD/AZN (Azerbaijani manat ₼) pair in the context of Azerbaijan's ...
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0
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25
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Where to find downloadable 1-hour data of DAX index? [duplicate]
I am looking for a page/site where I can download the historical data for the DAX index (or other stuff) with at least 1 hour resolution for the complete trading time window from 8:00 in the morning ...
- 101
1
vote
1
answer
186
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On the correct definition of ex-post variables
I recently had an interview with a quant from a hedge fund and we were discussing about properly defining ex-post variables when backtesting the forecasting ability of certain market variables.
For ...
- 2,862
1
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1
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163
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Getting historical data on cross-currency basis
I have a series of USD short-term bond yields that I would like to convert to CAD equivalents. Conceptually, one could do
\begin{equation}
r_t^\text{CA} = \text{CORRA}_t + (r_t^\text{US}-\text{SOFR}_t)...
- 11
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0
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49
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If the fixing happens 2 business days prior, do we also project with two business days adjusted?
For example, consider a forward-starting swap that will initiate at T1 and pay at T2.
If the "fixing" happens at T1 - 2 days, does that mean, standing at time 0, the projected coupon I ...
- 49
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1
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105
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Why doesn't the libor curve match libor fixings?
Consider the 6M Libor rate (in any ccy). This is a rate that is/was published every day.
For every one of those days, we also have 6M swap curves available, which are calibrated based on market ...
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2
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answers
165
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Fitting a multivariate t copula to stock return data
In the context of stress testing a portofolio, I am looking to model stock returns using multivariate student t copula. I already estimated the marginals law, fitting a student t univariate law to ...
- 31
1
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1
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146
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Data source(s) for LCH-CME SOFR swap basis
As far as I know SOFR swaps prices in Bloomberg can be found under the tickers USOSFR(Y) BGN Curncy, so for example USOSFR5 BGN Curncy is the 5 year SOFR swap.
However, as far as I know, USOSFR is the ...
- 3,813
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1
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183
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Carry and Return on Basis Trades and Asset Swaps
I have been looking into the return of the treasury bonds basis trade. I am trying to analyze the relative value between the different contracts. If one were to ignore any option values in the ...
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1
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95
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Where can I find financial ratios, ESG fundamentals, and bankruptcy/default data for European companies?
I’m developing a credit/default risk model as part of a research project and need time-series data for European companies, covering the following variables for each company-year (or company-quarter).
...
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1
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123
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Convexity in long end treasury bonds
According to published research, yield curves plotted against duration typically exhibit steepening forces as investors demand higher return for longer yields, but that often in the very long-end, ...
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1
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64
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Will the risk-neutral measure be different for different CLO tranches?
Consider the following derivative (mimicking a CLO):
B borrows 90 dollars from lender L.
B buys some bonds worth 100 dollars using his own 10 dollars and the 90 dollars he borrowed. The bonds pay ...
- 177
4
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4
answers
376
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What is the relationship between the risk-neutral and real-world probability measure for a random payoff?
Say there's some financial security that gives you 1 dollar with probability $p$ and zero otherwise. We know that the value of this is not the expected value $p$ but rather the expected value under ...
- 49
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63
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Early expiry volatilities in commodity futures markets
I'm trying to figure out what the short end of the volatility term structure for options on commodity futures looks like.
A concrete example:
Soybean (ZS / S A Cmmdty)
X25 -> short term weekly ...
