All Questions
22,267
questions
3
votes
1
answer
951
views
Correlation basket equities
One question: when asking for the correlation of a basket, a trader told me 50% whereas I expected him to give me asset pairwise correlations (i.e. the correlation matrix). What does this 50% mean ...
- 327
3
votes
2
answers
1k
views
Why do par-yield shifts grow faster across the curve than spot-rate shifts when looking at key-rates?
Consider the following 10y key-rate shifts of bond par yields and its implied shift of bond spot rates:
Assume we have the key-rates for 2y, 5y, 10y and 30y.
The y-axis is in basis points, and the x-...
- 439
4
votes
1
answer
451
views
Finite Difference method in Matlab for SABR volatility model fails to provide correct option values
Currently, I'm trying to implement a Finite Difference (FD) method in Matlab for my thesis (Quantitative Finance). I implemented the FD method for Black-Scholes already and got correct results. ...
- 117
5
votes
1
answer
1k
views
Comparing historical to implied volatility
As title states, I am trying to compare historical to implied volatility of a stock.
I approximate the single implied volatility (30 days forward) of the stock by first finding 2 series that ...
- 211
2
votes
1
answer
126
views
Does Weak stationarity imply ergodicity ?
My intuition of ergodicity is the Law of Large Numbers for time series i.e. Given sufficient, data points, their mean and standard deviation would converge to population mean and standard deviation.
...
- 269
11
votes
2
answers
1k
views
Does numeraire have to be a tradable asset
I thought we create replicating portfolios using underlying and the numeraire i.e. the numeraire has to be a tradable asset (assuming simple binomial model).
But I have seen some examples which ...
- 692
1
vote
0
answers
109
views
Cramer-Lundberg: Adjustment coefficient does not exist
The question is about Ruin theory and the Cramer-Lundberg model.
I am wondering if there is an example of distribution where the MGF is finite, but the adjustment coefficient does not exist.
Can you ...
2
votes
0
answers
56
views
Calibration of stock's intrinsic value under the gordon model
Assume we have the constant growth Gordon model, for a stock paying dividend $D$,Earnings per Share $EPS$, annual growth rate $g=ROE*(1-\frac{D}{EPS})$ and discount rate $r$.
Then:
$IV=\frac{D*(1+g)}...
- 1,416
1
vote
1
answer
234
views
Markowitz w/ riskless asset & CAPM
If risk free rate ($R_0$) is bigger than expected return on minimum variance portfolio ($\bar{\mu}$), so $R_0>\bar{\mu}$. I.e. the tanget portfolio is on the risky inefficient portfolio frontier ...
- 43
10
votes
1
answer
2k
views
How do I convert order book data into OHCL( Open,High,Low,close) format?
The image represents the order book data with columns having following attributes:
a0: Best ASK price (i.e. the lowest posted price at which someone is willing to sell an asset)
b0: Best BID price (...
- 101
4
votes
1
answer
2k
views
QuantLib-Python: What is "index = Euribor1Y(term_structure)" doing?
I am currently reading thorugh the QuantLib-Python cookbook to learn about this nice pice of software. On page 141 I encountered a block of code that made me wonder what it is exactly doing.
The code ...
- 342
2
votes
3
answers
4k
views
Negative variance?
Using the formula w*Cov*t(w) I can generate a negative portfolio variance. What are the implications of a negative variance? Should I just assume it's zero? A negative variance is troublesome ...
- 196
1
vote
0
answers
42
views
Negative abnormal stock return and permanent impact
Assume we have a day where stock price falls many standard deviations of the mean (e.g >3) . How could we test, in terms of time-series, if this negative shock is permanent or deminishes in the long ...
- 1,416
0
votes
0
answers
81
views
Structured product with coupons
What kind of structured product has the following payout?:
Guaranteed capital at maturity $T$
It pays a coupon at time $t$ equal to
$$C_0\sum_{i=1}^{\infty}\max(S(t)/S(t-1)-1-C_1 i;0)$$
with $C_0,...
- 1,527
1
vote
1
answer
6k
views
MtM of FX Forward
I had a look at pnl calculation of FX forward but it didn't quite match my question.
Say $X_{t,\tau}$ is the USDJPY FX Forward Rate as seen at time $t$ for expiry $t+\tau$. So $X_{t}^{spot} := X_{t,0}...
- 1,022
4
votes
1
answer
780
views
Ledoit Wolf shrinkage with constant correlation prior with tawny and Riskporfolios
I am trying to use R to perform the shrinkage of covariance matrix towards constant correlation as defined in 'Honey, I Shrunk the Sample Covariance Matrix'.
I see there are two packages where this ...
- 91
1
vote
4
answers
949
views
If equity returns are normally distributed, why are average equity returns not zero [closed]
So I am getting confused between assumption of equity returns normality and why then equity markets in the long term on average go up i.e equity risk premium.
Does this not already poke wholes in the ...
- 59
3
votes
1
answer
821
views
Quantlib - model changes in option value on day of expiry
I'm trying to model option value changes during the progression of the last trading day before expiry. All option pricing Quantlib examples that I've seen work with day-level granularity. I'm ...
- 133
-1
votes
1
answer
596
views
Portfolio turnover [closed]
Really easy question, but I am having doubts. If you want annual turnover, and you have monthly weights, wouldn't you just do in excel:
{=ABS(CurrentMonthsWeights-LastMonthsWeights)*12} for each ...
- 115
2
votes
1
answer
135
views
Adding a new strategy to an existing portfolio
I wanted some help in looking for suitable articles/literature. Suppose an investor has a bunch (bouquet?) of quantitative strategies already generating trading signals for him. If he comes up with a ...
3
votes
1
answer
203
views
Optimal portfolio construction for tactical asset allocation
This is the first time I post question here so if there is anything that does not follow the rule, please bear with me and let me know.
I am trying to solve this optimization question but I don't ...
- 31
7
votes
3
answers
321
views
Measuring alpha (Academia vs the Industry)
During academia, I learned to evaluate the performance of a portfolio by calculating alpha as the following:
$\alpha_{i} = (R_{it}-R_{ft})-[\beta_i(R_{BMK_t}-R_{ft})]$
where $\alpha_i$ and $\beta_i$ ...
- 488
4
votes
3
answers
2k
views
Put Call Symmetry
I want to show the Put Call Symmetry without using the explicite Black Scholes formula. In other words I want to show
Call(t, x, K, T) = Pull(t, K, x, T)
where $S_t = x $ for $t \in [0, T]$.
I ...
- 73
1
vote
2
answers
345
views
R: optimize timeseries to minimize "integral"
What I am looking to do is:
for a given time-series $P_t$ (which will be constructed from different timeseries itself):
$P_t$ = $\beta_1$$I_t^1$+$\beta_2$$I_t^2$+$\beta_3$$I_t^3$ $\qquad$ ($I_t^i$ ...
- 11
1
vote
1
answer
2k
views
Pricing fixed coupon bond with ytm in QuantLib python
I'm new to QuantLib and I'm confused about ZeroCurve in YieldTermStructureHandle
The start date is Oct 20, 2001. Assuming the ...
- 33
14
votes
3
answers
3k
views
Deciding how many trades to make
I recently sat a technical interview with a prop trading and market making firm. I didn't pass the interview, and I was wondering about answering one of the questions they asked me.
So the ...
- 243
1
vote
1
answer
336
views
Index implied repo gerater than the stock repo
I've observed that the repo rate implied from options on Euro Stoxx 50 is significantly higher than the repo rate implied from options on individual stocks that are constituents of the index. This is ...
- 11
-2
votes
1
answer
323
views
Derivative of Time Value of Money by time [closed]
I'm struggling with a (probably very simple) problem.
What i like to do is the following:
Lets assume we got a bullet bond (no calls, etc) which is currently trading above par. Under the assumption ...
- 245
-1
votes
1
answer
160
views
On the buyside, when people quote a 'price' for a plain vanilla interest rate swap, does it include accrued interest?
The valuation date falls in between coupon payment days on the swap, does the 'price' of a swap understood to include the accrued interest (interest from the previous payment date to the valuation ...
- 11
3
votes
2
answers
807
views
Does using adjusted closing prices constitute a lookahead bias?
One of my machine learning project involves the use of adjusted close prices (from Yahoo Finance, for better or worse) to determine the label – if a stock's adjusted close price increases by more than ...
- 243
0
votes
1
answer
170
views
Using Normal Distribution to forecast active return
I wanted advice on how to go about forecasting active return via a standard normal distribution,
The asset is a security with annual volatility of 6%. The benchmark is a 5% annual return with 0% ...
- 115
0
votes
1
answer
294
views
Accrued Interest on a bond [closed]
If I were to price a bond on one of its coupon payment days, does that day's coupon payment gets added to the cashflows, if so, do we just discount that by 1 (same day)? ie, C1*df1 + C2*df2 + ... ...
1
vote
1
answer
99
views
Confused About Ex-Ante vs. Ex-Post Pricing Representation
This is going to be a really simple question, but I am confused by it. The basic pricing formula is $p_t=E^p_t(m_{t+1}X_{t+1})$, where $p$ is the physical measure. We can also say that $R_{t+1}=\frac{...
- 113
2
votes
1
answer
280
views
What is the domain of the Black-Scholes operator?
By the Black-Scholes operator I mean the following.
$$L_{BS}u(x) = \frac{1}{2}\sigma^2x^2\frac{\partial^2}{\partial x^2}u(x) + rx\frac{\partial}{\partial x}u(x) - ru(x)$$
Obviously, the domain of $...
- 595
6
votes
1
answer
375
views
how are financial data with sparse and asynchronous features imputed in predictive modeling?
I watched a presentation from a large quantitative finance firm that spends a lot of effort around predictive modeling. One of the points the presenter emphasized was that they deal with a lot of ...
- 775
3
votes
2
answers
345
views
Markowitz; risky asset frontier w/o risk free asset
What is the intuition behind the "spanning" result in the following statement?
For a fixed pair of distinct frontier portfolios $\phi_p$ and $\phi_q$, any frontier portfolio $\phi$ can be obtained ...
- 43
1
vote
2
answers
3k
views
How does after-hours trading affect the next session prices? [closed]
I just read about after-hours trading (and here ), but remain unclear as to what happens to the price level of the next open session. In other words,
Do the prices change during after-market hours? (...
- 215
4
votes
0
answers
135
views
difference between Meucci fully flexible probability and markov regime swtiching models?
What is the difference between A. Meucci's Fully Flexible Probability (FFP) and Markov Regime Switching Models ? They seem very similar to me, FFP based on state variables that define regimes will ...
- 59
2
votes
1
answer
145
views
Sigma moves - annualize return or no?
This might be a very simple dumb question. But when you look at a security's annualized volatility over a 3 year period, assuming the security has an annualized vol of 5% and the drawdown over three ...
- 115
5
votes
1
answer
623
views
Why is the 1 month OIS rate so stable?
I was just playing around with bills prices data from CRSP.
It is well known that short term bills rates tend to be lower than corresponding maturity OIS rates this is often attributed to some ...
- 173
1
vote
0
answers
63
views
Differential Equation of Type Ricatti as part of Short Rate Model
I currently despair of the following solution of a differiental equation (Ricatti Type) as part of a short rate model:
$$
B_t=\frac{1}{2}aB^2+bB-1
$$
First I am "guessing" a particular solution
$$ ...
- 11
1
vote
1
answer
761
views
Portfolio duration
What is the correct way to calculate duration of a fixed income portfolio with long and short bond positions? And how to calculate portfolio YTM with long and short positions. For long only (or short ...
- 21
1
vote
0
answers
70
views
Optimal number of simulations for Monte Carlo [duplicate]
I am building a Monte Carlo simulation model for thousands of stocks. I am wondering is there a closed-form formula I can use to determine the optimal or at least minimum number of simulations need to ...
- 402
0
votes
3
answers
330
views
Does the Ito correction term in GBM result in 'real money', or is it illusory?
There are two ways to think about investment returns and randomness.
First is sort of like 'bank interest', with randomness. Suppose we invest 100 units of currency. Suppose each year there is a ...
- 435
2
votes
0
answers
70
views
Importing a zero coupon curve to RQuantLib
I am trying to use a zero coupon curve constructed elsewhere to price treasury bonds in RQuantLib.
The issue is that DiscountCurve does not take zero coupon yields as inputs, but rather swap rates. I ...
- 173
2
votes
1
answer
3k
views
Backtesting C++ Algorithms
What software is available for backtesting trading algorithms written in the C++ programming language?
I would not like to use an online service such as Quantopian or Quantconnect (they don’t offer C+...
- 1,172
6
votes
1
answer
7k
views
Which volatility as input in Black Scholes formula?
I am trying to price an option on an Index using Black Scholes formula. I estimated the daily volatility $\sigma_{day}$.
My question is should I use an annual volatility based on the business days of ...
- 73
3
votes
2
answers
747
views
Corporate Bond Yield Curve
I am an intern in a mutual fund and they have asked me to create in house yield curve for different type bonds in their portfolio
I need to know on what basis are different yield curves made. For ...
- 968
2
votes
1
answer
167
views
Optimal number of nodes for binomial lattice?
Let's suppose one is valuing a Euro call on a ZCB in a Black-Derman-Toy lattice. How many nodes/levels of discretization are optimal? Obviously too many creates computational issues and too few ...
- 981
2
votes
1
answer
474
views
How do you calculate or estimate the future gross basis of a treasury future?
Gross Basis for treasury futures = clean price - future price* conversion factor
Is there a way to estimate the gross basis, say 10 days from now, given that you know what the forward bond price is?
...
- 21