# All Questions

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### What is the best way to “fix” a covariance matrix that is not positive semi-definite?

I have a sample covariance matrix of S&P 500 security returns where the smallest k-th eigenvalues are negative and quite small (reflecting noise and some high correlations in the matrix). I am ...
7k views

### What exactly is meant by “microstructure noise”?

I see that term tossed around a lot, in articles relating to HFT, and ultra high frequency data. It says at higher frequencies, smaller intervals, microstructure noise is very dominant. What is ...
36k views

### How to check if a timeseries is stationary?

I'm using KPSS Method to check if the series is stationary, but I would also like to use another test to confirm if the series is stationary or not, what method coudl I use?
7k views

### Volatility pumping in practice

The fascinating thing about volatility pumping (or optimal growth portfolio, see e.g. here) is that here volatility is not the same as risk, rather it represents opportunity. Additionally it is a ...
6k views

### Algorithm to fit AR(1)/GARCH(1,1) model of log-returns

I am fitting numerically an AR(1)/GARCH(1,1) process to index and stock log-returns, $r_t=\log(P_t/P_{t-1})$, where $P_t$ is the price at time $t$, and thus far am not clear on where the observed log ...
3k views

### Model Validation Criteria

Let's say I have a brand new fancy model on some asset class (calibration porcedure included over a set of vanilla options) in which I truly believe I made a step forward comparing to existing ...
10k views

### Risk Neutral Probability

I read that an option prices is the expected value of the payout under the risk neutral probability. Intuitively why is the expectation taken with respect to risk neutral as opposed to the actual ...
1k views

### Pricing Treasury futures

I've recently learned that at the delivery of Treasury futures the short side can decide which of the $n$ Treasury bonds (with relevant maturities) to deliver. If the short side chooses to deliver the ...
13k views

### Probability of touching

For a vanilla option, I know that the probability of the option expiring in the money is simply the delta of the option... but how would I calculate the probability, without doing monte carlo, of the ...
15k views

### Discrete returns versus log returns of assets

There have been similar posts here already but nevertheless I find the question worth posting: why do some people claim that log returns of assets are more suitable for statistics than discrete ...
5k views

### How does one estimate the probability of the Fed increasing its benchmark rate based on Fed funds futures?

How was this 67% probability calculated from Fed funds futures? Fed funds futures show a 67 percent chance the central bank will increase its benchmark rate by year-end from virtually zero, ...
61k views

### How to compute the implied probability of default from a CDS spread?

I have two tasks: Given country's CDS spread draw implied probability of default. Given probability of default calculate CDS spread. If possible, refer to any papers.
9k views

### Carry calculation on an interest rate swap

I was hoping that I can get help on a simple yet not so straight forward topic : Looking at valuing the costs of holding an IRS in the books this would entail marketed-to-market due to price ...
13k views

### Fama-Macbeth second step confusion

I am confused on how to run the second step of the Fama Macbeth (1973) two step procedure. I have monthly stock returns and monthly Fama-French factors, for around 10,000 stocks. This creates an ...
14k views

### Bachelier model call option pricing formula

Does anybody have the Bachelier model call option pricing formula for $r > 0$? All the references I've read assume $r = 0$. I don't speak French, so I can't read Bachelier's original paper.
808 views

### Modeling Call Price w.r.t. Strike w Models that Capture Vol Smile

I am trying to model $C(K)$, the price of the call $C$ as a function of strike $K$. Because this is tied to Prob ITM - and in fact the probability density function of that particular expiration (https:...
2k views

### Question on pure carry for two bonds

If two bonds have yield of 5% and 2% and assume there's no price change, can we say that the carry is simply 5%-2% = 3% for a year. Does this take into account coupons? Equivalently, let's say the ...
13k views

### Why does the adjusted closing price take into account dividends?

I'm trying to get an intuition as to why the adjusted closing price includes a dividend adjustment: $$1 - \frac{dividend}{close}$$ I understand why the adjusted closing ...
3k views

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### Downward sloping smile in normal model

We consider an stock price $S$ following a normal model: $dS_t = \sigma dW_t$ We can write this as $\frac{dS_t}{S_t}=\frac{\sigma}{S_t}dW_t$ Hence we can see that $S$ follows a "log-normal" ...
2k views

I am trying to determine the parameters for the Nelson Siegel Svensson model and am solving a Non-Linear Optimization problem to do this. I am trying to solve: $$\min_\theta{\sum{(p_i - \hat p_i)^2}... 8answers 13k views ### Recommendations for books to understand the math in quantitative finance papers? Can anyone recommend books that explain the math used in quantitative finance academic papers? 8answers 21k views ### Time-series similarity measures Suppose I have two time series X and Y of stock prices. How do I measure the "similarity" of X and Y? (I'm being deliberately vague as I don't have a particular application, and I'm curious ... 8answers 13k views ### How are cryptography and speech recognition technology applied to forecasting financial markets? One of the answers to my previous question regarding the strategy of Renaissance Technologies, there was a reference to The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly ... 8answers 10k views ### What broker/feed/APIsetup allows for recording the most accurate data (cheaply)? I'm currently using IB's Java API and getting feeds through them. However the real-time feed is updated only every 250ms and the historical feed only every second. I'm primarily looking for ES data ... 10answers 34k views ### Are there any good tools for back testing options strategies? There are all kinds of tools for backtesting linear instruments (like stocks or stock indices). It is a completely different story when it comes to option strategies. Most of the tools used are ... 1answer 3k views ### academic papers about market making I am looking for academic articles which model the p&L of market makers. I have read the Ho-Stoll (1984) article. Is there any recent article on this subject? 11answers 90k views ### Mapping symbols between tickers, Reuters RICs and Bloomberg tickers Is there any known solution (preferably open source) to map between ticker symbols, Reuters and Bloomberg symbols. For example: Ticker: AAPL Reuters: AAPL.O (may be prefixed with RSF.ANY. dependent ... 4answers 8k views ### What is a stationary process? How do you explain what a stationary process is? In the first place, what is meant by process, and then what does the process have to be like so it can be called stationary? 8answers 4k views ### How to design a custom equity backtester? I was thinking about writing my own backtester and I realize I have to make some assumptions. So I was hoping I could post what I am planning on doing and hopefully some of you can give me some ideas ... 5answers 7k views ### Trading a synthetic replication of the VIX index One cannot directly buy and sell the VIX index. Theoretically, however, one could approximate the index by purchasing an at-the-money straddle on the SP500, then delta-hedging the straddle. Does ... 4answers 3k views ### How do I adjust a correlation matrix whose elements are generated from different market regimes? Say I want to calculate a correlation matrix for 50 stocks using 3-year historical daily data. And there are some stocks that were recently listed for one year. This is not technically challenging ... 6answers 9k views ### Earnings and valuation data sources online Are there any free/cheap sources for historical data on company earnings and valuations? I can get historical price data from Google and Yahoo, and it looks like I can get about five years of ... 1answer 813 views ### How much can be said about the Greeks without picking a model? Let C(S, K, \sigma, r, T) be the price of a call option. How much can be said about the Greeks without picking a model? Or at least without full Black-Scholes? Below, I write down everything I know ... 4answers 9k views ### Local Volatility vs. Stochastic Volatility Are there any empirical observations or practices when to prefer Local Volatility Model for pricing over Stochastic Model or vice versa? 1answer 12k views ### How to interpret the eigenmatrix from a Johansen cointegration test? I ran a Johansen cointegration test on 3 instruments, A B and C. The results that I got are: ... 9answers 48k views ### Exercising an American call option early I have seen the rationale behind why it is never optimal to exercise an American call option early, but have a question about it. If the option strike price is E=\20 and it expires at T=1yr, if ... 3answers 28k views ### Correlation between prices or returns? If you are interested in determining whether there is a correlation between the Federal Reserve Balance Sheet and PPI, would you calculate the correlation between values (prices) or period-to-period ... 13answers 77k views ### What is the difference between Option Adjusted Spread (OAS) and Z-spread? I am preparing for the CFA level 2 exam, I got confused by the concept Z-spread and OAS. When a call option is added to a bond, since it is not favorable to the bond buyer, they would require more ... 5answers 7k views ### Should Sharpe ratio be computed using log returns or relative returns? I am trying to reconcile some research with some published values of 'Sharpe ratio', and would like to know the 'standard' method for computing the same: Based on daily returns? Monthly? Weekly? ... 10answers 18k views ### Should I use an arithmetic or a geometric calculation for the Sharpe Ratio? What are the advantages/disadvantages of using the arithmetic Sharpe Ratio vs the geometric Sharpe Ratio? Is one more correct? Or is one better in certain circumstances? 3answers 5k views ### Total Return measurement paradox w/ Adjusted Close Prices Using total return calculations is critical in developing security selection models. The standard way to measure total return is to develop a series of price-adjusted data. Investopedia describes the ... 1answer 8k views ### Baye's rule for conditional expectations (Proof review) The Baye's rule for conditional expectations states$$ E^Q[X|\mathcal{F}]E^P[f|\mathcal{F}]=E^P[Xf|\mathcal{F}]  With $f=dQ/dP$ - thus being the Radon-Nikodyn derivative and $X$ being ...
What is the Delta of an at-the-money binary option with a payo out $0$ at $<100$ dollars, and payout $1$ at $>100$ dollars, as it approaches expiry? This is from a sample interview exam. I ...