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27
votes
5answers
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 ...
20
votes
8answers
35k 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?
21
votes
4answers
6k 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 ...
26
votes
5answers
2k 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 ...
24
votes
1answer
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 ...
20
votes
1answer
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 ...
11
votes
1answer
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 ...
11
votes
5answers
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 ...
8
votes
4answers
58k 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.
11
votes
2answers
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, ...
8
votes
3answers
12k 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.
7
votes
1answer
773 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:...
17
votes
2answers
12k 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 ...
5
votes
1answer
1k views

Calculating alpha and its meaning

According to wikipedia, CAPM model is described by: $E(R_{i})=R_{f}+\beta _{{i}}(E(R_{m})-R_{f})$ And according to website such as http://investexcel.net/jensens-alpha-excel/, $\alpha = E(R_{i}) - ...
3
votes
3answers
8k 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 ...
15
votes
3answers
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: \begin{equation} 1 - \frac{dividend}{close} \end{equation} I understand why the adjusted closing ...
12
votes
7answers
2k views

What is the fair price of this option?

Without having to use Black-Scholes, how do I price this option using a basic no-arbitrage argument? Question Assume zero interest rate and a stock with current price at \$$1$ that pays no dividend. ...
3
votes
1answer
1k 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 ...
7
votes
2answers
530 views

Why $N(d_1)$ and $N(d_2)$ are different in Black & Scholes

I'm struggling to understand the meaning of $d_1$ and $d_2$ in Black & Scholes formula and why they're different from each other. As per the formula, $$C = SN(d_1) - e^{-rT}XN(d_2)$$ which ...
2
votes
1answer
932 views

Does the unconditional variance implied by a GARCH equal the sample variance?

In the MATLAB default settings for GARCH estimation they say "presample conditional variance is the sample average of the squared disturbances of the offset-adjusted response data y". Am I right in ...
8
votes
2answers
16k views

question regarding carry & roll of a bond

I have a simple (and might be a dumb) question regarding the calculation of a bond's carry. If someone doesn't take into account cost of financing (e.g. the repo rate) then the bond's approximate ...
17
votes
3answers
7k views

How to calculate future distribution of price using volatility?

I want to create a lognormal distribution of future stock prices. Using a monte carlo simulation I came up with the standard deviation as being $\sqrt{(days/252)}$ $*volatility*mean*$ $\log(mean)$. ...
7
votes
2answers
1k views

Average correlation of index/portfolio

We try to analyze the average correlation of a portfolio as it can be found here in section 2 b), the same formula which is also used by the CBOE to calculate implied correlations: $$ \rho_{av(2)} = ...
6
votes
4answers
2k views

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" ...
1
vote
1answer
2k views

Setting input parameters for Nelson Siegel Svensson model

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}...
42
votes
8answers
12k 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?
41
votes
8answers
20k 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 ...
25
votes
8answers
12k 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 ...
41
votes
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 ...
30
votes
10answers
33k 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 ...
17
votes
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?
30
votes
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?
31
votes
11answers
87k 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 ...
29
votes
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 ...
24
votes
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 ...
30
votes
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 ...
13
votes
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 ...
12
votes
1answer
777 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 ...
22
votes
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: ...
19
votes
3answers
27k 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 ...
18
votes
9answers
46k 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 ...
18
votes
13answers
75k 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 ...
23
votes
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? ...
25
votes
10answers
17k 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?
14
votes
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 ...
8
votes
1answer
7k 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 ...
21
votes
2answers
3k views

Is there a standard method for getting a continuous time series from futures data?

I would like to be able to analyse futures prices as one continuous time series, so what kinds of methods exist for combining the prices for the various delivery dates into a single time series? I am ...
8
votes
2answers
7k views

Best method for interpolating yield curve? [Multiple questions]

I'm building a spot curve for US Treasuries. My original selection of cash treasury include all the on-the-run bills, notes, bonds from 6 months to 30 years, as well as some selected off-the-run ...
6
votes
5answers
2k views

Estimate probability of limit order execution over a large time frame

I have a negligible amount of money (\$5000) that I would like to invest in a stock. I would like to buy the stock at some point in the next year, and get the lowest possible price. I would like to ...
6
votes
2answers
6k views

How to calculate US treasury total return from yield?

I'm struggling to understand the meaning of US treasury total return. What is easily available to get is yield data. Yield can be directly translated to the bond price at that time. In other words, ...

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