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47
votes
5answers
3k views

What are the key risks to the quantitative strategy development process?

Prompted in part by this question on data snooping, I would be interested to know: What are the key risks that should be considered when developing a quantitative strategy based on: (a) historical ...
25
votes
2answers
52k views

What is the Swap Curve?

What is the so-called Swap Curve, and how does it relate to the Zero Curve (or spot yield curve)? Does it only refer to a curve of swap rates versus maturities found in the market? Or is it a swap ...
46
votes
4answers
18k views

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 ...
32
votes
5answers
5k views

Why aren't econometric models used more in Quant Finance?

There is a big body of literature on econometric models like ARIMA, ARIMAX or VAR. Yet to the best of my knowledge practically nobody is making use of that in Quantitative Finance. Yes, there is a ...
24
votes
10answers
54k views

Strategy of Renaissance Technologies Medallion fund: Holy Grail or next Madoff?

Renaissance Technologies Medallion fund is one of the most successful hedge funds - ever! Yet it is very secretive. Do you have information on the strategy used that is not yet mentioned in the ...
29
votes
5answers
8k 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 ...
19
votes
8answers
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?
21
votes
4answers
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 ...
25
votes
1answer
13k 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: ...
24
votes
1answer
7k 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 ...
14
votes
6answers
12k 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 ...
27
votes
6answers
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 ...
11
votes
1answer
2k 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 ...
12
votes
3answers
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, ...
18
votes
3answers
10k views

What causes the call and put volatility surface to differ?

I currently have a local volatility model that uses the standard Black Scholes assumptions. When calculating the volatility surface, what causes the difference between the call volatility surface, ...
18
votes
2answers
17k 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 ...
4
votes
4answers
11k 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 ...
9
votes
3answers
25k 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
946 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:...
4
votes
1answer
3k views

Calendar Arbitrage in a Vol Surface

I am trying to determine the condition such that my implied vol surface doesn't have calendar arbitrage. I have done research and found that one such condition is that total variance should increase ...
3
votes
1answer
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 ...
8
votes
2answers
3k views

Arbitrage Free Volatility Smile

When ATM implied volatility is higher than OTM put and call I believe that the volatility smile is no longer arbitrage free? Why is that? On the other hand, when ATM implied volatility is lower than ...
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
3k 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. ...
11
votes
2answers
4k views

How to use the stock as a numeraire to price a derivative with payoff of the form $(S_T f(S_T))^+$?

I have $\frac{dS_t}{S_t} = rdt + \sigma dW_t$ as usual under the money-market numéraire and I need to price options with payoffs $$(S_T f(S_T))^+$$ How do I express the stock dynamics using the ...
2
votes
1answer
1k 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 ...
11
votes
3answers
21k 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 ...
8
votes
2answers
665 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 ...
3
votes
3answers
7k views

Calculate strike from Black Scholes delta

I have a list of deltas and their corresponding volatilities in an FX market but I want to go from delta to strike price. In this Question similar problem is being discussed How can I calculate the ...
3
votes
3answers
229 views

How can we estimate new stock price after a large purchase?

Suppose someone buys $4bn of a particular stock over the period of a few weeks. Depending on how much that stock is being traded, you would expect that the price goes up in a visible way compared to ...
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
2k 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
3k 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
14k 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?
46
votes
8answers
24k 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 ...
26
votes
8answers
14k 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 ...
42
votes
8answers
11k 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 ...
35
votes
10answers
45k 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 ...
18
votes
1answer
4k 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?
32
votes
5answers
5k views

Random matrix theory (RMT) in finance

The new kid on the block in finance seems to be random matrix theory. Although RMT as a theory is not so new (about 50 years) and was first used in quantum mechanics it being used in finance is a ...
35
votes
11answers
102k 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 ...
28
votes
4answers
9k 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?
24
votes
11answers
53k 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 ...
14
votes
1answer
967 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 ...
28
votes
8answers
5k 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 ...
34
votes
5answers
8k 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 ...
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 ...
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 ...
27
votes
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?

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