11
votes
0answers
2k 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 ...
10
votes
3answers
5k views

What is Ito's lemma used for in quantitative finance?

Further to my question asked here: prior post and which left some points unanswered, I have reformulated the question as follows: What is Ito's lemma used for in quantitative finance? and when is it ...
10
votes
3answers
1k views

Hedging stocks with VIX futures

It seems that VIX futures could be a great hedge for a long-only stock portfolio since they rise when stocks fall. But how many VIX futures should I buy to hedge my portfolio, and which futures ...
10
votes
5answers
2k views

Is it possible to use a series of option prices to predict the most likely path of an asset?

I've always wondered about this. If you have a series of options, with the expires spaced let's say one week between them, and you search for each expiration date the option with the smallest ...
10
votes
5answers
1k views

Monte carlo methods for vanilla european options and Ito's lemma.

I understand that by applying Ito's lemma to the following SDE $$dX=\mu\,X\,dt+\sigma\,X\,dW$$ one obtains a solution to the above SDE which is as follows: $${X}\left( t\right) =\mathrm{X}\left( ...
10
votes
3answers
2k views

Hidden Markov Model & Its Application

I have started reading about HMM it gives an intuitive idea about what HMM is all about. I am looking out for example where its applied to Equity model using R / Excel. The material which I read so ...
10
votes
2answers
748 views

Why is the ratio of Hi-Low range to Open-Close range close to 2?

I tried it in several symbols and timeframes with the same result: $$\frac {mean(HIGH-LOW)}{mean(|CLOSE-OPEN|)}$$ ...
10
votes
5answers
5k views

Using linear regression on (lagged) returns of one stock to predict returns of another

Suppose I want to build a linear regression to see if returns of one stock can predict returns of another. For example, let's say I want to see if the VIX return on day X is predictive of the S&P ...
10
votes
3answers
1k views

What is a Quant

In the interest of having "canonical questions" on this site ... What is a Quant?
10
votes
1answer
2k views

Why is the first principal component a proxy for the market portfolio, and what other proxies exist?

Let's say that I have a universe of stocks from a certain sector. I want to compute the market portfolio of this sector. Beta is the covariance between each stock and the market. But how do you ...
10
votes
4answers
750 views

What are the risk factors in analysing strategies?

What do you think of strategies displayed on timelyportfolio.blogspot.com? I really like the fact that there is some code to reproduce the strategies, but they seem very elementary because he does ...
10
votes
5answers
3k views

Best way to store hourly/daily options data for research purposes

There are quite a few discussions here about storage, but I can't find quite what I'm looking for. I'm in need to design a database to store (mostly) option data (strikes, premiums bid / ask, etc.). ...
10
votes
3answers
17k views

Calculating log returns using R

I am trying to calculate the log returns of a dataset in R using the usual log differencing method. However, the calculated data is simply a vector of zeroes. I can't see what I'm doing wrong. Here ...
10
votes
3answers
488 views

How to group timeseries showing similar curve

I am trying to classify similar looking curves of a timeseries and was wondering what is the best algorithm to research. Reading R, it looks like k-means clustering could be applied - but I don't know ...
10
votes
2answers
3k views

How can I compare distributions using only mean and standard deviation?

I only have means and standard deviations of samples of two random variables. What technique can I use to determine how similar the distributions these describe are? Assume that the values are built ...
10
votes
3answers
2k views

Order submission strategies of a rational market maker?

Consider a market maker that has decided to try to make a round-trip trade in stock A in order to capture the bid-ask spread. Assume furthermore that he has no current inventory in the stock A. To ...
10
votes
7answers
790 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. ...
10
votes
1answer
1k 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?
10
votes
7answers
989 views

When hiring a quant, how can I protect my IP?

I am a one-man operation, and would like to hire a quant for around 4 weeks or work. I am worried that the person I hire might copy my data or the indicators that I have him work on. What have ...
10
votes
3answers
873 views

better estimator of volatility for small samples

One commonly used sample estimator of volatility is the standard deviation of the log returns. It is indeed a very good estimator (unbiased, ...) when the sample is large. But I don't like it for ...
10
votes
3answers
2k views

How to estimate real-world probabilities

In the world of finance, Risk-neutral pricing allow us to estimate the fair value of derivatives using the risk free rate as the expected return of the underlyings. However, the behavior of ...
10
votes
2answers
2k views

Why a self-financing replicating portfolio should always exist?

According to my understanding the derivation of the Black-Scholes PDE is based on the assumption that the price of the option should change in time in such a way that it should be possible to ...
10
votes
3answers
3k views

How do I calculate the skewness of a portfolio of assets?

I need to calculate the skewness of a portfolio consisting of 6 assets. I know that for that I would need the co-skewness matrix between the assets. Does anybody know the formula for co-skewness or ...
10
votes
3answers
809 views

Deterministic interpretation of stochastic differential equation

In Paul Wilmott on Quantitative Finance Sec. Ed. in vol. 3 on p. 784 and p. 809 the following stochastic differential equation: $$dS=\mu\ S\ dt\ +\sigma \ S\ dX$$ is approximated in discrete time by ...
10
votes
5answers
12k views

What open source trading platform are available

I would like to compile a list of open source trading platforms. Something that would give an overview and comparison of different architectures and approaches.
10
votes
4answers
7k views

Rationale for OIS discounting for collateralized derivatives?

Can someone explain to me the rationale for why the market may be moving towards OIS discounting for fully collateralized derivatives?
10
votes
2answers
746 views

Reference request: Survey article on GPU in Finance

I would like to get and idea of how people use GPUs in finance. I can find some specific papers or books on the subject. GPUs in binomial model, finite difference, monte carlo,... But I couldn't ...
10
votes
1answer
3k views

Skewness and Kurtosis under aggregation

Returns possess non-zero skewness and excess kurtosis. If these assets are temporally aggregated both will disappear due to the law of large numbers. To be exact, if we assume IID returns skewness ...
10
votes
5answers
911 views

Is it ever possible that---because of illiquidity---exercising an out-of-the-money option is better than directly buying the stock?

Is there a case, where due to illiquidity, exercising out-of-the-money options could be better than directly buying the stock? When a stock is too illiquid, there are some costs because of this ...
10
votes
2answers
1k views

What is the relationship between risk aversion and preference for skewness and kurtosis in portfolio optimization?

Is there any relationship between the risk aversion coefficient in an individual's utility function (commonly used in portfolio optimization) and the preference for higher moments such as skewness and ...
10
votes
3answers
2k views

How to simulate slippage

I'm backtesting a trading strategy, using free OHLC data from yahoo or google. I'm simulating friction by lopping a flat percentage (say 0.5%) off my returns for each day that I make a trade. Whats ...
10
votes
2answers
670 views

When is the LIBOR market model Markovian?

The question is inspired by a short passage on the LMM in Mark Joshi's book. The LMM cannot be truly Markovian in the underlying Brownian motions due to the presence of state-dependent drifts. ...
10
votes
3answers
1k views

Literature on generating synthetic time series for testing

I have some market data (daily time series) for bond prices and CDS indices and I would like to generate synthetic versions of these which are statistically "similar" for testing trading strategies. ...
10
votes
5answers
1k views

How to conduct Monte Carlo simulations to test validity of Black Scholes for a specific option?

In reference to the original Black Scholes model, what approach is best to test the model in a rigorous way? Is there a standard approach that can accomplish this in a reasonable amount of time? ...
10
votes
2answers
742 views

Missing step in stock price movement equations

Assuming a naive stochastic process for modelling movements in stock prices we have: $dS = \mu S dt + \sigma S \sqrt{dt}$ where S = Stock Price, t = time, mu is a drift constant and sigma is a ...
10
votes
1answer
4k views

Estimation of Geometric Brownian Motion drift

One can find many papers about estimators of the historical volatility of a geometric Brownian motion (GBM). I'm interested in the estimation of the drift of such a process. Any link on this topic ...
10
votes
2answers
766 views

How to compute performance attribution between daily rebalanced strategies?

I have a daily rebalanced portfolio of several strategies. After one month, I now want to attribute the performance to the different strategies. There are several ways to do it. For instance one ...
10
votes
3answers
843 views

How do I eliminate developed currency funding cross rate risk in an EMFX position?

Back in the "old days" (ie 5-10 years ago) when we wanted to be long or short an emerging currency (say the ZAR, BRL, or TRY) we simply did everything against the pre-eminent currency of the day, the ...
10
votes
3answers
6k views

What are the main limitations of Black Scholes?

Pls explain and discuss these limitations, and explain which models can I use to overcome these limitations. Alternatively, provide examples of how to modify the original Black Scholes to overcome ...
10
votes
2answers
6k views

Why using 3 months forward to hedge fx risk on a fund of funds portfolio?

In my previous job, a fund of funds, they used 3 months forward FX contracts (renewed every 3 months) to protect their portfolio against currency risk. If I do understand why forwards are useful for ...
10
votes
3answers
872 views

What is the expected return I should use for the momentum strategy in MV optimization framework?

As all research on the momentum strategies are focused on the indicator, i.e. the entry point, there seems not much discussion on its expected return? Though there are some discussions on the exit ...
10
votes
3answers
2k views

What is the ideal ratio of in-sample length to out-of-sample length?

Suppose you are running a portfolio of quantitative strategies and that you develop a new potential strategy to be added to the mix. Assume for simplicity that the new strategy is independent of the ...
10
votes
1answer
2k views

Easiest and most accessible derivation of Black-Scholes formula

I am preparing a QuantFinance lecture and I am looking for the easiest and most accessible derivation of the Black-Scholes formula (NB: the actual formula, not the differential equation). My favorite ...
10
votes
2answers
2k views

Drawbacks & Caveats of using (N)Esper for ESP/CEP in trading systems?

Esper and its .NET port NEsper are components that enable Complex Event Processing (CEP) and Event Stream Processing (ESP) engines. They are especially suitable for trading applications. They can, ...
10
votes
2answers
1k views

What are some computational bottlenecks that quants face? [closed]

What are the current computational (non-network) bottlenecks now in a quant's workflow? What computational tasks would be revolutionary with a 10-100x improvement in performance using general purpose ...
10
votes
3answers
366 views

How to account for market movement when some exchanges are closed?

Daily data, such as open and close prices, is often available for much longer periods than high-frequency data. However, whenever backtesting any strategy that examines instruments traded in different ...
10
votes
1answer
4k views

How to estimate probability of default from bond prices?

How do you use bond prices/yields to infer probabilities of default? I would think of it as follows: Create a relationship between default free (e.g., Germany) and defaultable (e.g., Greece) bond ...
10
votes
2answers
396 views

How to “uncluster” a set of financial data?

I am attempting to evaluate and compare the profit factor of different "test runs" of a FOREX trading strategy. My problem is that, despite an average time between orders of 2hr+, some of these runs ...
10
votes
1answer
1k views

Intuitive explanation of the Hansen-Jagannathan bound

The Hansen-Jagannathan bound states that the maximum Sharpe ratio of a portfolio can't exceed the ratio of the standard deviation of a stochastic discount factor to its mean. I more or less understand ...
10
votes
2answers
2k views

What are some examples of Compound Poisson processes in insurance?

I'm writing the Bachelor thesis but I need some information. I need to find some practical examples and applications of the Compound Poisson Process in insurance. Does anyone have any good examples?

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