# All Questions

147 views

### Covariance estimation

Shrinkage was much en-vogue before RMT took everybody's attention, however the latter also showed its limits. A plethora of other estimators has been presented, but I could not yet spot a golden ...
1k views

### Beta vs. Implied Volatility statistical arbitrage using options

Let two underlyings, $S_{1}$ and $S_{2}$, are correlated and $\beta$ is the slope of their returns linear regression, that is, it says how much $S_{1}$ co-variates with $S_{2}$ variance. For ...
89 views

### Simple way to get the crossing probabilities of a moving barrier

Hello Quant Finance StackExchange, Is there a simple way to find the crossing probabilities of a moving barrier, namely a barrier written in the form $U(t)=\alpha_1t^2 + \beta_1t + \gamma_1$ and ...
109 views

### Distribution of hitting time of the integrated CIR process

If an increasing process $X_t$ has a known Laplace transform $\mathbb{E} e^{-s X_t} = m_t(s)$, define its hitting time $\tau$ to some level $B$ to be $$\tau = \inf\{ u > 0 : X_u \geq B \}.$$ Can ...
231 views

### Simple EOD computations for tick data

As part of End-Of-Day calculations once a particular market/exchange has closed for all the tickers traded on that market one may typically compute the following properties: OHLC Bid/Ask Price ...
302 views

231 views

### How is the Sharpe Ratio presented in fund profiles usually calculated?

To compare my stock portfolio generator with managed funds performance, I want to calculate the Sharpe Ratio of my historic portfolios with the numbers found on the fund company web sites or in ...
420 views

### Stock prices using a monte carlo simulation with a normal inverse gauss distribution

I am supposed to model daily stock prices with a normal inverse gauss distribution in excel. I feel like I am misssing some basics because I cant transform the information from the academic papers ...
418 views

### expected value of the discounted payoff

I don't understand the following statement: The price of a contingent claim is the expected value of the discounted payoff value under the risk neutral probability measure Q deﬁned in complete markets ...
377 views

### Is duration really inversely related to the maturity time length of a bond?

It is always said that longer bonds are more sensitive to interest rates. Intuitively this makes perfect sense, since longer bonds have a larger portion of its cash flow being subjected to stronger ...
284 views

### Implied volatility and greeks for american option with discrete dividends

What methods are available to calculate IV and greeks for an american option with discrete dividends, and how do they compare? Should I use Roll-Geske-Whaley and solve for a given option price?
285 views

### Formula for variance of European call/put in Black Scholes

I have a quite basic question, but I can't find a reference with it. Recall that we can use the Black-Scholes formula to price a European call or put for a market consisting when: the underlying ...
2k views

### Implied interest rate from FX swap

This is not homework. I am trying to calculate the implied interest rate of one currency (C2) using an FX swap and the interest rate of another currency (C1 - base). I have the following: Spot: ...
291 views

### GJR-GARCH modeling in stata

I am wanting to run a GJR-Garch model in stata and I am having problems identifying what command I need to put into the system. When using the commands I receive two different ways to do so and I am ...
294 views

### Zero Curve Calculation for AUD, CAD (post LIBOR scandal)

In the end of May 2013 British Bankers Association (BBA) stopped publishing LIBOR rates for Australian and Canadian dollars in a light of recent scandals. LIBOR rates were essential for creating zero ...
2k views

### How to numerically obtain delta?

The delta in option pricing, also called the hedge ratio, is expressed as the sensitivity of the option price to the underlying price change. The analytical solution for the most common option ...
122 views

### ERP and FF 3-factor model

In a more conservative estimate than a simple historical average, Fama & French estimate (US) equity risk premium at 3-4% (e.g., Equity Risk Premium, JF, 2002). This suggests that in an APT-like ...
656 views

### Principle Component Analysis vs. Cholesky Decomposition for MonteCarlo

Let's assume we have a portfolio containing large number (~500) of risk factors. We want to simulate the portfolio dynamics. PCA based simulation would be faster as we can reduce the dimensionality. ...
273 views

### Black-Scholes fastest computation method

What is the fastest way to numerically compute Black-Scholes-Merton option prices? I'm trying to find fastest and still precise method. Currently I'm using numerical approximation of Normal cdf with ...
196 views

### Magnitude of Transaction Cost for Institutional Investors

For my thesis, I'm writing about robust portfolio allocation. I have the idea to include a measure of transaction cost, since ignoring them seems too simplifying for a real-world problem. Comparing a ...
73 views

### Can the equity premium puzzle be explained by volatility-induced financial growth?

Citing the paper Volatility-induced ﬁnancial growth (2007) by Dempster et al.: when asset returns are stationary ergodic, their volatility, together with any ﬁxed-mix trading strategy, generates a ...
115 views

### Pricing Assets in the S&P Dynamic Asset Exchange

I am attempting to recreate the S&P Dynamic Asset Exchange using the methodology outlined in this paper. I am struggling to 'normalize' the prices of the assets properly. On page 6 of the ...
130 views

358 views

### Is there a name for, or any research on, a system where you try to predict future price by finding a similar price history in the past?

Allow me to explain. You look back from some period to the present. Say a week ago to now, using a per-minute view. You then crawl through your database of past price data, and you try to find a ...
109 views

### Approximating a function with trignometric polynomials

Let’s say I have a function, which is a time series of data points, I am trying to find a polynomial of fixed sine's and cosines that bests approximate the data points. I know Chebyshev Approximation ...
59 views

### % Return on backtest with variable positions and notional amounts

I have a 14 year backtest for a systematic strategy that uses a static notional per each position. On any given day I could have multiple positions long and short and notional long and short. How do ...
629 views

### How to calculate the conditional variance of a time series?

I am reading a paper where the term conditional variance is mentioned, but I am not really sure what is meant by this and how this can be calculated: Fig. 2 shows the conditional variances of the ...
2k views

### Why Drifts are not in the Black Scholes Formula

This question has puzzled me for a while. We all know geometric brownian motions have drifts $\mu$: $dS / S = \mu dt + \sigma dW$ and different stocks have different drifts of $\mu$. Why would ...
233 views

### Heston - How important are the initial guess in calibration and if it is very important, what would be a good way to get initial guess?

So I have been trying to implement a simple Heston calibration using crude MC with 10k scenarios and 1000 time steps and the best I could get is 3x of the observed implied volatility. I suspect it ...
252 views

### Heston MC Simulations - Speed up in Matlab

At the moment I am running a Quad Core Xeon PC with 12GB of RAM doing crude MC with 10k scenarios and 1000 time steps. And using fminsearch for calibration, and it takes about half an hour to an hour ...
128 views

### At what volume would you move the price at the opening auction?

At many exchanges the opening price is set using an auction which takes place pre-opening (see here for example). During the auction you are allowed to place orders according to certain rules (you ...
451 views

### Multi Fractals Models

From a quant point of view, how would you explain Multi Fractals Models in few words ? I have the level to take these courses, but won't be able to do it next year, so I want to know what I am ...
209 views

### why banks shall keep short term gap position low?

I'm reading "Insights for Bank Directors" (http://www.stlouisfed.org/col/director/reference_view.htm), a good introduction to commercial banks, based on a virtual bank "Insight". It talks about Gap ...
2k 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 ...
2k views

### How to calculate the implied volatility using the binomial options pricing model

I want to calculate IV for american options with dividends. So far I have found algorithms to calculate the option price given a volatility. Please can you point me to paper or implementation (R, ...
369 views

### Malliavin Calculus

From a quant point of view, how would you explain Malliavin calculus in few words ? I have the level to take these courses, but won't be able to do it next year, so I want to know what I am missing. ...
280 views

### Are minimum-risk and minimum-variance portfolios equivalent?

When reading a paper by DeMiguel and Nogales (2007; http://papers.ssrn.com/sol3/papers.cfm?abstract_id=911596), I came across the following formulation: Comparing the proposed minimum-risk ...
136 views

### Black-Scholes PDE to heat equation, nonconstant coefficients

Can someone provide me with details or a reference on how to transform the Black-Scholes PDE with nonconstant coefficients (i.e. $r=r\left(S,t\right)$, $\sigma=\sigma\left(S,t\right)$) to the heat ...
242 views

### Volatility Estimation

Let say I ran two strategies and got its weights at each rebalance and equity curves. I would like to combine these systems to get the performance if I were to trade them concurrently from a portfolio ...
Under the Black-Scholes model, we have the European put option is $\mathbb{E} [e^{-rt}(K-S_t)]$, where we take $\log(S_t)=X_t$ and $dX_t= \sigma dW_t - \dfrac{1}{2}\sigma^2 dt + rdt$. Here the option ...