0
votes
1answer
3k 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 ...
0
votes
2answers
883 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 ...
4
votes
2answers
890 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 ...
1
vote
0answers
621 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?
2
votes
1answer
794 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 ...
2
votes
1answer
7k 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: ...
0
votes
1answer
643 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 ...
7
votes
2answers
9k 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 ...
4
votes
0answers
169 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 ...
6
votes
2answers
1k 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. ...
4
votes
2answers
400 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 ...
3
votes
1answer
347 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 ...
2
votes
2answers
152 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 ...
4
votes
1answer
148 views

What is the analytic value of an asset's risk contribution, if $n=2$?

The marginal risk contribution of asset $i$ is defined by Roncalli in his paper on ERC as follows: $$\frac{\partial \sigma(x)}{\partial x_i} = \frac{1}{\sigma(x)} \left( w_i \sigma_i^2 + ...
2
votes
1answer
110 views

if market is always assumed right, what happened when LIBOR was manupulated?

Recently Monetary Authority of Singapore (MAS) raps banks in rate-rigging. This is nothing new, LIBOR was also manupulated before, by some "major" banks. however, before the censorship, did any ...
2
votes
0answers
195 views

Dual curves and short rate calibration

When I calibrate a short rate model to market swaption vols, what curve am I getting when I plug in the calibrated parameters into the analytical formulae (assuming they exist for the model I'm ...
1
vote
0answers
242 views

How to statistically compare the pricing errors of various option pricing models?

I have three different option pricing models, for which I computed the in-sample and out-of-sample pricing errors. Now I want to test the pricing performance of these three option pricing models ...
-4
votes
1answer
63 views

Does YTM represent interest? [closed]

Does a bond's Yield to Maturity represent the amount of interest one gets at maturity even though it's expressed as a percentage? I read that it is a rate of return on a bond at maturity, but what is ...
8
votes
2answers
3k views

Difference between google finance and yahoo finance?

I am wondering about the huge differences of the data provider google finance and yahoo finance. I am interested in the monthly data from adidas listed on xetra. In google: ETR:ADS and in yahoo ...
12
votes
4answers
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 ...
12
votes
2answers
813 views

Applicability of PCA to get historical volatilities to calibrate interest rates trees

My question in short is as follows: can I take main principal component of historical covariance matrix and use it as historical volatilities when fitting a binomial tree? Here's more detailed ...
2
votes
0answers
2k views

Models for simulating FX movements

My goal is to develop a model to simulate long term FX movements. (I am not sure if long term makes any difference, but if it does I am more interested in long term fx movements) These Monte Carlo ...
10
votes
1answer
564 views

Is creating constrained random portfolios a hard problem?

Creating random portfolios with weights $x_i$ can be thought of as sampling from the surface of a simplex given by $$Ex = f$$ and $$Ax \le b$$ Where $E$ and $A$ are constraint matrices for equality ...
4
votes
5answers
407 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 ...
2
votes
2answers
130 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 ...
0
votes
0answers
86 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 ...
5
votes
1answer
2k 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 ...
16
votes
9answers
6k 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 ...
4
votes
2answers
542 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 ...
1
vote
1answer
488 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 ...
3
votes
1answer
144 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 ...
6
votes
1answer
778 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 ...
1
vote
1answer
459 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 ...
10
votes
2answers
7k 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 ...
4
votes
4answers
4k 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, ...
5
votes
2answers
532 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. ...
4
votes
3answers
385 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 ...
3
votes
0answers
181 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 ...
1
vote
1answer
278 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 ...
0
votes
1answer
287 views

Required Rate of Return vs Expected Return

I faced a problem that gives the following information: market risk premium, and risk free rate is given You currently have a portfolio of amount of x, beta b1. Now there is a new investment ...
8
votes
3answers
634 views

Is the price of European put option monotone in volatility if we replace BM in Black-Scholes with a general Levy process?

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 ...
4
votes
1answer
389 views

Volatility Return Distribution/Garch Modeling

For simplicity sake, if stock returns are normally distrusted, would that imply that second moment, variance/volatility, is chi-squared distrusted? If so wouldn't that imply the statistics(employed to ...
1
vote
1answer
317 views

Initial margin requirement as percentage, not dollar value

Problem from Finan, FM/2 On 12-30-1998, you decided to bet on the January effect. ON that day, you bought 400 shares of Microsoft on margin at the price of 139 per share. The initial margin ...
0
votes
2answers
286 views

Change option B&S pricing

Consider a market composed by two stocks whose prices $X$ and $Y$ are given by B&S diffusion $$dX_t= \mu X_t dt+ \sigma X_tdW_t$$ $$dY_t= \mu Y_t dt+ \sigma Y_tdB_t$$ Supposing the market is ...
2
votes
1answer
738 views

Continuous returns for negative roll-adjusted futures data

I've generated roll adjusted notional futures data by adding a roll adjustment to the settlement price then multiplying by contract multiplier through time. For example, for crude oil CL, on 15 March ...
2
votes
1answer
78 views

Creditworthiness indicator for copula one-factor model

In this paper in equation 15 on page 261 dealing with one factor copula model, one is using creditworthiness indicator as one of a variables. It is defined as \begin{equation} Y_c = \sqrt{\rho_c} Z ...
5
votes
1answer
300 views

Futures Contract Fair Values Accuracy

I have recently been tasked to work on fair value derivation for futures on equity indices (non-US). I know that the FVD function in Bloomberg can have a huge discrepancy from markets: where cheap is ...
2
votes
2answers
280 views

Block Bootstrapping Relative Returns

I want to run a block bootstrap on the relative returns, but I'm not sure if subtracting the mean is important. A bootstrap sequence is a synthetic sequence generated using the original sequence. If ...
0
votes
1answer
203 views

Floor and Cap problem

So I have a problem from Marcel Finan's "A Basic Course in the Theory of Interest and Derivative Markets." We are going over floors and caps, covered puts and covered calls. Consider the following ...
5
votes
4answers
1k views

Usage of Bollinger bands

I looked through several sources on Bollinger bands and I do not see clear recipes of their usage. Wikipedia says "The use of Bollinger Bands varies widely among traders. " QSE discussion seems also ...

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