# All Questions

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### Problem with Naive Bootstrapping (US Government Bonds)

I am using the formula here to determine the discount factor function and eventually the zero-coupon yields for the yield curve. I get the data for the Coupons, Face Values and Closing Prices from ...
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### Geometric Brownian Motion in a general interval $[t_1,t_2]$

I know that the Geomtric Brownian Motion, with the expresion $dX_t = v X_t dt + \sigma X_t dW_t$ has the next solution $$X_t = X_0 e^{\sigma W_t+ (v-\frac{\sigma ^2}{2})t}$$ on the interval [0,t]. ...
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### Time discretisations, FDM vs FEM

I am interested in adaptive mesh methods for numerical solution of PDEs with applications to finance. As part of a school project, I have been pricing vanilla European call and put options using 2D ...
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### Examples using PyOpenCL for backtesting trading strategies?

Anyone used PyOpenCL for backtesting trading strategies? Any qualitative/quantitative benchmarks of implementations in Python, Cython, PyOpenCl? Is it worth it spending time implementing extra Lines ...
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### What is the machine learning language of choice in this industry for unsupervised learning

I was wondering from those with commercial machine learning financial experience, what the machine learning language of choice in this industry in the most general sense. Also, what would be the ...
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### Closed form solution of PDE of Option Price

Let $V=V(S_t,t)$ be the option price and \begin{align} V_t+\mu\,S\,V_S+\frac{1}{2}\sigma^2\,S^2\,V_{SS}=0\\ V(S_T,T)=\ln (S_T)^{2}. \end{align} My question: How can I obtain a closed form solution of ...
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### What's the best proffesional forex market data feed out there?

I trade forex latency arbs and find it harder and harder to get a reliable New York market data feed to server my purpose. Reuters and EBS send timesliced updates every 500ms for 5k/month which is ...
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### What is the best data structure/implementation for representing a time series in C#?

I'm looking for a tick by tick high performance container. So far I've been using List where Tick is a simple struct with a DateTime and double field. I'm using Linq for date lookups but it's ...
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### Is probability implied by binary FX options risk neutral or real world?

If we consider binary FX options in the market and estimate the market implied probabilities of certain FX rates occurring, would these resulting probabilities be risk neutral or real world? I hear ...
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### What are the different algorithmic trading strategies available for an individual trader [on hold]

I am new to algorithmic trading (automatic or semi-automatic) and i am really curious about its working. To understand more about algo trading I am reading the book An introduction to algorithmic ...
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### Distribution of stochastic integral

Suppose that $f(t)$ is a deterministic square integrable function. I want to show $$\int_{0}^{t}f(\tau)dW_{\tau}\sim N(0,\int_{0}^{t}|f(\tau)|^{2}d\tau)$$. I want to know if the following approach is ...
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### Do futures follow physical or risk-neutral distributions

I've spent a while looking for an answer to this question and while I feel it is a simple question I have not found an answer. I know prices of option contracts follow an implied, risk-neutral ...
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### Proving $\mathbb{E}(g(X)) = \int_{\mathbb{R}} g(x) f(x) dx$

Let $X$ be a random variable on a probability space $(\Omega, \mathcal{F}, P)$ and let $g$ be a Borel-measurable function on $\mathbb{R}$. In Shreve II (p 28) he proves, using the standard machine, ...
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### According to Lo and MacKinlay (1990), momentum profits can be divided in 3 parts. What do they represent exactly?

At first, Lo and MacKinlay (When are Contrarian Profits Due to Stock Market Overreaction?, 1990) didn't do it for momentum precisely. However,Kyung-In Park and Dongcheol Kim (Sources of Momentum ...
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### Boundary Condition for Convertible Bond under Two-factor Model Interest Rate

I want to find Boundary conditions for Convertible Bond under Two-factor Model Interest Rate.The portfolio contains stock where stochastic differential equation for the stock price is \begin{align} ...
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### Fractals indicator (Bill Williams) R Quantstrat

Hi has anyone seen or know how to create an indicator for fractals in quantstrat? fractals explained http://forex-indicators.net/bill-williams/fractals example code (only interested in type 1 ...
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### Total market cap in country, and average p/e per country and continent(europe) [on hold]

I want to invest my monthly saving on index fund. However, I am not sure to pick which country index fund that I want to invest. I am afraid i am investing in an index fund that is so overvalued goes ...
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### Can you tell me what this RBloomberg formula means?

I've been asked to re-create a spreadsheet that used RBloomberg using a different data source. But I'm having trouble figuring out exactly what one of the spreadsheet's formulas does. Can anyone tell ...
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### Range options in BS

I know how barrier options are priced in Black-Scholes scheme. I'm wondering if an analytical formula exists also for range (corridor) digital options i.e. options paying only if the price remains ...
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### Garch model newbie. help needed with variables

I am very new to using stata and very new to using Garch models. I am currently doing my final dissertation for my MSc in Finance studies and regarding my topic I understood that i had to use garch to ...
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### how to create folder and csv files for each row in each sheet (VBA) [on hold]

I have an excel workbook. In this workbook,I have 3 worksheets, named by"First","second" and "third". Each sheet has 4 columns such as Date X1,X2,Oneletter.I'm trying to run a VBA program.But I have ...
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### Calculating rate of renewal for Certificate of Deposit

I am trying to calculate the rate of renewal for a large stock of Certificates of Deposit. These contracts are given on a fixed amount of time and some of them get renewed every time they reach ...
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### Calculate the return of an equally weighted portfolio? [on hold]

This is my initial positionn. I have 40 stocks and their corresponding arithmetic return for the following month. Now I have to build an equally- weighted portfolio of these stocks and calculate its ...
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### volatility factor

I am trying to add a volatility factor to Fama-French factor model. Does anybody know of a source where I can get data for "volatility mimicking factor" or suggest a simple methodology for ...
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### Stochastic Calculus Rescale Exercise

I have the following system of SDE's $dA_t = \kappa_A(\bar{A}-A_t)dt + \sigma_A \sqrt{B_t}dW^A_t \\ dB_t = \kappa_B(\bar{B} - B_t)dt + \sigma_B \sqrt{B_t}dW^B_t$ If $\sigma_B > \sigma_A$ I ...
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### good R package for vectorized option pricing

I am using for now the package fOptions but it doesn't allow for vectorized computation of black76 prices and delta. Which package can be used to do that? As noted ...
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### Comparing a money-weighted return of my own portfolio with a benchmark ETF/other portfolio that is subject to the same cashflows

I am able to calculate the money-weighted return (XIRR equivalent in Excel) of my portfolio. Whilst I can compare this with ‘headline’ returns of ETF’s, Mutual Funds etc, I want to isolate the timing ...
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### Speed of mean reversion of an interest rate model

I would like to have a bit more of intuition about the concept of "speed of mean reversion" for an interest rate model, e.g. Vasicek or CIR. In particular, is a negative speed of mean reversion ...
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### Long-Term Government Bond Yields

On the Federal Reserve of St. Louis FRED website we can find the 10-year government bond yields: https://research.stlouisfed.org/fred2/data/IRLTLT01USM156N.txt. I chose monthly frequency and percent ...
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### What is type of Operating income to total assets ratio?

What is type of Operating income to total assets ratio? Leverage, Profitability, Asset composition or Liquidity? and why?
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### Reflection Principle

Let $(\Omega,\mathcal{F},P)$ be a probability space and $\{W_t ∶ t ≥ 0\}$ be a standard Wiener process. By setting $\tau$ as a stopping time and defining \begin{align} ...
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### List of momentum indicators

Is there a definite list of momentum indicators? A quick search on Google did not yield much, so I thought to ask this here.
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### Why risk-free interest is needed for Margrabe's Formula?

The source code for Margarble's formula in QuantLib is here. The implementation requires a forward price be computed: ...
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### Ito's formula for Jump process

Let $\{N_t\,|\,0\leq t\leq T\}$ be a Poisson process with intensity $\lambda>0$ defined on the probability space $(\Omega,\mathcal{F}_t,P)$ with respect to the filtration $\mathcal{F}_t$ and ...