All Questions

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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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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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Measure the effect of a natural disaster on a stock market index

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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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 ...
66 views

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 ...
63 views

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 ...
148 views

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 ...
41 views

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? [closed]

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

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} ...
93 views

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.
39 views

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: ...
163 views

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 ...
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The difference in sign bias test in detecting the exist of asymmetric effects and the adequacy of symmetric GARCH model.

The question is that I want to know whether there is difference in the applying of sign bias test in detecting the exist of asymmetric effects and the adequacy of symmetric GARCH model. In the ...
24 views

Yield for valuation of illiquid corporate bond

I am trying to value a illiquid corporate bond issued at a discount to face value by a privately held company in India. The corporate bond is a sinkable bond (amortizing principle) with coupon rate of ...
47 views

Finding the Interest Compounded with Bank Advertising Yield

A bank is advertising 9.5% accounts that yield 9.84% annually. How often is the interest compounded. Answer is Quarterly. I've been trying to look for the formula for this; it doesnt seem to be ...
24 views

Major categories of tradable securities and the ETF's that track them?

I'm just starting to learn about quantitative finance and I'm overwhelmed by the amount of tradable securities out there. I'm seeing all these things like VXX, TLT, TMF, SPY, SPXL, HYG, VWEHX and so ...
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Why $W_{t}^3$ is not a martigale?(by Definition)

If $W_t$ be a wiener process then,how can i show that $W_{t}^{3}$ is not a martingale by definition?
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I'm having trouble with the Ho-Lee model for short rates and differentiating between how to find the values for the free parameter λ versus using the model to predict future rates. The Ho-Lee model ...
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How can I calculate $Cov\left(\int_{0}^{s}W_u\,du\,\,\,,\,\int_{0}^{t}W_v\,dv\right)$

How can I calculate? \begin{align} Cov\left(\int_{0}^{s}W_u\,du\,\,\,,\,\int_{0}^{t}W_v\,dv\right) \end{align} Thank you for your attention.
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Are there references about liquidation, transaction, market impact costs in portfolio optimization

I am looking for some references treating of what I would call liquidation cost market impact cost transaction cost(*) in the usual "portfolio optimization problem under linear constraints". Let ...
56 views

Pricing employee stock options

ESOs are typically priced using the black-scholes model, but with an additional parameter for for the employee turnover rates . An example ...