4
votes
0answers
194 views

Taking into account the correlation in Barrier options on a Basket

In a Barrier option (where the contract cancels when the underlying hits the barrier) I succesfully found the way to compute the probability of a single underlying touching the barrier (with constant ...
4
votes
0answers
481 views

Algorithms for predicting a couple points in the future

I'm familiar with supervised learning algorithms like regression and neural networks which look at a bunch of input points and learn a function which outputs a value (the value varying depending on ...
4
votes
0answers
599 views

Hasbrouck's information share

Given a cointegrated set of price series, I am trying to compute the Hasbrouck's information share, as described in page 12-13 of this article. page 7-8 of this article I have the vector error ...
4
votes
0answers
162 views

Use of Local Times in Option Pricing

I know two applications of local time in option pricing theory. First, it allows a derivation of Dupire's formula on local volatility in a neat way (i.e. without resorting to differential operator ...
3
votes
0answers
52 views

What are recent important papers on credit portfolio risk modeling?

I'm interested in papers which consider mathematical models of risks of different portfolios of retail credit. This is not my area of research, so I may be misusing some terms. The idea is simple: I ...
3
votes
0answers
76 views

Constructing Volatility Smile from American Options

My question is about best practices for reconstructing volatility smiles for a fixed tenor from American option data. For simplicity/liquidity, I am currently considering options on SPY. I am ...
3
votes
0answers
42 views

Dixit & Pindyck (1993) Chapter 4, equation 13

Starting with the Bellman equation for the optimal stopping problem: $$F(x,t)=max\{\Omega(x,t), \pi(x,t)+(1+\rho dt)^{-1} E[F(x+dx, t+dt)|x]\}$$ In the continuation region where the second term is the ...
3
votes
0answers
30 views

Basket Default Swap (BDS)

I would like to understand better the $n^{th}$ to default pair spreads of a basket default swap containing $m>n$ entities. For example, consider 2 single name CDS's with same spread and same ...
3
votes
0answers
136 views

Portfolio Optimization with Monte Carlo Simulation - How to do it with Excel?

If I have three asset classes and their historical weekly returns for five years, how can I construct a minimum variance portfolio and an efficient frontier plot with Excel? To do that do I have to ...
3
votes
0answers
90 views

How do I calculate the probability of a stock being above or below a value using the Heston model?

How can I use the Heston Model to calculate the probability of a stock being above or below a certain value on a given date in the future?
3
votes
0answers
55 views

Estimating Number of “Day Trades” from Total Volume of Commodity Futures Contract

Looking at futures data I am trying to calculate/estimate the number of "day trades", i.e. positions that were initiated and closed during the same day, as distinct from those positions that were ...
3
votes
0answers
71 views

Filtering out AR(1) effects before using stochastic volatility model

I wonder if I first filter out AR(1) (autoregressive model with lag 1) effects from univariate time series and then fit stochastic volatility model does above procedure introduce any bias at first or ...
3
votes
0answers
47 views

I want to Derive $P(t)=P(t,T_{n})+\sum_{i=1}^{n}[P(t,T_{i-1})-P(t,T_{i})]$

Derive the pricing formula $$P(t)=P(t,T_{n})+\sum_{i=1}^{n}[P(t,T_{i-1})-P(t,T_{i})]$$directly, by constructing a self-financing portfolio which replicates the cash flow of the floating rate bond. ...
3
votes
0answers
96 views

ISLAMIC FINANCE WACC

I need to calculate WACC for copany operating in the coutry with islamic finance system. I used build-up method to calculate cost of equity. But still searching for cost of debt in the economy. Has ...
3
votes
0answers
134 views

GMM time-series regression factor model with factors that are not returns

Factor models with factors that are not returns are usually estimated and tested by cross-sectional regressions. However, there is a way to use time-series regression to estimate and test the model. ...
3
votes
0answers
33 views

For an affine process, how do we know the second order term is positive definite?

A regular affine process is defined to have the generator $Af(x) = \sum_{k,l=1}^d(a_{kl}+\langle a_{I,kl},y\rangle)\frac{\partial^2f(x)}{\partial x_k\partial x_l}+\langle b+\beta x,\nabla f(x)\rangle ...
3
votes
0answers
149 views

Mid-Point calculation with execution probability

Referring Cao, Hansch, and Wang (2004) "The Informational Content of an Open Limit Order Book" $$ \mbox{WP}^{n_1 - n_2} = \frac{\sum_{j=n_1}^{n_2} (Q_j^d P_j^d + Q_j^s P_j^s)}{(Q_j^d + Q_j^s)} $$ ...
3
votes
0answers
82 views

Particular Conditional Expectation of Geometric Brownian Motion

If we have the density function $$f_{Y}(y,t)=\frac{1}{y \sqrt {2\pi\sigma^2t}}exp(-\frac{(ln \ y - \mu t)^2}{2\sigma^2t})$$ Then the mean of $Y(t)=e^{X(t)}$ conditional on $Y(0)=y_0$ is found to be ...
3
votes
0answers
128 views

What is the most convenient data structure for backtesting a model of futures options prices?

I have an empirical model for the dynamics of futures prices in a particular market that I have implemented using a long series of the front five contracts. (I account for the roll in my model.) I ...
3
votes
0answers
96 views

How to de-seasonalize natural gas term structure data?

I need to de-seasonalize Nat Gas futures data for a project and am hoping to get good suggestions. As we all know natural gas futures are priced higher for the winter months and to analyze/model the ...
3
votes
0answers
129 views

“Stable-Floating” model for non-maturing deposit for FTP purpose

Non-maturing deposits (NMD) is a deposit without maturity date. The deposit rate is normally low. Banks could adjust the rate at any time. The customer can withdraw without penalty, however, in real ...
3
votes
0answers
89 views

Pre- Versus post-2008 Crisis Rates Modeling

Modeling for interest rate derivatives (such as bermudan swaptions) is said to have undergone significant changes since the crisis. Prior to the crisis, counterparty default risk was often ignored, ...
3
votes
0answers
43 views

Characterizing relation “ has no less information than” between information systems represented by Markovian matrices

I crossposted this question on math.stackexchange. Background: Suppose that an investor's utility is both determined by the state and her action taken. A fact of life is that she can't observe the ...
3
votes
0answers
42 views

Is there evidence that illiquid stocks, held less by institutions, have more price momentum?

(One of) the standard explanation people gave for momentum is under-reaction of stockholders to firm-specific news. If this is true, then it seems that these stocks should have more momentum, and ...
3
votes
0answers
186 views

How are quants able to verify whether their calculated prices are any good

This question is related to the discussion on Model Validation Criteria However it appeard to be very high level to me and I would like to go more into detail. Not working at a pricing desk the ...
3
votes
0answers
278 views

Explanation or implementation of Ledoit-Wolf estimator (without math packages)

I have calculated weights of selected assets in a market-neutral portfolio (presumably with min variance) using PCA and simple data covariance matrix. The question is : It is obvious that Cov Matrix ...
3
votes
0answers
52 views

FTAP in the model independent case, paper by Schachermayer

I have a question about the following paper by Beatrice Acciaio, Mathias Beiglböck, Friedrich Penkner, Walter Schachermayer. At the very beginning of the paper, on page 3, there are two definitions ...
3
votes
0answers
65 views

How is the redemption right on delisting of underlying shares held by holder in the convertible bond valued?

As title, If there is no delisting constraint, then I can treat the redemption right as the put right on the convertible bond. If there is redemption right on delisting, what is the conventional ...
3
votes
0answers
3k views

Difference between S&P 500 index and S&P 500 Total Return index?

There's the standard S&P 500 index (SPX) and the rarer used S&P 500 Total Return index (SPTR). If you compare graphs, you'll find that the latter grows faster. Supposedly, SPTR assumes ...
3
votes
0answers
402 views

mean reversion with Kalman Filter - Spread calculation

Ernest Chan in its book "Algorithmic Trading" shows how to use the Kalman Filter for mean reversion pair trading. I have seen that he uses the measurement prediction error for calculating the spread ...
3
votes
0answers
162 views

Time series (stochastic process) estimating parameters using characteristic function

I have a time series of assets ${A_1, A_2, ..., A_n}$, which is described by a sophisticated distribution having the following characteristic function: $\phi(u; t;\theta)$, where $\theta$ is a vector ...
3
votes
0answers
109 views

default probability

Suppose the hazard rate is $\lambda$ the default probability density function follow exponential $f(t) = \lambda e^{-\lambda t}$ and cumulative probability function is $F(t) = 1 - e^{-\lambda t}$ ...
3
votes
0answers
188 views

Fitting Student t-distributions to log-returns

It seems that some tail-risk centric groups are bent on using Paretian and t-distributions to account for tail risk when fitting log-returns. It has been observed, however, that with and without ...
3
votes
0answers
166 views

How can I introduce exogenous variables in the equation of the conditional variance?

Is it possible to introduce dummy variables or explanatory variables in the GARCH variance equation (garchset and garchfit).This is done in the mean (ARMAX) equation through the input 'Regress' in ...
3
votes
0answers
105 views

Estimating risk aversion (power or exponential utility) from options prices

I came across this literature and it seems like there are a number of ways people do this. You can do it for an option on any underlying as long as you can create the risk-neutral p.d.f. If you agree ...
3
votes
0answers
78 views

Dividend Index Futures

My question is dealing with the proportionality between Dividend Index Futures prices and Index prices. Indeed, we in the past we used to do a simple regression between these variables and use the ...
3
votes
0answers
259 views

pairs trading detrend the spread

I have calculated a hedge ratio that generates a mean reverting spread (stationary, without trends) 60-70% of the time. But the remaining 30% of the time, it seems like there is a trend in the spread. ...
3
votes
0answers
72 views

LSM American Option pricing with dividends

Under the Longstaff-Schwartz LSM method for an American call, how should I account for a continuous dividend paying stock? I assume that it'll needs to be accounted for when simulating the underlying ...
3
votes
0answers
159 views

Credit Rating vs Bond Yield

I am looking for some references on quantifying the dependence between credit rating and bond yield. I have some data (found some Bloomberg indices which give average yield based on credit rating), ...
3
votes
0answers
310 views

Is this methodology to calculate Alpha using multi-factor regression model correct?

I am trying to find out Historical Alphas of a bunch of fund returns ${F_i}$ by Using Regression Model$(stepwise)$ with regressors as its underlying exposure-returns(risk-free rate subtracted) i.e. ...
3
votes
0answers
162 views

Should I use Resampling or Expectation Maximization to compute a robust covariance matrix?

I have several assets, each with different return histories. Some of the assets have 75 days of return history, others have 40 or so days. In calculating a robust covariance matrix, should I be using ...
3
votes
0answers
481 views

Testing Valuation, Size and Momentum (proprietary factors) from 1988-2013: No evidence of driving cross-sectional returns

I am currently testing whether three proprietary factors - Valuation, Size and Momentum - explain cross-sectional returns. A sample of 3000 securities was tested using Fama-MacBeth two-pass ...
3
votes
0answers
647 views

FIGARCH estimation in R

I am trying to estimate a FIGARCH(1,1) model in R for Value-at-Risk purposes. As I understand it, the rugarch package does not support FIGARCH or FIEGARCH. To that end, I used the garchOxFit function ...
3
votes
0answers
319 views

Definition of risk factors for market risk scenario testing

I am doing a research for stress testing in market risk. The usual process I found out for scenario testing is: Define risk factors upon the portfolio Define the desired scenarios Vary the risk ...
3
votes
0answers
258 views

Market risk stress testing?

I am doing a research for a paper for market risk stress testing. In fact I found some information on the web about this important topic such as: Stress Testing from Art to Science Stress Testing ...
3
votes
0answers
163 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 ...
3
votes
0answers
74 views

Standard Assumption Terminology

Regulators are starting to analyse (or at least they are talking about it) model assumptions. We all know that too often our assumptions are just in the model documentation. Furthermore, we have no ...
3
votes
0answers
62 views

Discount of Asian vs European vols

I understand the discount for Asian vs. European vol depends on time to expiry and length of averaging period. This makes sense intuitively; a short averaging period far away blurs into a single ...
3
votes
0answers
93 views

Optimal mortgage rate strategy

When buying a mortgage, you can choose to "lock in" a rate at any point within 60 days of your closing date. Once locked in, you can't revert. This makes it a secretary problem - in the traditional ...
3
votes
0answers
140 views

Is it random walk?

I would like to ask a question about random walk. Campbell, Lo & Mackinlay defined the random walk, in the following way (RW3): $$ cov[f(r_{t}),g(r_{t+k})]=0,\qquad k\neq0 $$ for all $f(\cdot)$ ...

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