10
votes
2answers
430 views

How to estimate the following model?

Suppose I have the following model: $$r_t=\sigma_t * \epsilon_t$$ where $r_t$ is the return at time t, $\sigma_t$ is the volatility, the model used to model this volatility is an exponentially ...
1
vote
1answer
170 views

How to deal with different amount of td's in computing Sharpe Ratio

In calculating the Sharpe Ratio, should I take into account the days were I have 0 return due to non-trading day? Another user posted a similar question but this was related to trading days with no ...
3
votes
2answers
231 views

Iterating through every path of a Trinomial Tree

I am attempting to come up with an algorithm to iterate through every possible path of a trinomial tree and am having difficulties coming up with one. Is there any literature on this or has anyone ...
3
votes
1answer
190 views

Foward-start option pricing

Consider a probability filtred space $(\Omega, \mathcal F, \mathbb F, \mathbb P)$, where $\mathbb F = (\mathcal F_t)_{0\leq t\leq T}$ satisfing the habitual conditions and is generated by $1 d $- ...
4
votes
1answer
263 views

Non-arbitrage theory and existence of a risk premium

Consider a probability filtred space $(\Omega, \mathcal F, \mathbb F, \mathbb P)$, where $\mathbb F = (\mathcal F_t)_{0\leq t\leq T}$ satisfing the habitual conditions and isgenerated by $1 d $- ...
8
votes
3answers
2k views

Gamma vs. Volatility Risk

Original Question: What is the link between Gamma and the Volatility Risk? It leads me to ask: - What is the Volatility Risk definition and what are the good practices to measure it? Thinking about ...
3
votes
2answers
615 views

Software for backtesting outside strategies (CSV transaction upload)

I've developed some software which generates sets of trades, and I'd like to backtest those trades. My software currently outputs a CSV file with details of each trade: ...
1
vote
1answer
429 views

Testing Significance of Correlation

Lets say I have the returns of two stocks(stock1 and stock2). Now without running a regression, I lag one of the variables, calculate the correlation between the two stocks and repeat this process as ...
2
votes
1answer
1k views

High-Frequency Traders and Front Running: What order types are they using? [closed]

I often hear in the news that High-Frequency Traders can front-run incoming trades because they are faster at acquiring information and to execute trades. I also read that speed is only a necessary ...
4
votes
2answers
932 views

Fitting distributions to financial data using volatility model to estimate VaR

I want to fit a distribution to my financial data using a volatility model to estimate the VaR. So in case of a normal distribution, this would be very easy, I assume the returns to follow a normal ...
2
votes
1answer
1k views

Value at Risk Monte-Carlo using Generalized Pareto Distribution(GPD)

I have created a VBA program to calculate VaR by using Monte Carlo, I have simulated Brownian Motion. This method might be ok for 100% equity portfolio, but let's say this portfolio may have fixed ...
0
votes
2answers
516 views

Regression with Lagged variables

I am new to regression analysis. Let's say initially I have a linear regression x = alag(x1) + blag(x2) + clag(x3) -- eq 1 I want to predict the price x based on the the price of x from previous ...
1
vote
2answers
174 views

monthly contract volume required for penny increments?

Have the exchanges disclosed their criteria? Does anyone have a best guess based upon observations of volume (however you wish to define it)? Please no qualitative answers.
7
votes
2answers
4k views

Using variance ratios to test for mean reversion

Can you use the variance ratio test to determine whether or not a time series is mean reverting? I'm using the Lo.Mac function in the ...
1
vote
1answer
238 views

Testing Black Scholes Analytical Options Pricer

I've written some code to calculate European option prices using the Black-Scholes analytical method. Can somebody recommend a good way to test that code? I have looked at option pricers online like ...
5
votes
3answers
2k views

Stochastic modeling of stock price process

Apart from the model of Geometric Brownian motion is there any other "widely accepted" stochastic model to characterize the dynamics of a stock price process?
4
votes
2answers
315 views

Obtaining a consistent covariance matrix for stochastic volatility processes

What is the condition for underlying stochastic volatility processes to give a consistent covariance matrix? I read in Hull that in order to have a consistent covariance matrix, volatility parameters ...
1
vote
0answers
108 views

Risk factors for derivatives on dividends

I consider pricing and risk analysis of derivatives on dividends of the members of equity indices (such as Dow Jones EuroStoxx). There are options but I focus on futures. What are the main risk ...
5
votes
3answers
1k views

Data Synchronization

I'm working on market trends. I have daily prices for 33 assets from different markets. I was wondering if there is a way to cancel the effects of different opening/closing times. I have been told ...
2
votes
3answers
457 views

Why do long-term equity return forecast models use dependent observations?

I've been reading up on different models used to forecast the equity risk premium, and I've seen a couple of papers that had questionable methods. For example, this paper by Javier Estrada goes into ...
2
votes
0answers
600 views

Does the geometric Ornstein-Uhlenbeck process have stationary variance?

I know that the long run variance of the standard OU process is $\lim_{s\rightarrow \infty}\mbox{Var}(P_{t+s}|P_t) = \frac{\sigma^2}{2\theta}$ I'm using the geometric version of the process. I ...
0
votes
1answer
106 views

Assessing Forcasting with Correlated Residuals

Trying to use a linear regression model to forcast the CPI. I noticed that when I took a moving average of the residuals, though homsokedatisc and nonautocorrelated(ie they squiggle up&down with ...
3
votes
3answers
980 views

YTM and current yield

Which of the following statements is correct? a. If a bond’s yield to maturity exceeds its coupon rate, the bond’s current yield must also exceed its coupon rate. b. If a bond’s yield to maturity ...
2
votes
2answers
230 views

Portfolio risk-return when assets have limited and inconsistent historical data / time series?

Lets say we have "today's" snapshot of asset allocation and need to determine the 6mo, 1 yr and 5 yr risk and returns of this portfolio. If the time series for every asset is very long, longer than ...
10
votes
2answers
489 views

Stochastic modelling of derivatives on dividends

I consider pricing and risk analysis of derivatives on dividends of the members of equity indices (such as Dow Jones EuroStoxx). There are options but I focus on futures. What are common stochastic ...
0
votes
1answer
112 views

What is the meaning of the discounted process defined from the interest rate process?

Assume a money market has interest rate process $R(t)$. In Shreve's Stochastic Calculus for Finance II, formula (5.2.17) on page 215 defines the discounted process as $$ D(t) = e^{-\int_0^t R(s) ds}. ...
5
votes
2answers
194 views

How does the number of free dimensions of a model affect its required size of sample?

Adding more variables to a model usually increases its accuracy. However, without adequate analysis it could also lead to curve fitting. Another question (How much data is needed to validate a ...
2
votes
1answer
433 views

Calculating the probability of a price change using an options pricing formula

I don't know if I'm doing this right and I'd greatly appreciate help. I'm trying to use an option pricing formula to backout the likelihood of the Euro dropping below $1.27, even for a minute, at any ...
1
vote
2answers
217 views

changes in open interest vs changes in underlying volume

Has a relationship been noted? Mostly, I'd like to know if the open interest increases on an underlying, does the underlying usually see increased trading? My guess would be "yes" since MMs can ...
3
votes
3answers
5k views

Does implied vol vary for calls vs puts?

Volatility skew tells us that options with the same maturity at different strikes can have different implied vol. However, can a corresponding call and put for the same strike and maturity have ...
4
votes
1answer
190 views

Hedging with actual volatility: problem understanding the math behind the result

From this paper. page 3 We get that the total profit at expiration is the difference in value between the price of the option with actual volatility and the one with implied volatility. I have tried ...
3
votes
1answer
443 views

Where can I get historical ticker change database?

There's 30 days worth of data at http://www.otcmarkets.com/marketActivity/symbol-changes - but I'm really looking for the past 10 years, or 5 years if only that is possible. Any dice? The closest ...
0
votes
0answers
406 views

Mean Reverting Spread

I have constructed a mean reverting spread using two indexes. I know they have to be mean reverting, but when plotted side by side they are mean reverting for a little bit and then deviate and head ...
3
votes
2answers
304 views

Black-Scholes and Fundamentals

So basically $dS_t=\mu S_tdt+\sigma S_tdWt$ and $\mu=r-\frac12\sigma^2$ I have just been thinking about this later equation. This is very interesting because it ties together risk-free ...
11
votes
1answer
365 views

Are BSDE's used in practice?

In the academic applied probability/math finance community, Backwards Stochastic Differential Equations (BSDE's) are extremely popular, and they provide a single framework for several different ...
1
vote
0answers
371 views

Call options portfolio: what would the underlyings' moments to be maximized?

Let you have only three underlyings, like SPY, TLT and GLD, and you want to buy $n_{1}$ Call options on SPY, $n_{2}$ Call options on TLT and $n_{3}$ Call options on GLD... with a limited budget, that ...
1
vote
0answers
93 views

Problems with exact Heston simulations

I am just wondering if there is any problem with the so-called "exact" Heston simulations? So far what I have seen are the good things about it, what are the disadvantages? Because if it is so ...
0
votes
1answer
1k views

Matlab - Differences between rng and rand

I was trying to run some Monte-Carlo simulations and if I used: rng(seed, 'Twister'); For some reason I would get "Option Values Can not be Negative" errors in the blsimpv function, but if I just ...
1
vote
2answers
238 views

Credit risk data

I am trying to get historical data for credit risk and do some analysis on it as a school project. I thought CDX index might be a good proxy for typical credit risk data, but I am not sure. Typically ...
7
votes
3answers
204 views

How to justify a model that could not predict external factors?

I'm building some models, for example, Bad Loan (NPL) rate. It's based on historical simulation method -- basically it's saying the future behavior could be predicted by history data. However, this ...
18
votes
5answers
38k views

Mapping symbols between tickers, Reuters RICs and Bloomberg tickers

Is there any known solution (preferably open source) to map between ticker symbols, Reuters and Bloomberg symbols. For example: Ticker: AAPL Reuters: RSF.ANY.AAPL.OQ Bloomberg: AAPL US Equity ...
0
votes
0answers
360 views

Correlation Sensitivity

Suppose I have 2 stocks $S_{1}$ and $S_{2}$: \begin{align} & dS_{1}=rS_{1}dt+\sigma_{1}S_{1}dB_{1}\\ & dS_{2}=rS_{2}dt+\sigma_{2}S_{2}dB_{2}\\ & dB_{1}dB_{2}=\rho dt \end{align} Then I ...
0
votes
2answers
549 views

Why the implied volatilities calculated are so different

I Calculated facebook option(expired in 12/4/13) Implied Volatility with the Bisection Method. The program will be attached at the end. The results for different strike prices are so different: ...
4
votes
3answers
636 views

Central Limit Theorem and Lévy processes

Lévy processes are self-decomposable and independent on any non-overlapping interval, so how come the distribution of the process at time T,$\phi(T)$, which is the sum of N i.i.d with law $\phi(T/N)$ ...
2
votes
1answer
407 views

Stepwise Cointegration

This is more of a general question at this point, but if my thought process makes sense I will follow up with an R implementation. I have read a number of papers on cointegration analysis for pairs ...
3
votes
2answers
120 views

Endogeniety of Black-Scholes

I know this is a naïve question but how does the BS formula have a closed form solution? It seems from what I am reading Price impacts delta, price influences volatility which in turn influeces delta ...
5
votes
1answer
310 views

Examples of investable factors via factor funds/ETFs

In the draft chapter about hedge funds of his forthcoming book Andrew Ang postulates the dawn of new factor funds (p. 35 ff.), i.e. funds that directly target factors like volatility, value-growth, ...
1
vote
3answers
450 views

Kolmogorov-Smirnov test

Is Kolmogorov-Smirnov test self-sufficient to prove normal distribution of a time series? And then test efficiency of a market?
4
votes
2answers
1k views

Is drift rate the same as interest rate in risk-neutral random walk when using Monte Carlo for option pricing?

When using following risk-neutral random walk $$\delta S = rS \delta t + \sigma S \sqrt{\delta t} \phi$$ where $\phi \sim N(0,1)$. Now when a text mentions drift = 5% does that mean that interest ...
3
votes
2answers
2k views

Theta's effect for OTM options

How does $\Theta$ change for deep out-of-the money options? Looking at the below graph, it seems the time decay is highest for ATM options and increases rapidly as we approach maturity of the option. ...

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