3
votes
1answer
172 views

Auto-correlation of GBM

The GBM is defined by $ dS(t) = \mu S(t)dt + \sigma S(t) dW_t, $ with analytical solution $ S(t^\prime) = S(t) ...
1
vote
1answer
121 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
182 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 ...
6
votes
10answers
2k views

Using Black-Scholes equations to “buy” stocks

From what I understand, Black-Scholes equation in finance is used to price options which are a contract between a potential buyer and a seller. Can I use this mathematical framework to "buy" a stock? ...
2
votes
1answer
646 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 ...
14
votes
7answers
10k views

Is the Interactive Brokers API suitable for hft?

By hft here I mean anything with holding period less than 5-10mins... Any empirical/anecdotal evidence of using it successfully on even higher frequencies?
1
vote
1answer
355 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 ...
3
votes
2answers
410 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: ...
0
votes
2answers
354 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 ...
5
votes
2answers
176 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
135 views

OTC Equity Options' Dynamics

This only applies to options that do not have marketable equivalents since margin can be marked to them. I've never been able to find this on my goog. How is margin typically calculated for OTC ...
0
votes
2answers
149 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.
0
votes
2answers
147 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 ...
0
votes
1answer
105 views

Regression extensions

I'm trying to find extensions for my regression and obviously would like to use PE, BV and CFO. But I've got monthly data, while all company's fundamentals are semi-annually... Can I deal with it ...
0
votes
2answers
422 views

What information do stock exchange colocated servers have access to?

In high frequency and low latency trading, decisions are done on the spot by servers colocated in stock exchanges. This implies that those servers have immediate access to the information they need to ...
1
vote
1answer
735 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 ...
10
votes
2answers
305 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 ...
1
vote
1answer
184 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 ...
1
vote
0answers
79 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 ...
2
votes
0answers
374 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 ...
14
votes
2answers
1k views

From a high frequency point of view, with a price prediction and assuming infinite leverage, how do you determine optimal trade size?

I have read about something like Kelly criterion for long term expectation maximization assuming a fixed starting bankroll. But if one can assume unlimited leverage, and one has a signal for a price ...
0
votes
1answer
99 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
488 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
178 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 ...
1
vote
2answers
368 views

What is the instantaneous P&L of a Variance Swap?

What is the instantaneous P&L of a variance swap. Is it $(\sigma^{2}_{t}-\sigma^{2}_{implied})dt$?
6
votes
3answers
1k views

What really drives option implied volatility?

A common and oft repeated belief regarding options volatility is that implied volatility increases due to people bidding up a contract, usually related to anticipation of the outcome of an expected ...
4
votes
2answers
240 views

How to reactivate a risk mangement rule in an automated process

If some conditions are met (stop loss, trailing stop, take profit...) we will close ours positions (sell/buy) to avoid having more loss or to ensure profit. In an automatic trading system, it is easy ...
0
votes
1answer
88 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}. ...
3
votes
1answer
245 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 ...
3
votes
3answers
677 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 ...
2
votes
1answer
317 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 ...
11
votes
1answer
281 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 ...
4
votes
1answer
178 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 ...
0
votes
0answers
282 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 ...
1
vote
0answers
228 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 ...
0
votes
2answers
355 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: ...
3
votes
2answers
258 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 ...
20
votes
8answers
8k views

Digital Signal Processing in Trading

There is a concept of trading or observing the market with signal processing originally created by John Ehler. He wrote three books about it. Cybernetic Analysis for Stocks and Futures Rocket Science ...
4
votes
3answers
467 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 $\phi(T/N)$ ...
7
votes
3answers
170 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 ...
0
votes
2answers
151 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 ...
0
votes
1answer
354 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
0answers
68 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 ...
5
votes
0answers
689 views

VaR model Unconditional Coverage Tests: Is this extension of Kupiec POF test correct?

Background: Kupiec P. in 1995, published paper "Techniques for Verifying the Accuracy of Risk Management Models" on Journal of Derivatives, v3, P73-84, it's a Unconditional Coverage Tests designe for ...
3
votes
2answers
114 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 ...
3
votes
1answer
220 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, ...
0
votes
0answers
156 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 ...
4
votes
0answers
235 views
0
votes
1answer
2k views

Calculating pre-tax cost of debt

This is a simple problem but I'm not sure about one aspect of it. A company has 15 year bonds outstanding, with a 5% annual coupon, a face value of \$1000, and a current market value of \$1100. ...
1
vote
2answers
142 views

Reasoning behind multiple names for the equivalent risk measures AVaR/ETL/ES/CVaR

Doe's any one know the history behind, or background of the multiple naming conventions for the equivalent risk functions. Different quant authors prefer using different names, does any one know why? ...

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