# All Questions

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### Transaction costs on option trades

It looks like the commissions alone for a non-index option trade is around 2-5%. For example, a BAC June ATM Call is currently trading at \$0.20; Interactive Brokers charges$0.7 per contract, which ...
158 views

### Why is $C(t,S_t)/B_t$ a martingale?

In the derivation of the Black-Scholes formula given by Joshi (extract below), he says $C(t,S_t)/B_t$ is a martingale. Why? I understand this can be deduced from the Black-Scholes PDE since the drift ...
45 views

### Derivation of Stochastic Vol PDE

A couple questions regarding stochastic vol PDE derivation. Following Gatheral, a general stochastic vol model is given by \begin{align*} dS(t) & = \mu(t) S(t) dt + \sqrt{v(t)}S(t) dW_1, \\ dv(t) ...
68 views

### Stochastic calculus: what am I doing wrong?

it is just the computation of a second moment but however is creating debate !!... Can someone spot the error?
64 views

### How can index futures trade 24/7 when the index doesn't change?

I have read that the E-Mini S&P 500 Futures trade 24/7, how is that possible? I mean the underlying stocks which form the index are traded from 9:30am-4pm - so outside of these hours the S&P ...
74 views

### GARCH modelling and forecasting

I have a few questions regarding GARCH modelling and forecasting and it would be great if someone could help me. I am modelling the log return of oil spot prices using various GARCH models: GARCH, ...
85 views

### Sums of random variables and independence

I'm having troubles with this proof: Let $\{Z_i\}_{i\in\mathbb{Z}}$ be i.i.d. random variables with zero mean and unit standard deviation. For $(a_0, a_1, ..., a_r)$ a sequence of $r$ real numbers ...
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### Regression model when samples are small and not correlated

I received this question during an onsite interview for a quant job and I'm still scratching my head on how to solve this problem. Any help would be appreciated. Mr Quant thinks that there is a ...
94 views

### Is the Brownian motion multiplication rule a definition or is it a theorem?

Is the Brownian motion multiplication rule a definition or is it a theorem? Refer to the highlight part of http://i.stack.imgur.com/doQuT.png where $dw_1(t)dw_1(t)=dt$
42 views

### Binomial pricing model: When the Cox-Ross-Rubinstein assumption is not arbitrage-free

I understand that in an arbitrage-free Binomial model, we assume that $S_{t+1} = S_t \cdot u$ in the event of an up-jump and $S_{t+1} = S_t \cdot d$ in the event of a down-jump. We call $u$ and $d$ ...
38 views

### The State-Price Deflator in a Binomial pricing model

This question comes from a Financial Economics exam and I'm very confused about a state-price deflator which doesn't seem to exist. I've included the whole question for completeness, but my actual ...
56 views

### Multivariate Itô's lemma

Hey guys I'm looking for worked examples who show how to apply Itô's lemma in several variables, starting from the very basics. Thank you in advance!
88 views

### Modern portfolio theory in practice

I am wondering about the Markowitz theory of portfolio construction in practice. Hence, if one wants to know the efficient frontier, what variances can one use. The only method that I can think is the ...
128 views

### How google finance calculates beta of a stock

How google finance calculates beta of a stock - What is the proxy for the market? - What is the time period it uses for regression?
53 views

### How can I calculate the Maximum Drawdown MDD in python

I need to calculate the a time dynamic Maximum Drawdown in Python. The problem is that e.g.: ( df.CLOSE_SPX.max() - df.CLOSE_SPX.min() ) / df.CLOSE_SPX.max() ...
35 views

### SEC 10-Q/K Filings

I am working on some research that requires parsing of SEC 10 K/Q filings. We have built a parser that will parse the raw txt SEC filing that usually contains many blocks of unencoded files (html, ...
37 views

### Realized Volatility: errors correlation

When using Realized Volatility (sum of squared intraday returns) to estimate volatility, following the model: $$r_t = \sigma_t \epsilon_t$$ where $\sigma^2_t$ is the volatility at time $t$ and ...
41 views

### calculate YTD return / find first available datapoint of a year in python

I need to calculate the year-to-date relative return of a given dataset. I usually caculate the cumulative relative return with this simple function: ...
37 views

### What are your list of concept or model in standard textbooks that are always reliable to used in working?

What are your list of concept or model in standard textbooks that are always reliable to used in working? As opposed back to this: What concepts are the most dangerous ones in quantitative finance ...
45 views

### Best way to do multithread Monte-Carlo in QuantLib

QuantLib has great facilities for Monte-Carlo pricing engines, classes McSimulation and MonteCarloModel do a lot of work. But they do it in a single thread. What is best way to introduce parallel run ...
40 views

### Underlying mechanics of paired class shares ETFs

I came across an interesting pair of VIX ETPs, VXUP and VXDN. This new product referred to as "paired class shares" ETFs are quite different from traditional ETPs. Some interesting highlights from the ...
54 views

### returns of Bonds and exchange rates

which are the best distributions in order to model the bonds and exchange rate returns distributions. I am searching for a distribution such as the log-normal one of the stocks ( N(m-0.5*v),Sqrt[v])
30 views

### bootstrap asset allocation

I want to ask if the bootstrap method for asset allocation is preferable. For instance, suppose that we have data for the past returns for two stocks. Is it wise to generate the efficient frontierby ...
49 views

### Calibration Merton Jump-Diffusion

Consider the following SDE $dV_t = rV_tdt +\sigma V_t dW_t + dJ_t$ where $J_t$ is a Compound poisson process with log-Normal jump size $Y_i$. How am I supposed to calibrate this model to CDS ...
24 views

### Hypothesis Testing for Portfolio Weights

Investigating international diversification is an ongoing topic in portfolio allocation literature. Britten-Jones and Kempf-Memmel , for example, use derived properties of the distribution of ...
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I'm reading Uwe Wystup's "FX Options and Structured Products" to understand Vanna-Volga pricing, which, in his book Chapter $\S3.1$ is called "The Trader's Rule of Thumb". I generally got the idea ...
41 views

### Variance of a stochastic integral

Ok guys, I'm new to stochastic calculus and I did an exercise that I don't know if it is correct, so I need somebody with more experience to check if it is true. Compute the variance of the R.V. ...
62 views

### Effect of volatility on the delta of a call option

In the book 'Dynamic Hedging', Nassim Taleb writes: ...
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### How to compute/find the volatility of an index like the S&P 500 to be used to control risk exposure? [closed]

I've asked two related questions. First this one on the money stack exchange and this one on the math stack exchange. But have not yet found a complete answer. Given an index such as the S&P ...
94 views

### Difference between ito process, brownian motion and random walk

Can someone explain to a non-math person (myself) what is the difference between these three? If they are so different that a comparison does not even make sense, please point it out. 1.Ito process ...
125 views

### How can put options be more expensive than call options in an efficient market?

I noticed that for some securities, puts were more expensive than calls (with same expiration). For example, suppose the underlying security is trading at 50. A put with a strike of 45 is more ...
23 views

### Relation between Parkinson number and historical volatility

In his book 'Dynamic Hedging', Nassim Taleb gives the relation: P = 1.67*historical volatility, where P is the Parkinson number. What is the basis of this relationship. Does this hold under special ...
78 views

### How can a beginner trader make use of 'volatility of volatility'

For a beginner option trader in equity options, how can he use this metric that is provided by his broker/data vendor? How can he use this metric to gain an added understanding of the option ...
117 views

### Interpretation of Correlation

I have two geometric Brownian motions (GBMs) driven by the same underlying Brownin motion, namely \begin{align*} S_t^1 = S_0^1\exp\left(\left(\mu_1 - \frac{\sigma_1^2}{2}\right)t + \sigma_1 ...
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### Bond yield: is it martingale with respect to risk-neutral probability measure of some numeraire?

Let $t$ mean current time, let $T_0, T_n$ mean two times such that $T_0\le T_n$, and let $y_t[T_0, T_n]$ mean the forward swap rate of a swap starting at $T_0$ and ending at $T_n$. (I am ignoring ...
39 views

### ASX level 2 data via API

Is anybody aware of Java/C++/Python API's available for ASX stock market depth? I'm currently using IB which is ok but has a number of limitations / issues - the one I care most about is the limit of ...
22 views

### How to calculate beta against a multi-asset benchmark

Lets say that I have a benchmark, $BM$ that consists of 3 assets- 30% asset $A$, 30% asset $B$ and 40% asset $C$. Now, lets further assume I am trying to construct a portfolio that uses $BM$ as its ...
139 views

### Math background required to understand geometric brownian motion

What mathematical concepts are required before I can understand what exactly is a Geometric Brownian motion as applicable to stock prices? I mean which branches of probability, calculus, statistics ...
97 views

### Is Trading in the Underlying Necessary for Replication?

In a simple one-period binomial model we have two possible payoffs: $f(S^u)$ and $f(S^d)$. To replicate this we must trade in two assets, usually the stock $S$ and the money market account (assumed ...
43 views

### Which kind of normalization to prefer before PCA (generic solution for any factor analysis)

I have financial assets with totally different volatilities, thus I must standardize them before PCA, otherwise, assets with high variance may be considered as principle components, which is wrong. ...
11 views

### Leveraged ETFs Holding Period; Compare LETF with DITM

Why the "standard recommendation" is that LETFs are only for short periods (< 1 day) while their performance charts indicate that the leveraging is retained once the period EXCEEDs several days? ...
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### How does a stop loss affect the P/L of a trader

In his book 'Dynamic Hedging', Nassim Taleb writes: Problem: A trader is given a stop loss of 100,000 in any given month (he would have to close his books and go home until the end of the month). ...
125 views

### Pricing Treasury futures

I've recently learned that at the delivery of Treasury futures the short side can decide which of the $n$ Treasury bonds (with relevant maturities) to deliver. If the short side chooses to deliver the ...
162 views

### Speeding up computations: when to use Quasi and standard Monte-Carlo in pricing

I am familiar with the theory of Monte-Carlo techniques in the numerical integration, and recently I have started my experiments with these methods applied to derivatives pricing. I am using ...
57 views

### Questions on the relationship between option price and maturity

From the plot of volatility surface, as maturity goes up, the implied volatility will decrease. Dose it mean that options with the same strike have higher value when maturity is larger. If so why ...
71 views

### Using FX ATM/RR/BF Volatility to Estimate Smile

Suppose $S$ is some FX rate, EUR/USD say, and $\sigma_{S}(K,T)$ is the implied volatility for some option written on $S$, sourced from the surface $\sigma_{S}(\cdot,\cdot)$ (alternatively, consider ...
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### Pie-chart (or alternative) representation with negative values/liabilities

I'd like to represent graphically/visually a fund/portfolio by something that resembles a pie chart. But... the fund/portfolio contains things that have negative value (think of liabilities such as: ...
122 views

### Variance replication using options

I would like to understand the intuition behind the following question: Why a certain weighted sum of prices of put and calls is equivalent to the implied variance of an underlying? A variance swap ...