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3 views

Expectation and variance of $\int_0^t (W_s)^n ds$ for any positive integer $n$?

It is well known that the integral $$\int_0^t W_s ds,$$ where $(W_s)_s$ is a Brownian motion, can be derived using Ito's Lemma. More precisely, Ito's lemma on $d(tW_t)$ implies that $$d(tW_t) = ...
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0answers
7 views

Why it's related to stock price

I am reading a paper High-frequency trading in a limit order book I verified the formula (6) should be correct. However it doesn't make sense to me when I use it for different stock price. Let's say ...
0
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1answer
6 views

Arbitrage opportunity between two call options with strike price \$40, \$30 and cost \$4, \$3 respectively?

Question: Given two call options $c_1$ and $c_2$ with strike price $30$ and $40$ respectively. If $c_1$ costs \$3 and $c_2$ costs \$4, is there an arbitrage opportunity? My attempt: Short $c_2$ and ...
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0answers
3 views

Autocorrelation and frequency of occurence

Recently, I started reading Zuckerman's biography of Jim Simons - "The Man Who Solved the Market". There is an interesting para on page 110 - "When you flip a coin, you have a 25% chance of getting ...
1
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0answers
6 views

Black Scholes PDE

I seen two variations of the Black-Scholes PDE with either $+{\frac {\partial V}{\partial t}}$ or $-{\frac {\partial V}{\partial t}}$, and wanted to ask why that is? a) https://en.wikipedia.org/wiki/...
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0answers
6 views

Realized Variance as an approximation of the Integrated Variance

Realized Variance is written as $RV_{[0,T]}^{n} = \sum_{j = 1}^{n} r_{j,n}^2$, where $r_{j,n}$ is the log return for the $j$th increment, and $n$ is the total number of sample points in the time ...
0
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1answer
31 views

What does a regression of squared returns of stock on squared index returns and lags show?

We have a squared stock return at t regressed on 3 variables: squared index return, squared stock return at t-1, and squared index return at t-1. My two questions would be: 1. What does this test ...
1
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0answers
22 views

Example how to model stock price with Pareto distribution according to Mandelbrot and Taleb

There's a paper by B. Mandelbrot and N. Taleb Mild vs Wild Randomness that says that Pareto distributions is a better fit for modelling price changes. ...
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0answers
22 views
0
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1answer
13 views

Normalization of volume

suppose we have volumes every minute like below 100, 200 , 19, 0 , 200 , 12 , 100 I want to convert all these numbers to less than 10 , where 10 is max and 1 is ...
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0answers
16 views

Symmetric Power law or Pareto distribution

Also known as Pareto-distribution ...
3
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1answer
29 views

Ito isometry and the covariance of an Ito process

Let $(B_t)_{t \geq 0}$ et $(W_t)_{t \geq 0}$ be two independent Brownian motions and let $f: \mathbb{R} \rightarrow \mathbb{R}$ a deterministic function of time. We define the following process: \...
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0answers
38 views

Correlation between the perfect market-timing strategy and the market itself?

What would be the correlation between a perfect market-timing strategy [that it always goes long (short) one unit of the market the day before the market goes up (down)] and the market itself, given ...
2
votes
1answer
40 views

Repo risk - how the desk operate

I am trying to understand how repo traders are being measured(pnl/risk). I understand the amount of repo that can be done is limited by regulation but want to dig deeper on how the performance is ...
2
votes
1answer
38 views

Three proofs regarding brownian motions and martingales

1. Let $(B_t)_{t \geq 0}$ and $(W_t)_{t \geq 0}$ be two standard Brownian motions and let $X_t := B_t W_t$. Is $(X_t)_{t \geq 0}$ a martingale? The easiest way to proceed seems to be to apply Ito's ...
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1answer
42 views

What does volume dimension means?

In an exchange documentation, I see a definition for Volume Dimension parameter, Volume dimension: Shares are normally traded in Quantity, bonds in Nominal. Ok I can understand quantity but what ...
-1
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1answer
32 views

Graph of European call option value versus future price

Given a standard European call option on a non-dividend-paying stock. Draw the graph of call price at time $t$ versus the future price $F(t,T)$. The future price $F(t,T)$ is observed at time $t$, ...
0
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1answer
41 views

Delta of an option which is approaching expiration when stock price decreases

The following is an interview question. It is 10 months since you sold a one-year European call option to a customer. You have been delta-hedging your exposure to the written call since it was sold....
-3
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1answer
78 views

How to derive the CDF and the probability density function [closed]

Is there something missing in this question i dont seem to understand, can anyone help explaining what is required?
2
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1answer
82 views

Correlation of a portfolio of trading strategies to a benchmark [closed]

I have two trading strategies, both having a correlation of 0.5 to an indicator 'i'. If I take a portfolio of these two strategies, what will be the correlation of this portfolio with the indicator 'i'...
-1
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0answers
44 views

How to handle the volume spikes near expiration for futures contracts?

Are there any common practices to handle the volume spikes that occur near expiration of a futures contract?
3
votes
1answer
49 views

Boundaries for Call Spread

I'm reading an interview book called A Practical Guide to Quantitative Finance Interview and I have some doubts regarding part of its solution and highlighted them in bold: Question: What are the ...
1
vote
1answer
38 views

What is market sensitivity and momentum sensitivity?

I have daily data of about 29 stock prices and 1 index prices of past 7 years I calculated beta as the ratio of covariance(Rm,Ri) / variance(Rm) I also calculated 200 days rolling momentum score as ...
0
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2answers
65 views

Why are put and call options worth the same despite that put has no upside whereas call has unlimited upsides?

The following is an interview question. All Black-Scholes assumptions hold. Assume no dividends. Consider a standard European call and a standard European put on the same stock. Assume that each ...
1
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0answers
69 views

What is $W(t) \cdot dt$ where $W(t)$ is a Wiener Process

When I derive the stochastic differential equation for a particular case, I came across $W(t) \cdot dt$, what is the result for it? I know $dW(t) \cdot dt = 0$, could any expert give me some advice?
4
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0answers
145 views

Which finance models have enjoyed particular success in recent years?

I am looking for a list of recent developments of models in mathematical finance. By recent, I mean this last decade. Which models have been developed and introduced during this period, being met ...
1
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2answers
105 views

how to calculate implied volatility

I have some options prices I found using the Heston Model. How do I calculate the implied volatility? In Matlab there exist a blsimpv function, but is this the right tool for me since I'm working with ...
3
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0answers
36 views

Dynamic Programming: Dynamic Card Game

I'm reading an interview book called A Practical Guide to Quantitative Finance Interview and I have some doubts about the solution provided by the book, so I really appreciate your advice if my doubt ...
1
vote
0answers
25 views

Johansen cointegration Test for spread generation

I'm using the python statsmodels version of the johansen cointegration test and I'm looking for some advice on how best to generate the spread used within a pairs trading algorithm. For example I've ...
1
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0answers
40 views

Simulate option prices [closed]

Starting value = 3110.29 K = 3100 Trading days = 20 Need to simulate the price of an option by using these 2 methods. ( For homoscedastic errors ). *This is what I have already set up <...
-1
votes
1answer
17 views

What's the relationship between the risk-neutral probability in HJM and the risk-neural probability under domestic money market?

In shreve's book, we model the stock price dynamics as: $$S_i(t) = \alpha(t)S_i(t)dt +S_i(t)\sum ^d_{j=1}\sigma _{ij}(t)dW_j(t)$$ and the forward rate can be written as : $$df(t,T) = \gamma(t,T)dt + \...
0
votes
1answer
35 views

Dollar/time weighted rate of return of Stock Investment

Question: Stock initially trades for \$120 per share. An investor decides to purchase 1300 shares. After 5 years, the portfolio is worth \$245,570.00. At that time, the investor decides to purchase an ...
1
vote
2answers
140 views

Assumptions in using risk-neutral pricing formula

The well-known risk-neutral pricing formula goes as follows (extracted from Shreve's Volume 2, section $5.2.4$ (Pricing Under the Risk-Neutral Measure)): Given any $T>0$ and any $t\in[0,T],$ if $V(...
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0answers
16 views

Investment Analysis NPV [closed]

I am working on an Actuarial Science question: Find the NPV of a project that has an initial cost of $49000$, and produces cash flows of $7000$ for 5 years, followed by $3000$ for the following 3 ...
0
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0answers
30 views

Derivatives - how to build the term structure of the cost of carry

1) By using the settlement prices, build the term structure of the cost of carry for the contract. Use the first two contracts to extract the implicit index that you will be using for all the ...
0
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0answers
17 views

Why meta-labeling is is robust?

With all due respect, I saw this technique in the book , Advances in financial machine learning, but I found that it acts like a filter for the trades only. And it seems doing the job of overfitting ...
0
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0answers
29 views

How key rate durations are calculated

I just had a question regarding how key rate durations are calculated in practise. I Know it involves changing the key rates and calculating new bond prices. But how are these new bond prices ...
2
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2answers
78 views

Understanding Mechanics and Specifics of Cross-Currency Basis Swap

I am looking at a Bloomberg Ticker for the JPY-USD Basis Swap (JYBS5 BGN Curncy). This is a 5yr term, settling on Dec 05 2019 and maturing on Dec 05 2024. The last price is -41. Several questions I ...
0
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0answers
43 views

How to derivate Dupire's local volatility?

I want to calculate the expression of local volatility expressed in terms of implied volatility given by Fabrice Douglas Rouah in Derivation of Local Volatility : $v_{l} = \frac{ \frac{\partial w}{\...
0
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1answer
57 views

How do you price an option on multiple things>

Suppose, for simplicity, I want to cover the U.S. stock market by buying ETFs for the Russell 1000 and Russell 2000. But I want to overweight small cap, so the Russell 3000 won't do. Also, let's ...
0
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0answers
22 views

Pricing Data/Regressions in R

I'm working on a project for my econometrics class and trying to replicate a few papers relating to Fama-French factor models. I got data from CRSP and Compustat, but I'm a bit unsure how to ...
0
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0answers
16 views

Costly reversibility and countercyclical cost of risk - confusion

I'm currently working on potential explanations behind the value premium. As there're two school of thoughts, rational pricing describing fundamental risk in value stocks vs. irrational behavior, I ...
2
votes
1answer
77 views

Hull-White calibration volatility as a function of time

I need some help for the parametrization of the volatility parameter in the Hull-White model. I have the necessary Caplet vols and I calibrated the HW model to match the Caplet and hence the Cap ...
2
votes
2answers
40 views

Cash flows regression on macroeconomic data

I'm looking into a research project and am struggling to find any existing work on this or whether I'm asking the right question. My question is to test the relationship between macroeconomic ...
0
votes
1answer
48 views

Estimation of volatility into Black-76 formula

I am trying to estimate the (annualized) volatility that should go into an European Swaption (such as 2y5y). Given we take the black76-formula, where the discounting is the term outside the ...
0
votes
0answers
35 views

What is momentum factor and how is it calculated based on three parameters?

I have 7 year prices of a group of stocks and index prices for the same time period now I want to calculate momentum factor, depending on the three relevant parameters (rebalancing frequency, rolling ...
0
votes
2answers
72 views

Treasury Futures Wild Card

I am looking at some empirical methods to model the Treasury Futures wild card. I was looking through some sell side reports and found this statement. "Wildcard fair BNOC is the net basis under ...
0
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1answer
68 views

A financial market is complete if and only iff there exists a unique equivalent martingale measure

Do you have any intuition behind the following theorem : A financial market is complete if and only iff there exists a unique equivalent martingale measure. I understand the easier version of ...
0
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0answers
18 views

How can I use both Stochastic and RSI in technical analysis?

Stochastic and RSI both are momentum indicator but they both show momentum in different way. It leading me to confusion how to use them in trading.
1
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1answer
64 views

Hedging delta when gamma is positive

If I have an aggregate position with a positive gamma, should I still be delta neutral? I feel like I'm giving up the positive benefits of being gamma positive because I'm killing my delta constantly.

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