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8 views

Why is variance of brownian geometric motion equal to t?

I know that, for the random variable $B_t$, $B_t \sim N(0, t) = X\sqrt{t}$ where $X \sim N(0,1)$. However, what I am confused by is why the variance of the GBM variable is assumed to be $t$ in the ...
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0answers
12 views

Why does the rate of inflation vary over time?

Interest rates have varied significantly over the last 50+ years (source: https://www.macrotrends.net/2016/10-year-treasury-bond-rate-yield-chart ). Is it possible to comprehensively and succinctly ...
0
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0answers
21 views

Black-Scholes with two options

I have got a Black-Scholes model with portoflio with two options which prices are $V_1$ and $V_2$ (with different maturities or strikes) $$ \Pi = V_1 - \Delta V_2 $$ and I need to prove that $$\frac{\...
1
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0answers
11 views

Checking Regression Inputs & Outputs (Factor Regression)

I am looking to check the assumptions and interpretation of the output of a regression that I have run for factor exposures in a long/short equity portfolio: Portfolio is long/short equity with a net ...
-2
votes
1answer
26 views

One-Period Binomial Model

So, I'm required to consider the one-period Binomial market model for a particular question. We're told that the savings account is \$1 at time 0 and \$β at time 1. The stock price is given by S0 = 1 ...
0
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0answers
13 views

Interpretation of holding lower beta assets leveraged to a beta of one and short high beta de-leveraged to a beta of one

I was reading the famous paper "Betting against Beta" by Frazzini et al. They created BAB factor in which a portfolio is created by holding low beta assets, leveraged to a beta of one" ...
0
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1answer
29 views

Covariance Shrinkage - Am I getting the right variances?

I am looking into a quite simple task: shrinking the sample covariance matrix of a minor sample of monthly returns data on 5 different assets. I am using Python to process my data and have been using ...
2
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1answer
54 views

Conditional expectation of integral of brownian motion

I am trying to calculate $$\mathbb{E}\biggl[\biggl(\int_s^t W_u du\biggl)^2 \biggl|W_s=x, W_t=y\biggl] $$ where $W$ is a Standard Brownian Motion and $s\leq u \leq t$. Any help or tips would be ...
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0answers
28 views

Monte carlo simulations giving biased output

I wrote code to simulate the stock price using geometric brownian motion. My code is as follows: ...
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0answers
20 views

Calculating E^2[σ^2] where σ is a GARCH(1,1) Proces

Given that α =0,113079 β = 0,873884 ω = 0,0000081 Need the calculate a call price using garch volatility I alsa calculated the kurtosis = 235 enter image description here: https://www.researchgate.net/...
3
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1answer
37 views

EMM for Bachelier model

The stock price is assumed to evolve as $S_{t}=S_{0}+\mu t+\sigma B_{t}$, where $S_{0}>0, \mu>0$ and the process $B_{t}$ is Brownian motion. The saving account is assumed to be $\beta_{t}=e^{r t}...
1
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1answer
29 views

R - Plotting a 3-dimensional sample path in yuima?

Apologies if this is not the appropriate place to post this - this my very first contribution to Quantitative Finance Stack Exchange. I was hoping someone could help me with the following issue. I am ...
0
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1answer
16 views

How to set up the industry-level variables in an international study based on North America data?

In some international studies, authors usually use the industry-level in North America (US and Canada) to control for all-even non-North American-countries. I am quite confused about how to do that in ...
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0answers
22 views

Python Libraries for candle stick analysis

I'm a complete newbie to technical analysis so please forgive the rookie question. I'm looking for python libraries that can classify different types of candle sticks and maybe even provide some ...
1
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1answer
26 views

Replicating Portfolio / Complete Market / Attainable Claim

Attempt So Far: 1) First Part: I have shown that the market is arbitrage-free since the only possible portfolio for which $V_1^h\geq0 \ $ given that $V_0^h=0 \ $ is $h=(0,0,0)$ and this clearly ...
1
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0answers
24 views

Feynman-Kac representation of Black-Cox model

Consider the standard setup from Black and Cox (1976, Journal of Finance). A firm issues a defaultable coupon bond to finance a productive asset that follows a geometric brownian motion: $$dx_t = \mu ...
0
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0answers
49 views

Optimise the Sharpe ratio of a portfolio of uncorrelated assets

Given a portfolio of $n$ assets, mean returns vector $\mu$, covariance matrix $K$, one can calculate the portfolio weights $w^*$ that maximise the portfolio Sharpe ratio, by solving: $$w^*=\text{...
0
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0answers
22 views

Tracking error contribution due to exchange rate

Given a fund in currency A, and a benchmark in currency B, in order to calculate the tracking error I am applying the exchange rate so that the benchmark and the fund are expressed in the same ...
3
votes
1answer
107 views

EGARCH(1,1) mean

I'm trying to model an EGARCH(1,1). However, I dont understand why the mean from the general to (1,1) becomes $\sqrt{(\frac{2}{\pi})}$. The following I am refering to is:
1
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1answer
26 views

What about autocorrelation and heteroskedasticity in Fama French?

I am analysing ESG and conventional mutual funds. I decided to measure the extra performance of each category using the Fama French 4 factor model, but it seems to me that in previous literature they ...
2
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2answers
239 views

Risk-neutral Probability, Risk-Adjusted Returns & Risk Aversion

When we employ the Fundamental Theorem of Asset Pricing and the existence of an equivalent probability measure, say $Q$ with respect to the historical probability $P$, we often say the expectation ...
0
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1answer
29 views

Black-Litterman model with only positive weights

I'm trying to realize Black-Litterman Model for my stocks portfolio, but under optimization, I get a subset of weights with negative values. I want to get only positive weights. IS it possible to add ...
3
votes
2answers
80 views

EPE for interest rate swap

Hey how to calculate Expected positive exposure in the case of interest rate swap? Assume that I simulate $M$ interest rate paths for time grid $0=t_0\le t_1 \le ... \le t_N = T.$ What is the ...
0
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0answers
32 views

Delta calculation [closed]

Can you clarify how delta is usually calculated for non interest rate risk factors (eg FX, equities, etc.)? The two most common methods seem to be these two (relative bump of 1%): a) V(FX*1.01) - V(...
0
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0answers
17 views

Being confused with how the author describe the time frame in a DID setting

Dasgupta,2019,p.2597 said that the treated group comprises all firms that are headquartered in countries that have passed a leniency law by year t. The control group comprises firms in countries that ...
0
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0answers
22 views

Z-spread or asset swap spread - which is a better indicator for bond relative value ? or neither [duplicate]

Z-Spread and asset spread are similar conceptually in the sense that they both measure the difference between the swap and the bond market ? In relative value analysis, which one is a better choice ? ...
0
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0answers
27 views

What would be the ideal way to develop ECL model for startup fintech when there is no historical data

What would be the ideal way to develop the IFRS9 ECL model for startup fintech when there is no historical data.
0
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1answer
32 views

price alignment interest on future contract

why this is no PAI (price alignment interest) on a future contact like cleared swaps have? Am I right that you may get interest from your margin account, but you do not need to pay the interest back ...
1
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0answers
40 views

How to backtest with fixed-income instruments

I'm running a backtest with the 5-yr and the 30-yr treasury bills going back to 1990, both with a weighting of 25%. How do I use their daily yields to adjust the portfolio through time? I've thought ...
4
votes
1answer
140 views

Covariance of two Brownian Motions

During revision, I came across the following question in a past paper: Suppose $(B_t, t\geq0)$ is a standard Brownian motion. Compute for $0<s<t$ the covariance $$cov(tB_{3t}-B_{2t}+5, B_s-1).$$ ...
0
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3answers
97 views

List of Option Payoffs [closed]

Does anyone know of a good resource which lists all commonly used options together with their payoff functions? I'm specifically interested in non-path-dependent options.
0
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0answers
20 views

SEC Ownership Filings (3,4,5), how are dead Insiders reported? [closed]

I recently looked into 3,4 and 5 filings on the sec, they are basically required when insiders (CEO’s, Officers, 10% owners, …) purchase stocks or derivates of their company. These documents are ...
1
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1answer
33 views

Dividend Discount Model for a stock and its derivatives

This might be a bit basic but I've found this question and I'm definitely over-thinking it and now I've just completely confused myself. I'm just looking for some clarification. I've been given the ...
1
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0answers
58 views

Index CDS Option (Spread Quoted) - Black's Formula

I have looked at the question and answers here and I have read Chapter 11 of Dominic O'Kane's book Modelling Single-name and Multi-name Credit Derivatives. The book is very clear and has some in-depth ...
0
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0answers
59 views

How does the break even volatility work in practice?

We know that the break even volatility is given by $$\sqrt{\dfrac{2\Theta}{\Gamma}}.$$ Let's say on day 1 we buy the option with spot = 16.32 and have a net delta of 0, gamma is 0.218, theta = -.001 ...
0
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0answers
15 views

Question about the coverage of Datastream compared to WorldScope regarding US data

Thomson Reuters Datastream is claimed as a very comprehensive data source. I did some comparisons and also conducted research myself and cast doubt on that, especially for US data. I used the paper of ...
5
votes
2answers
295 views

Is SOFR to replace LIBOR or Fed Fund Rate or both

I am a bit confused on what is going on regarding the new benchmark rate SOFR. My understanding is that SOFR is to replace Libor. However, I also get information on Fed fund OIS discounting is ...
0
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0answers
57 views

Expected value of P&L based on option prices

How can we compute the expected value of P&L assuming the option price is given? Do we need to have more information to calculate P&L?
3
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0answers
52 views

Derivation of option pricing PIDE: Why does the drift need to be zero?

I started studying PIDE methods for option pricing and am struggling to understand or find the necessary theory that shows why the PIDE is obtained by the condition that the drift term has to be zero. ...
1
vote
1answer
136 views

How is the formula of Quadratic Variation of Brownian Motion derived? [closed]

This is a follow up on this question on quant SE: The question mentions for a Brownian motion : $X_t = X_0 + \int_0^t\mu ds + \int_0^t\sigma dW_t $ , the quadratic variation is calculated as $dX_t ...
3
votes
2answers
117 views

Covariance between integral of brownian motion and brownian motion

Let $$ I = \int_0^1W_tdt, $$ where $W_t$ is a Brownian motion. From Integral of Brownian motion w.r.t. time we have that $$ \mathbb{E}[I]=0, $$ by Fubini's theorem. And that $$ \mathbb{V}\text{ar}[I] =...
0
votes
2answers
46 views

Factors impacting default risk

Currently I am wondering if there is any link between the default risk of an organisation and it's carbon footprints. Currently there are many regulations coming to address the climate risk most ...
1
vote
3answers
116 views

Future Value: the functions in Excel, Matlab and Numpy Financial don't work when the number of periods is large

The Future Value function and its expected behaviour Excel's function FV(rate, nper, pmt, pv) calculates the future value of an investment based on periodic, ...
3
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1answer
212 views

Market price versus theoretical price of varswaps

When I traded varswaps several years ago, for some indices there was a significant mismatch between market price and theoretical price. The theoretical price assumes continuous monitoring and infinite ...
0
votes
1answer
64 views

A decent model to calculate hedges

Is there an option pricing model that wouldn't be too time consuming to set up in Python (for example) and that would provide better delta hedges than Black-Scholes? This would be mainly for equity ...
0
votes
0answers
27 views

Futures positioning reported by CFTC

How is the net futures position calculated by the CFTC? For instance, GBPUSD net contract is positive in the CFTC report, what does it mean given that for each buyer there is a seller?
-2
votes
0answers
36 views

Buying long dated call options at the bottom of a crash [closed]

Thanks in advance. When the S&P corrects badly, many new people like me may want to buy a call option 2 months out. But isn't volatility high during the crash? If the S&P corrects and heads ...
1
vote
0answers
30 views

How does one explain the negative returns around the event of stock inclusion in DAX indices?

Greetings there friends, I am doing a small research on the effects of the event of inclusion and exclusion of a stock from DAX indices (german indices), to cut the story short, i have downloaded data ...
0
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0answers
20 views

How to calculate Annualized tracking error of an Index fund given daily historical data?

Let's say I have Fund A and Benchmark B and the daily data for both, stretching back 5 years. To find the Annualized Tracking Error (ATE), would this method be correct: Compute percentage change of A'...
1
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0answers
26 views

Pricing a amortizing callable danish mortgage bond using quantlib

I am trying to price a callable fixed rate amortizing danish mortgage bond. since QuantLib only has CallableFixedRateBond i have created a dervived class called <...

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