Questions tagged [models]
The models tag has no usage guidance.
3
votes
1answer
62 views
Problem at deriving Bachelier formula with interest rates
In the Bachelier model, I have difficulties with a certain step. I want to figure out the distribution of $S_T$, which is the price process in the Bachelier model.
So far I could state that ($\mathbb{...
1
vote
0answers
29 views
Has there been studies done on changes in model performance post-crisis?
My question is, has there been done any studies on whether the efficiency and accuracy of pricing and risk-management of derivatives using different models and algorithms has changed after the ...
0
votes
2answers
55 views
Is it possible to adapt Fama French Model with a 6 factor Model?
I am currently working on my thesis and I was wondering if it was possible to add a new factor to the five model one. This new factor would include the ESG's characteristic of the stock. I would like ...
1
vote
1answer
47 views
CRR model arbitrage free
I'm currently studying this proof
In this proof the author defines a probability measure
$$P^*[\{\omega\}]=(p^*)^{k(\omega)}(1-p^*)^{T-k(\omega)}$$
on
$$\Omega=\{\omega=(y_1,\ldots,y_T)|y_i=\pm1\}$$...
1
vote
1answer
42 views
rationale for maturity adjustment formula in basel IRB formula
For capital requirement, rwa is computed as a product of terms including a K (unexpected losses).
(As shown is the summary from wikipedia :
https://en.m.wikipedia.org/wiki/Advanced_IRB
)
K is ...
2
votes
1answer
98 views
What's the logic behind binomial model ups and downs?
I want to understand what is the underlying logic in the calculation of u and d in a binomial model.
$$
u = \exp\Bigl(\sigma \sqrt{\Delta t} \Bigr), \quad d = \exp\Bigl(-\sigma \sqrt{\Delta t} \Bigr)...
0
votes
1answer
45 views
Sum disappearing when we assume constant some elements to be constant over time [closed]
I have the dividend discount model, which is the following expression:
$$
P_{j,t} = \sum_{\tau=1}^{\infty}D_\tau(1+g)^\tau(1+r)^{-\tau}=\frac{D_{\tau+1}}{r-g}
$$
Where $D_t$, is the dividend at time ...
2
votes
0answers
79 views
Architecture of a global pricing library with immutable payoffs
By global pricing library I mean a library
handling equity, rate etc, hybrid products
having several models (BS, LV, SV, LSV)
having several numerical methods (analytic formula, MC, PDE FD/FE)
I ...
0
votes
1answer
169 views
What is market standard model in equity, FX and interest rates exotics?
Is there any industry consensus about the model to use for pricing exotics in equity, FX and interest rates?
I assume that for vanilla options they all use Black model, but how about exotics?
Also, ...
1
vote
0answers
66 views
Standard GARCH(1,1) model with external regressors
I have a queastion how does a standard GARCH(1,1) model with external regressors in mean and variance euqations look like ?
I know that standard GARCH(1,1) model without external regressors has the ...
1
vote
0answers
62 views
What kind of ARMA-GARCH model is that?
My question is what kind of ARMA-GARCH model is the following equation and how to specify it in rugarch R module:
$$r_{t+1}- r_t = \alpha_0 + \alpha_1r_t+\...
1
vote
1answer
116 views
Good references on Heston Model?
I am looking for good bibliographic references on Heston Model and Stochastic volatility models in general.
Does anyone know any good introductory/intermediate references on this topic?
1
vote
1answer
202 views
Natural Gas Modelling
In job adverts for natural gas/power trading it states knowledge of supply and demands models for these commodities. Does anyone know of any good papers or primers on S&D modelling?
1
vote
0answers
31 views
Determining the Relationship Between Monte Carlo Breaks and Model Volatility
I'm looking for a statistical test to understand the relationship (if any) between the model volatilities of a stochastic process, and the occurrence of 'break', defined as the instance when an ...
0
votes
1answer
77 views
Spreadlock derivatives
I would like to price a spreadlock forward swap and a spreadlock swaption but I don't find in the web any research article. Would you please provide me with some freely accessible papers on the web ? ...
0
votes
1answer
63 views
Single Model Accuracy Estimation
I'm working on a model to estimate CDS prices, and want to backtest it against a historical timeseries. What are some error/goodness of fit measures that I can use for this purpose outside of RMSE?
I'...
0
votes
1answer
82 views
different Z-spreads for a same company
A same company has two different bonds.
I expected the Z-spread to be close for both bonds (since my representation of the Z-spread is the spread due to credit-risk proper to the company).
Here is an ...
1
vote
3answers
134 views
Besides arbitrage opportunities, are there other properties that real world markets cannot have
The article "What is ... a Free Lunch?" nicely explains why market models with arbitrage opportunity are unlikely to describe financial markets of the real world.
Are there other properties of ...
3
votes
1answer
304 views
Scaling (Data prep) & Feature selection for the financial Data for LSTM Models
Overview
I'm training an index e.g. FTSE100, where I have 8 years of past data (daily). I also have a list of its constituents.
For each stock, I have the following features:
...
1
vote
0answers
133 views
Proof positiveness condition CIR dynamic
Ciao All.
I'm studying the CIR model and this question came out.
Usually the Ornstein-Uhnlenbeck dynamic is used to build the CIR model:
let
$$
dX_t = aX_t + \sigma dW_t
$$
where $a \in \mathbb{R}$ ...
5
votes
2answers
694 views
What is model-free finance?
I have run across the term "model-free finance" (e.g. there was a Thalesian talk in London recently), yet haven't found any real definition of it nor anything really substantial.
Could you point me ...
5
votes
1answer
150 views
Are processes with independent increments (which are not Lévy) used in finance?
From Jacod and Shiryaev's Limit Theorems for Stochastic Processes, we get the following definitions.
Definitions:
A process with independent increments (abbreviated PII) $X = (X_t)_{t \geq 0}$ on a ...
1
vote
1answer
72 views
Use of fBm when $H<1/2$
Let H be the Hurst parameter of the Fractional Brownian Motion. Are there any useful areas in mathematical finance where the fractional brownian motion with H<1/2 is used? From all the articles I ...
0
votes
1answer
302 views
Short-Interest Rates Models - Geometric Brownian Motion?
in a paper of Brennon&Schwartz (1977), they model embedded bond options by using an stochastic interest rate model which follows a geometric Brownian Motion.
Now they claim that this assumption ...
6
votes
2answers
709 views
What are the significant implications of the long-run average variance rate and why Engle won the Nobel Prize for ARCH model development?
In a ARCH(m) model we have
$$
\sigma_n^2=\sum_{i=1}^{m} \alpha_i u_{n-i}^2
$$
where $u_i$ is defined as the continuously compounded return during day $i$ (between the end of day $i-1$ and the end of ...
3
votes
1answer
280 views
Relation between price changes and trading volume (market impact)
It is quite a well-know phenomenon that trading volume has an impact on a stock price: the more you buy the higher is a price because of demand increment. I'm wondering about models that can describe ...
3
votes
0answers
96 views
VAR models when examining relationships between financial markets
When researchers examine lead-lag relationships between credit default swaps and (as an example) stock markets, many use Vector Autoregressive Models (VAR). They want to find out what market "is ...
3
votes
0answers
88 views
Electricity Prices: Change of measure in practice
I'm working on a model of electricity prices. I have empirical data $X(t)$ and managed to find a reasonable fit given by a Levy process $\hat{X}(t)$. I understand in theory what a risk-neutral ...
1
vote
1answer
162 views
Why change numeraire for the LIBOR Market Model
There are two form of LIBOR Market Model that has a drift introduced. I would like to know in plain english explanation why do practitioners use these changes of measure. Are there any significance to ...
1
vote
1answer
118 views
How to compute the Value-at-Risk of an equity portfolio hedged using futures contracts?
I would like to have your opinions about how to calculate the VaR of a hedged portfolio using futures contracts.
I have tried several "black box" softwares and none of them make too much sense. The ...
1
vote
1answer
255 views
Use of ACD to model transaction durations
I am using a simple ACD (autoregressive conditional duration) model with expoential or Burr distributed residuals and 1 lag, i.e. ACD(1,1).
I am modelling durations for transactions data on a 'medium'...
0
votes
0answers
37 views
What is the whole list of assumption that Ho Lee model was under?
What is the whole list of assumption that Ho Lee model was under?
Please briefly describe how was each assumption match the real world finance/economics applications so that it shows how the model ...
8
votes
2answers
359 views
Confusion with volatility smiles implied by different models
I am reading a book "The concepts and practice of mathematical finance" by Mark Joshi. In Chapter 18 he discusses the shapes and dynamics of smiles under different models. I do not understand what is ...
1
vote
0answers
278 views
Basel Basic CVA Approach Model Foundations
I am working on CVA (credit valuation adjustments). The Basel committee released consultative document reviewing the CVA Risk Framework 'Review of the Credit Valuation Adjustment Risk Framework (2015)'...
0
votes
2answers
102 views
Model which fully incorporate OHLC data (higl ald low also)
OHLC data are one of the most popular kind of data available.
Are there models which could incorporate all the information provided by OHLC - regular 1-minute frequency data for example ? Usually only ...
2
votes
1answer
188 views
Mix of Arithmetic and Geometric Brownian Motion
Talking with some traders the other day, I found out that they were using a pricing model based on a mix between a geometric brownian motion and an arithmetic brownian motion to price certain ...
2
votes
1answer
114 views
Help understanding factor modeling, solving for residuals
I am trying to understand and implement a factor model, and I think I might be having some issues. I am trying to solve for the residuals in the equation:
$$
R_{i} = \sum_{A=1}^{K}\beta_{iA} f_{A} + ...
30
votes
5answers
5k views
Why aren't econometric models used more in Quant Finance?
There is a big body of literature on econometric models like ARIMA, ARIMAX or VAR. Yet to the best of my knowledge practically nobody is making use of that in Quantitative Finance. Yes, there is a ...
2
votes
1answer
187 views
Loss given default for Agency MBS
The question is regarding the LGD of Agency MBS. Although Agencies never defaulted, the Basel framework requires to calculate the Agency MBS LGD for capital requirement. The closest benchmark I can ...
1
vote
0answers
169 views
How to perofrm a simple GARCH simulation example?
How is it possible to simulate one million of tick data for, say EUR-USD price, using a GARCH model?
For example, how do I simulate $X_i$ for $i = 1 \dots 1000000$, with
$\text{mean}(X)=X_0 \...
5
votes
2answers
285 views
How to derive this approximation of the risk-neutral expectation of the variance?
On the paper Bollerslev, Tauchen and Zhou (2009 RFS) the authors say about equation (15):
The corresponding model implied risk-neutral conditional expectation
$$E^Q_t(\sigma^2_{r,t+1})=E_t(\sigma^...
0
votes
1answer
94 views
Motivation: Stochastic Interest rate model
what is a reason that someone might be interested in a stochastic-interest model such as the Chen model?
Also can you provide me with a link to an easy to read motivational paper/part of a paper on ...
0
votes
1answer
107 views
Why is the forward rate used for the underlying in Black's model?
Why is the forward rate suitable for being used as the underlying in Black's model?
Thanks
12
votes
3answers
833 views
Validating a Credit Scoring Model without Data
Fellow Quants,
Suppose you have a credit scoring model that is developed without the aid of statistics, because (unfortunately) there is no historical default/loss data in your portfolio. The ...
-1
votes
1answer
135 views
Where can I find data source for structural models?
I am starting a project to implement the Black-Merton-Scholes model from this book in R.
However, I am looking for, ideally free, data sources. Still I have access to a Bloomberg terminal.
Can you ...
8
votes
2answers
2k views
KMV-Merton Probabilties of Default vs Moody's EDF
Moody's used to publish probability of default estimates from their Moody's EDF model, but they have temporarily discontinued it. I understand that the Moody's EDF model is closely based on the Merton ...
2
votes
0answers
37 views
Specifying integration level of time series [closed]
Following model was estimated on 200 observations. How to specify the level of integration of $X_t?$ In brackets there are standard errors and p-value of Breusch-Godfrey test is also shown.
$X_t=0,02+...
5
votes
2answers
764 views
Ideas about Stochastic volatility models
I am currently working on comparing different models for modelling the volatility and then pricing vanilla options (I use option prices on real stocks in order to calibrate my models and then I ...
1
vote
0answers
592 views
PDE vs TREE vs MC vs Analytical
One what basis the pricing model can be differentiated for particular trade pricing. For exapmle why PDE or Binomial tree or MC or Analytical method will be consider for pricing any trade.
Question ...
3
votes
3answers
158 views
Parameters variation in fundraising financial model
I have created quite a large financial model in Excel with lots of input parameters which (after all calculations) have an influence on the output business indicators.
Among the input parameters are
...
