Questions tagged [models]
The models tag has no usage guidance.
125
questions
0
votes
0answers
24 views
swap discrete market model
Let be $M = (S_0,E,\Phi)$ a market where the risk-free rate is $r = 0$ and the Euribor $E$ evolves (annually) in discrete time following a three-period binomial model. Assume that $E_0 = 0.031$, the ...
0
votes
0answers
28 views
How to model the different returns of agents with different information information
For a seminar, I would like to graphically represent the returns made by agents of different information standpoints. In other words, say I have a market tuple $(\Omega, \mathbb{F}, P,S)$ where $S$ is ...
0
votes
0answers
52 views
How does modeling provide an edge to banks in the derivatives space?
I was thinking about the actual need for creating quantitative financial models, especially for derivative products. Consider simple calls and puts for different strikes and expiries on stocks and ...
2
votes
2answers
83 views
Does the non-causal nature of quant models limit their applicability?
I understand that to describe financial data, we build stochastic models and calibrate their parameters to past data. When coming up with new algorithms, we rely on rigorous backtesting to convince ...
3
votes
1answer
69 views
Are Lévy processes absolutely continuous?
If $X_t$ is a Lévy process, is it absolutely continuous? Meaning, does it have a density?
1
vote
1answer
46 views
Which models have non-smooth densities?
By smooth, I mean a density $f$ that lies in the space $C^\infty$, infinitely differentiable.
Are there, in the literature, some known models where the underlying density of the state process is non-...
1
vote
0answers
38 views
Real world interest rate models for pension funds
Which interest rate models are used by pension funds for their real world projections / ALM models? The life-insurance sector is using often variants of LMM or Black-Karasinski, but I am wondering if ...
1
vote
1answer
52 views
CEV Model Primer
Could someone please point out to a good primer on CEV model?
I am trying to get a basic grasp of the model: The dynamics, advantages & disadvantages, for which payoff it is usually used (Hybrid ...
0
votes
2answers
70 views
How and why is there a restriction on short sales?
I'm taking a course on the fundamentals of financial mathematics. This is my first quantitative finance course, so I'm still getting acquainted with a lot of the ideas.
We covered the notion of a ...
1
vote
2answers
115 views
Are densities used in finance square integrable?
Let $f$ be the density of the stock asset under some model (Heston, SABR, Black Scholes, Variance-Gamma, etc).
Is $f$ square-integrable in these models?
1
vote
1answer
172 views
Vasicek Model Parameters Estimation
I'm currently trying to estimate the market price of risk (lambda) in the Vasicek Model, and am running into difficulties.
Using the Excel Solver tool and the Maximum Likelihood Estimation method ...
4
votes
0answers
184 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
vote
1answer
89 views
Proper Data Partitioning For Building a Forecasting Model
Goal: A team and I are looking to build a model that performs a predictive action for the state of the market on day T + n, using the data at hand on day ...
1
vote
1answer
44 views
Understanding Walter's Dividend Policy Model
I'm trying to understand the justification for the mathematical formulation of the Walter model (1956), which provides an equation for the price of a stock based on present value of dividends and ...
1
vote
0answers
54 views
Calibrate an HJM model in a multicurve setup
I am a mathematician and I'm working on my thesis on Financial Mathematics.
I studied this model HJM in a multicurve setup:
$$
\begin{cases}
df(t,T)=a(t,T)dt+\sigma(t,T)dW_t & (\mbox{rik-free})\...
1
vote
0answers
73 views
Is there a good book/blog on applying statistical methods in finance? [closed]
I am learning a lot of tools in statistics, but I am having a hard time figuring out where I could apply these methods in finance, especially in relation to investment and trading.
Is there a good ...
4
votes
1answer
53 views
Negatively Correlated Assets with similar medium-term trends
Theoretically, one could have stock prices with returns $\rho_1(k)$ and $\rho_2(k)$ having mean values $\mu_1$ and $\mu_2$, but still be negatively correlated with
$$
\mathbb{E}[(\rho_1(k)-\mu_1)(\...
2
votes
0answers
65 views
What model do market makers in equity derivatives commonly use to price, hedge, and fit the IV surface?
What is the industry standard/common model used by market makers in equity derivatives to trade across the IV surface?
1
vote
0answers
31 views
Free DCF model database
Over the years, I have accumulated quite a few DCF models (some are my own and some are from others). I am wondering if there is any website where I can upload mine and download those of others so ...
0
votes
0answers
51 views
looking for a simple realistic parametric volatility model
Which parametric volatility is realistic to test quickly and qualitatively a model?
I do not wish to fit market quotes but would like to have a non-trivial volatility with skew or smile to do some MC ...
0
votes
0answers
57 views
8
votes
2answers
511 views
Interest Rate Models cheat sheet - Need for advice
I'm trying to get through the litterature of interest rate models for some time now. As I don't have any experience working with them, I started looking for some kind of a cheat sheet that would ...
3
votes
1answer
141 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
158 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
59 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
314 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
113 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.
$$
u = \exp\Bigl(\sigma \sqrt{\Delta t} \Bigr), \quad d = \exp\Bigl(-\sigma \sqrt{\Delta t} \Bigr)...
0
votes
1answer
46 views
Sum disappearing when we assume constant some elements to be constant over time [closed]
I have the dividend discount model, which is the following expression:
$$
P_{j,t} = \sum_{\tau=1}^{\infty}D_\tau(1+g)^\tau(1+r)^{-\tau}=\frac{D_{\tau+1}}{r-g}
$$
Where $D_t$, is the dividend at time ...
2
votes
0answers
126 views
Architecture of a global pricing library with immutable payoffs
By global pricing library I mean a library
handling equity, rate etc, hybrid products
having several models (BS, LV, SV, LSV)
having several numerical methods (analytic formula, MC, PDE FD/FE)
I ...
1
vote
1answer
395 views
What is market standard model in equity, FX and interest rates exotics?
Is there any industry consensus about the model to use for pricing exotics in equity, FX and interest rates?
I assume that for vanilla options they all use Black model, but how about exotics?
Also, ...
2
votes
1answer
146 views
Standard GARCH(1,1) model with external regressors
I have a queastion how does a standard GARCH(1,1) model with external regressors in mean and variance euqations look like ?
I know that standard GARCH(1,1) model without external regressors has the ...
1
vote
0answers
66 views
What kind of ARMA-GARCH model is that?
My question is what kind of ARMA-GARCH model is the following equation and how to specify it in rugarch R module:
$$r_{t+1}- r_t = \alpha_0 + \alpha_1r_t+\...
1
vote
1answer
184 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
250 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
33 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
135 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
84 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
98 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
145 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
369 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
250 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
747 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
157 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
80 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
380 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
825 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
306 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
99 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
92 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 ...
