Questions tagged [finance-mathematics]

The tag has no usage guidance.

105 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
148 views

Why were Laguerre polynomials a good choice of basis functions for American Monte Carlo?

I am implementing LSMC to price American options based on a custom model. I now need to make a choice of basis functions, so I am looking for the theoretical justification for using Laguerre ...
87 views

Where is the Quadratic Variation Coming from in this One-Factor Cheyette Model?

I am having difficulty switching from a general interest rate model (the quasi-gaussian or cheyette model) and a specific version of this model. In particular, I assume the following instantaneous ...
132 views

Characteristic function of the Bates model

I have a misunderstanding concerning the derivation of the SVJ model : Firsty,I understand how to reach the final differential equation from : \begin{gather} dS_t = (r - q - \lambda t (e^{m-\frac{\nu}{...
168 views

Summary of Stochastic Derivatives, Integrals, Expectations, and Variances

I wanted to make a summary table of stochastic functions to improve my understanding. Maybe the following should be a wiki page on this site so others can add functions and examples? Does the ...
50 views

Modeling regulations of middlemen

I am searching for some paper that models the regulations of market makers in stock or OTC markets. Is there anybody who have seen some marekt microstructure paper for modeling regulations and what ...
118 views

Why does risk-neutral price processes do not, in general, compose all arbitrage-free price processes?

I was reading reviewing my mathematical finance notes and I came across a remark I cant understand fully Remark :Contrary to discrete time models, the risk-neutral price processes do not, in general, ...
48 views

53 views

Zero coupon price using Vasiceks model under the Real-world P measure model

I'm wondering if there is a way to work out the formula for the price of the zero-coupon bond using the Vasicek's model (P measure). I have tried to find reference on it but could not, I don't know if ...
56 views

A question in information strucutres and probability measures - How are they connected?

Suppose that $\mathcal{I}=(X,\sigma^{\mathcal{X}},\mu)$ is an information strucutre, which is a probability space, where $X=X^1\times X^2$ is the cartesian product of the individual finite sets of ...
38 views

Equivalence of expectation condition for contingent claims attainable and contingent claims super replicable

We have the following definitions for set of contingent claims attainable and contingent claims super replicable I want to prove the following result How do I show iii $\implies$ ii.I understand ...
61 views

How can you interpret one of the parameters of optimal consumption at the Merton portfolio problem?

Statement: Let the dynamics of wealth of the agent satisfy $$dX_{t} = \pi_tX_t\Big(\mu dt+\sigma dB_{t}\Big)- c_t X_t dt, \qquad \textrm{with}\quad X_0=x_0 \in \mathbb{R},$$ where $(\pi,c)$ is an ...
446 views

Why does the Hurst exponent pseudo code not match the Python implementation?

I am working on understanding the Hurst exponent calculation by Ernest Chan; however, the description of the algorithm does not match the Python implementation. Chan [Algorithmic Trading: Winning ...
77 views

EMA with different resolutions

I am trying to understand something: If I calculate an EMA over 5 days, using the hourly close, I have to go over 5 * 24 points. If I calculate an EMA over 5 days, using the minutes close, I have to ...
59 views

How to calculate the multiple integrals where the integral domain is based on the sum of normal distribution random variables?

The integral is shown below: And how to use python to calculate pi (better if we don't need to code for each pi)?
217 views

Term structure equation in the Vasicek model

Consider the SDE $$dr_t = (b-ar_t)dt +\sigma dW_t, \text{with } a; b > 0.$$ Let $$F(t; r) = E(\exp(-\int_{t}^{T}r_sds)| r_t = r).$$ (F can be interpreted as price of a zero coupon bond with ...
52 views

Transformation of random variables and second-order stochastic dominance

Suppose $X$ and $Y$ are two random variables where $X$ SOSD* $Y$. Let $g(\bullet)$ be a monotonic function and $X'=g(X)$ and $Y'=g(Y)$. Under what conditions of $g$ is $X'$ SOSD $Y'$? I know if $g$ ...
43 views

I ask my question here because I want to know more about the cumulative Parisian options introduced by M. Chesney, Mr. Jeanblanc-Picué and Mr. Yor in 1997, then developed by Hugonnier in 1999 and F. ...
335 views

Pricing caplet with Bachelier (normal dynamic) using forward measure

I'm trying to price caplet with Bachelier under forward measure, but I can't find any solution. Remind that Bachelier assumed rates follow a normal dynamic. So here what I was doing : $C_t(T,T+d)$ ...
213 views

98 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 ...
61 views

Concentration of measure phenomena in financial mathematics

Concentration of measure is a small area of statistics and probability theory that proved inequalities regarding the statistical properties of sets of random variables that exclude one of those random ...
30 views

No Arbitrage condition for assets with different time frame

In the classic literature, one always assumes that the assets in the market are all available from the very beginning ($t=0$). And under such condition the market is arbitrage free iff there exists an ...
70 views

Unique risk neutral measure for jumps or incomplete markets for jumps

I wanted to understand why the market is incomplete in jump-diffusion models. whereas if we have a model following geometric Brownian motion then we can get a risk-neutral measure and hence a complete ...
93 views

Is there a scientific significance to Fibonacci numbers in economics?

I am new to the field and have read popular articles on Fibonacci numbers, but I did not find it grounded in academic research and would love to know if there is a research basis for this and whether ...
87 views

Proof of variance reduction of bagging

In Lecture 4 of the following course: Advances in Financial Machine Learning: 10 Lectures by Marcos Lopez de Prado link in the proof of variance reduction for a ...
99 views

How does negative performance of a portfolio constituent affect its weight?

This is an easy question, I hope. Suppose we have a swap A with a long position, which, originally, has a weight of 30%. Over time, it has a positive performance of 3%, meaning we have a multiplier ...