Questions tagged [finance-mathematics]
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321
questions
2
votes
0answers
49 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 ...
1
vote
0answers
37 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 ...
0
votes
1answer
69 views
How can we unwind a Index ( SPX ) Variance swap?
Client A comes to dealer to trade variance notional $1m at T=0. The trade is executed with dealer short volatility with strike of 20.
term Payoff of dealer = notional*( Stike^2 - realized vol^2 )
now ...
1
vote
0answers
79 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 ...
1
vote
0answers
80 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 ...
1
vote
2answers
97 views
May someone please explain the intuition behind the Black-Scholes Equation?
Consider the Black-Scholes equation for a European Call Option,
\begin{equation}
\begin{cases}\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + r\frac{\...
0
votes
0answers
10 views
Derive the equilibrium of the economy Arrow Debreu Economy
Consider a competitive financial economy with two securities and two dates, i.e. date 0 and date 1. There is only one commodity (consumption good), and consumption takes place only at date 1, while ...
0
votes
1answer
31 views
How does Linear-Exponential Loss (Linex) function tend towards Quadratic Loss function?
Thank you for your help everyone, and I apologise beforehand if this is a lousy or dumb question.
I am looking to read up more on Quadratic Loss & Linex Loss, and forecast optimality.
In my ...
0
votes
1answer
51 views
Expected return rate greater than required return rate
I am a beginner to finance, today I found a question looks very simple that I am not quite sure about it.
Question: Given I am paid \$50,000 now, growing at $6\%$ per year for a total of 10 years, ...
1
vote
0answers
88 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 ...
0
votes
0answers
24 views
CIR from the summation of Ornstein–Uhlenbeck processes with different parameters?
Here I see how the CIR developed from OU s with the same parameters. I wonder how the solution will change if we are adding squared of OU processes with different parameters? In this proof, it is ...
5
votes
5answers
324 views
Quantitative finance for physicists
I am looking for good books to learn quantitative finance. As I have strong background in physics, I would appreciate introductions that do not hesitate to show the equations, but in the same time ...
1
vote
0answers
112 views
Dynamic programming and Bellman equation to obtain the maximum
This is the problem of Marhsall (1992) "Inflation and Asset Returns in a Monetary Economy" and Balvers and Huang (2009) "Money and the C-CAPM"
Suppose an endowment economy where the representative ...
4
votes
0answers
46 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 ...
2
votes
1answer
71 views
yield curve basics
Suppose we observe the following term structure (of annualised spot rates):
0-3 Months $\rightarrow$ 4.0%.
0-6 Months $\rightarrow$ 4.2%.
0-9 Months $\rightarrow$ 4.4%.
Question1) How can we ...
1
vote
1answer
42 views
Why are the risk neutral probabilities constant in the Cox Rubinstein model when delta needs to be changed at each time step
Consider the Cox Rubinstein binomial pricing model with N steps, with stock price change given by parameters u and d so that at step $i$ we have $S_{i+1} = uS_{i}$ or $S_{i+1} = dS_{i}$ with $0\leq i \...
1
vote
0answers
29 views
Excel rate function with nper as decimal returns unexpected result [closed]
I set up a simple problem
Payment after 0.4 year is 25. The rate is 10%. I calculated PV as $\frac{25}{(1+10\%)^{0.4}} = 24.77$
Then I did Rate(0.4,25,-24.77,0) in ...
0
votes
0answers
31 views
Stock returns: Exponential time decay
I am replicating some research that uses two years of single stock returns (i.e. N= 250*2= 500) and then applies an exponential decay with a half-life of one year to these returns.
Does this mean ...
0
votes
0answers
19 views
Contingent Claim Bounds
In my course on discrete-time finance we derived the following equality for a lower bound for the value of a not necessarily replicable contingent claim $D$. Here we are looking at a single period ...
0
votes
0answers
28 views
How to find the derivative for a multi-factor geometric brownian motion model
Does anyone know how to find the derivative for a multi-factor geometric brownian motion model $ \frac { dS_{i}}{S_{i}} $. I have seen solutions for the standard GBM model however I suspect that the ...
0
votes
1answer
76 views
Stochastic Interest Rates in Option pricing
My lecturer has written the slide below. The function B^T(t) is a zero coupon bond. I don't understand how V(t) can be a negative integral from 0 to ...
1
vote
1answer
99 views
Relation of risk-neutral probability measures to arbitrage opportunities
Could someone describe how risk-neutral probability measures are linked to arbitrage opportunities and also to whether or not a market is complete? I've been asked this question and am unsure how to ...
2
votes
1answer
35 views
How can I convert rolling annual returns back to quarterly returns?
I have a series of rolling annual returns and would like to convert these back to quarterly returns, which have not been provided. Is this possible formulaically, or is something like Excel's solver ...
-2
votes
2answers
80 views
What the … are all of you studying/working for asking such questions? [closed]
Sry, I'm new here. But I am just astonished by all those sick questions and answers you ask/provide... Are most of you studying mathematics or are your finance programs that good, that you can ask/...
0
votes
0answers
25 views
Linear programming and minimum cost network flows vs nonlinear and discrete optimization
At my college I have an option: To take either of these two classes. My intended career pathway is into quantitative finance and I wanted to know which one would have more use as a quant.
Here is the ...
0
votes
1answer
41 views
Radon-Nikodim Derivative at time 0
I have a very basic question about filtrations and Radon-Nikodym derivatives. I am reading the Andersen-Piterbarg, more in particular Eq. (1.12). They define the process $\zeta(t) = E^P_t[\frac{dQ}{dP}...
0
votes
0answers
45 views
Mutual fund theorem
Theorem (Mutual fund theorem in the case that there is one risk-less asset and at least one risky asset). Suppose that all preced- ing assumptions in this subsection are valid. Consider the constant ...
1
vote
1answer
34 views
The NA price of a caplet with payoff
Prove the following statement:
The NA price of a caplet with payoff
$$\delta \cdot (L(T;T,T+\delta)-k)^{+} $$
at time $T+\delta$ equals the NA price of a put option with the payoff
$$(1+\delta \cdot k)...
0
votes
0answers
32 views
Question about financial mathematics, meeting a claim
I have a question regarding exercise 12, chapter 1 of "A course in Financial Calculus" by Alison Etheridge. It is as follows:
"Suppose that the value of a certain stock at time $T$ is a random ...
1
vote
1answer
101 views
Where does the 50.14348112 coefficent in the US Dollar Index formula come from?
The formula for the US Dollar Index (DXY) that every resource on the internet provides is:
$$DXY = 50.14348112 × EURUSD^{-0.576} × USDJPY^{0.136} × GBPUSD^{-0.119} × USDCAD^{0.091} × USDSEK^{0.042} × ...
0
votes
0answers
25 views
Calculate percentage change within sliding window
i have aggregated minute OHLC data and looking to find large percentage changes of y% within a sliding time window of t for the close value - for example a change of 4% within 15 minutes would be the ...
1
vote
1answer
75 views
Integrable cumulative income process
I am trying to read Karatzas/Shreve "Methods of Mathematical Finance". In ch. 1, Definition 5.5, a cumulative income process $\Gamma(t)=\Gamma^{\mathrm{fv}}(t)+\Gamma^\mathrm{lm}(t)$ (a semimartingale ...
2
votes
1answer
102 views
Rigorous proof that volatility target strategies actually tend to the target
I'm working on a paper about volatility timing and target strategies, practical implementation included.
While writing down the mathematical description of the model I wanted to include a rigorous ...
0
votes
0answers
17 views
How to calculate the revenue yield?
Origination fee is charged as 3.0 % of average funded loan size. How to calculate the revenue yield in the table below?
0
votes
1answer
66 views
What is the R code for estimating copula parameters of BB1 with dim=2? And what's the code for gof test of BB1?
Kindly assist with R code for BB1 copula. Text books and research articles provide codes for clayton, gumbel, frank, normal and t copulas. However, I can't find code for BB1.
For example, this is ...
0
votes
1answer
80 views
Boyles Model for Trinomial Tree
I know that the risk neutral probabilities in Boyle's Model for the Trinomial Tree by recombining where
$m=1, u.d=1$ and $u=e^{\lambda\sigma \Delta t}$
$p_u=\frac{u(V+M^2-M)-(M-1)}{(u^2-1)(u-1)}$
...
1
vote
1answer
152 views
Throwing a dice and risk neutral probability
Consider the game of throwing a "fair" dice. Not sure if the answer is obvious but is there any proof (e.g. replication argument) that under the risk neutral measure the probability of any outcome is ...
0
votes
2answers
131 views
Option pricing without analytical solutions
I am quite new to the topic of financial options. I'm aware of options with analytical solutions (e.g. European options in Black-Scholes and Ornstein-Uhlenbeck models). I read that sometimes (most ...
1
vote
0answers
48 views
Equilibrium with H agents when some of them are not aware of some assets
Assume there are H agents with constant absolute risk aversion $\alpha$. There is a risk-free asset, and two risky assets with distribution $S1$ ~ $N(\mu; \Sigma)$, where $\mu \in \mathbb{R}^2$ and $\...
0
votes
0answers
29 views
Yearly Performance of US Mutual Funds
Does anyone if there is a dataset, possibly free, that has data on the historical performance of US mutual funds? It would be fantastic if it also includes their fee structure also.
Thanks!
3
votes
1answer
111 views
Why sub-replication is not studied in literature
There are numerous paper about super-hedging and super-replication in an incomplete market where the risk neutral measures are not unique. The most fundamental result is that the super-replication ...
0
votes
1answer
853 views
Forward Contract Price on Zero Coupon Bond
I'm trying to calculate the forward contract on a zero coupon bond where the forward contract matures at t=4.
The zero coupon bond matures at t=10 and has a face value of 100. The price of that bond ...
1
vote
0answers
35 views
Information asymmetry models
I am searching for some textbook in financial mathematics that presents information asymmetry models (maybe more advanced models), so as to make some practice. Does anbody know such a book?
1
vote
1answer
103 views
What is the SDE of this equation? [closed]
I am new and struggling to understand how to solve this using Ito lemma.
Can someone please explain it to me:
$$dS_t=-\frac{1}{2}\sigma^2 S_t dW_t$$
what is the solution with explanation please
0
votes
1answer
62 views
What is Variance of delta of brownian motion [closed]
I am new to this.
If variance of Brownian motion b is t, what is the variance of db?
db is delta of b
0
votes
1answer
100 views
Constructing an arbitrage opportunity for a company involving Forwards
Let's say an investor enters a long forward contract on 100 units of underlying assets $S$ and maturity $T$ = 4 years. The asset $S$ pays no dividends and the spot price of one asset is $S_0$ = £5. ...
0
votes
0answers
41 views
Classical Ruin Theory - Lundberg Model
In classical risk/ ruin theory, I see this formula crop up in my notes but my lecturer didn't explain to me why/ when it's employed:
$M_X(r) = \int_{-\infty}^{\infty} e^{rx} f(x) dx$
I understand ...
1
vote
1answer
107 views
Using the call option to solve this linear program
Hello I have to do a project for a finance class and the Professor has given us the following problem. I'm not a finance student and am just now being introduced to the subject. I do not understand ...
0
votes
0answers
15 views
Future wealth calculation with investment
Task: The student is 25 years old now. He say, that next year his salary will be 15000€ per year. His salary will grow +5% each year until his pension (when he will be 65 years old). Calculate how ...
0
votes
2answers
69 views
Interest rate calculation [closed]
The task: With what interest rate given 2000 Euros after 2 years and 3000 Euros after 4 years, the actual value will be equal 4000 Euros.
This task sounds confusing for me, I tried to calculate, but ...
