Questions tagged [finance-mathematics]

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58 views

Advice for senior thesis [closed]

I'd like to get my degree in mathematical finance, or eventually in quantitative finance. Could you give me some (original) ideas, maybe transversal between the two, on which to focus my thesis? ...
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1answer
117 views

Need help with understanding the Mathematical notation in a research paper

Shown below is a snippet from the paper Arbitrage-free SVI volatility surfaces by Jim Gatheral and Antoine Jacquier (2013) (https://arxiv.org/pdf/1204.0646.pdf) . The formulae shown below are on page ...
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2answers
149 views

Utility Function with respect to Quantitative Finance

I am trying to understand utility function and its application in quantitative finance. I have done some preliminary research on the same (have gone through Paul Wilmott on Quantitative Finance) but ...
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2answers
127 views

Forward skew generated by Local Vol model

I'm digging into the properties of the Local Vol model and I become confused with statements made by authors in papers/textbooks (without explanations) like, "The forward skew in local vol model ...
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0answers
21 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 ...
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0answers
57 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 ...
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0answers
40 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 ...
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1answer
70 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 ...
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0answers
80 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 ...
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0answers
81 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 ...
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2answers
103 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{\...
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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 ...
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1answer
38 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 ...
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1answer
53 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, ...
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0answers
89 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 ...
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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 ...
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5answers
348 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 ...
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0answers
113 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 ...
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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 ...
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1answer
75 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 ...
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1answer
47 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 \...
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0answers
30 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 ...
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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 ...
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1answer
37 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 ...
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30 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 ...
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1answer
80 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 ...
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1answer
106 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
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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 ...
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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/...
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0answers
28 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 ...
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1answer
44 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}...
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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 ...
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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)...
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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 ...
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1answer
132 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} × ...
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26 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 ...
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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 ...
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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 ...
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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?
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1answer
69 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 ...
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1answer
83 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
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1answer
172 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 ...
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2answers
136 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 ...
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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 $\...
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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
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1answer
113 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 ...
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1answer
1k 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 ...
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0answers
36 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?
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1answer
105 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
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1answer
68 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

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