Skip to main content

Questions tagged [finance-mathematics]

Financial mathematics, or mathematical finance, is a set of mathematical tools allowing to express use cases on financial markets a way that can (or could) be solved using mathematics.

Filter by
Sorted by
Tagged with
1 vote
0 answers
26 views

Showing a basic market admits no arbitrage

I'm learning the fundamentals of financial mathematics and came across the following problem I cannot solve Setting We work in $\left(\Omega, \mathcal{F},\left(\mathcal{F}_t\right)_{t=0}^1, \mathbb{P}\...
portero's user avatar
  • 11
1 vote
0 answers
72 views

Learning resources - Any good websites for learning about quantitative finance with a focus on the underlying mathematics? [closed]

Typically when I have ventured into a new subject in my sparetime, I have been able to find an interactive website with reading materials, exercises and the like. To name a few there is https://...
BurgerMan's user avatar
4 votes
1 answer
71 views

What are the downsides of using Kim's integral equation (1990) to determine the exercise boundary of an American option?

I'm new to the industry and trying to wrap my head around American options pricing. The integral equation(1) from Kim (1990) doesn't seem to make any strong assumptions, and approximating the integral ...
Eashan Gandotra's user avatar
0 votes
1 answer
53 views

Possibility of obtaining a positive mathematical expectation in a quoted currency

There is a currency pair C/USD = 1. C - currency in which I want to invest in order to make a profit in USD. Suppose its price changes discretely: 50% - increases by 20%, 50% - decreases by 20%. This ...
Randomuser's user avatar
0 votes
1 answer
104 views

Can someone please help me answer this question about Black-Scholes model? (risk-neutral & true probability of the call option) [closed]

I don't even know where to get started with this question...can someone please help me? How do I answer it?
Jolie's user avatar
  • 1
1 vote
2 answers
141 views

Is this arbitrage? Infinite payoff / infinite loss (energy generation investment problem)

I'm a student using stochastic optimization in energy systems and I have a particular phenomena in an optimization problem that I think must occur in finance aswell, so I have been trying to find ...
waxcomb's user avatar
  • 11
0 votes
1 answer
68 views

Two-period binomial model probability question

I have started to work with given two period binomial model S(0)=100 u=1.25 d=0.8 r=0.05 and the market probability of stock going up each period is p=0.55. I am trying to calculate two probabilities; ...
mva's user avatar
  • 3
0 votes
0 answers
39 views

IFRS 9 - Amortized cost - Daily or Annual EIR

Let's consider a scenario where a bank issued a loan of USD 80,000 at some point in 2022 and expects to receive USD 17,809.33 in interest and the 80k on October 9, 2023. The Effective Interest Rate (...
user70927's user avatar
0 votes
0 answers
47 views

Cost of debenture using IRR method

Question: A company issued $10000$, $10\%$ debentures of $\\\$100$ each on 1.4.2020 to be matured on 1.4.2025. Market price of the debenture is $\\\$80$. Tax rate is $35\%$. Then what would be the ...
Hmmmmm's user avatar
  • 101
0 votes
1 answer
191 views

Breaking down gamma PnL by time

Let's say in one day time, underlying price S goes up by $2.4. Then the gamma PnL should be $\frac{1}{2}\gamma_0 (2.4)^2$. Let's assume that in every hour the underlying goes up by $0.1. Then how do ...
crr1210's user avatar
1 vote
0 answers
62 views

How to solve for Kyle's $\lambda$ that emerges in the demand functions of the informed and uninformed traders in the $1989$ model?

I will restate here a problem that I am finding a bit difficult to solve and I have already posted here. I summarized the problem as it follows. From Albert S. Kyle's 1989 model. Suppose that the are ...
Oliver Queen's user avatar
1 vote
1 answer
148 views

Option pricing under distribution assumption

For simplicity assume zero interest rates in the following. Given the price of a (European) put option with strike K and maturity T at time point t. $P_t(K, T)$ for a given underlying S with values $...
MrLCh's user avatar
  • 121
0 votes
1 answer
119 views

Fama-French Regression Output Interpretation (Intercept/Alpha)

I am currently doing a report regarding Fama and French 3 and 5 factors model. I was provided 3 companies with each of its daily stock return from 2015-2020, and the values of all 5 factors during ...
NewbieFinance's user avatar
0 votes
1 answer
58 views

Is sorting stocks into portfolio mandatory in Fama-French model?

I am currently doing a report regarding Fama and French 3 and 5 factors model. I was provided 3 companies with each of its daily stock return from 2015-2020, and the values of all 5 factors during ...
NewbieFinance's user avatar
0 votes
1 answer
170 views

How to calculate VaR given mean and sd?

Sarah manages a hedge fund with a portfolio valued at \$2,000,000. The portfolio's daily returns have a standard deviation of \$3,000 and an average daily return of \$1,200. Calculate the five-day VAR ...
Ankita Datta's user avatar
0 votes
0 answers
35 views

Standard practice to round values in ARM loans

I have an application that calculates payments schedule of ARM (Adjustable Rate Mortgage) loans, where these loans are in the books of commercial banks. It seems to work fine, with the exception of ...
ps0604's user avatar
  • 50
0 votes
0 answers
44 views

Estimating implied probability based on prediction betting odds

I am attempting to estimate prediction betting market efficiency for a project, and I am hoping for assistance with a couple of questions. The prediction market makers add a commission to the betting ...
findingmyway's user avatar
0 votes
0 answers
158 views

Straddle Approximation - Directly from Integral

The ATMF straddle approximation formula, given by $V_\text{Str}(S, T) \approx \sqrt{\frac{2}{\pi}} S_0 \sigma \sqrt{T}$ where $S_0$ is the current underlying spot price, $T$ is the time remaining ...
aarongroff's user avatar
0 votes
0 answers
69 views

Machine learning techniques for small datasets

I am dealing with financial data which is available on a Monthly basis. I am planning to apply machine learning techniques like LSTM but issue here is that overall I have very limited training dataset ...
Add's user avatar
  • 1,397
1 vote
0 answers
94 views

Lopez de Prado Advances in Financial Machine Learning- entropy for adverse selection

In chapter 18: Entropy Features, Lopez de Prado discusses how entropy can be used to estimate adverse selection. He suggests a method where order imbalance is mapped to quantiles and entropy is ...
Cameron's user avatar
  • 11
0 votes
1 answer
110 views

Advances in retail modelling

The risk-neutral modelling framework leads to very advanced and mathematically rich approach to contingent claims modelling. However, in my experience, retail modelling in Banks is done using generic ...
Who cares's user avatar
  • 123
2 votes
1 answer
138 views

Characteristic Function for Wishart Heston Model

I don't know if this is the right place (at most they will close the post). Anyway, I am trying to implement the characteristic function of the Heston Wishart Stochastic Volatility model illustrated ...
SimoPape's user avatar
0 votes
0 answers
60 views

Commercial bank mortgages schedule calculation

I need to calculate the schedule of a fixed rate mortgage and an adjustable rate mortgage. Is there an open source library, preferable in python, that already makes these calculations? I tried ...
ps0604's user avatar
  • 50
1 vote
0 answers
150 views

Expectation of the realized volatility

I was reading Zhang and Wang 2023 and I have some doubts regarding it. The realized Stochastic Volatility Model is expressed as follows: $$\begin{matrix} y_t = \exp \big( \frac{h_t}{2} \big) \...
XY0's user avatar
  • 115
0 votes
0 answers
69 views

Can anyone help me to understand why the GMV point is not on the efficient frontier?

I am following a course about portfolio construction with Python. I am able to successfully draw the efficient frontier and capital market line (CML), and the global minimum variance (GMV) point using ...
user3741124's user avatar
2 votes
1 answer
79 views

Hypothesis Test Contradiction?

I have a question regarding hypothesis testing. I used the t-test (2-tailed) for these hypotheses: Whether the (monthly) mean return of company A's stock is different from 0 Whether the (monthly) ...
hungnguyen9's user avatar
0 votes
1 answer
158 views

Risk Neutral Pricing Exercise

I have the following exercise: A financial security pays off a dollar amount of $S_T^2$. Using Ito`s Lemma, what is the price today $V_t$ of this security? (S follows a Geometric Brownian Motion $dS = ...
Otto's user avatar
  • 1
4 votes
1 answer
195 views

Why is the stochastic process of the volatility of a stock price square integrable?

I am taking a course in financial mathematics(Ito-Integrals, Black-Scholes,...) and there is something that is not immediately clear to me. When constructing our stock price model, the integral $\...
Josh.K's user avatar
  • 41
0 votes
0 answers
35 views

References/Direction on what functional of wealth to optimize for a given goal?

I seem to have gotten stuck trying to approach trading strategy development from a financial mathematics(?) perspective. To start, let: $T \gt 0.$ $\mathcal{T}$ be a closed non-empty set of $\mathbb{...
QMath's user avatar
  • 249
0 votes
0 answers
77 views

American Contingent Claim vs European Option pricing

Suppose $Y$ is an American Contingent Claim (ACC) defined as $Y = \{Y_t, t \in 0,1,...,T\}$ and asssume $U_t$ is its fair price. Also suppose $C_t$ is the arbitrage-free price at time $t$ of a ...
Jennifer's user avatar
2 votes
1 answer
198 views

Check for arbitrage - European calls with same strike price, different duration and price

I tried a lot of different things to check for arbitrage on the following calls but didn't succeed. Let's suppose we have a stock that is currently valued at 40. The interest rate is 0.05 and the ...
LunaStorm's user avatar
0 votes
0 answers
70 views

Is the self-financing condition necessary/"useful" in practice outside of replication/valuation?

I know that the need for a portfolio/strategy to be self-financing (the purchase of a new asset needs to be funded by selling of an older one/ones) is very helpful when attempting to price derivatives ...
QMath's user avatar
  • 249
2 votes
1 answer
374 views

Incorporating the I-Spread and Parallel Shift for Accurate Bond Pricing

I am currently working on pricing bonds and intend to utilize the S490 curve sourced from Bloomberg. This curve is constructed exclusively using swap rates. However, I have encountered challenges when ...
TourEiffel's user avatar
1 vote
1 answer
181 views

Discrete self financing strategy

Let $H$ be an investment strategy in a discrete price model. Proof $H$ is self financing if and only if the following holds for the portfolio process $P_t$: $$P_t = P_0 + \sum_{s=1}^tH_{s-1}(X_s-X_{s-...
uhmmm's user avatar
  • 11
0 votes
0 answers
71 views

Follow-up Fixed Payment at Default - Pricing

This question is a follow-up of this question Fixed Payment at Default - Pricing for more clarity. Starting from the following expression of payoff: $$ D(0,T) = E(\exp(-\int_{0}^{\tau} r(t)dt) \cdot \...
cp123456's user avatar
  • 109
2 votes
1 answer
202 views

Fixed Payment at Default - Pricing

Let us consider a product paying an amount of 1 if default (τ<T that is the time of default arrives before maturity time), and 0 otherwise. The payoff of such a product would be given by: $$D(0, T) ...
cp123456's user avatar
  • 109
4 votes
1 answer
106 views

Law of iterated expectation for the pricing of a Zero Recovery Risky Zero Coupon Bond

I am currently reading "Modelling single-name and multi-name credit derivatives" by Dom O'Kane but I struggle at one point that should be relatively easy. Let us consider a Zero Recovery ...
cp123456's user avatar
  • 109
3 votes
1 answer
392 views

Proper way to backtest strategy using bootstrap method

Should I back-test in a single (original) price series and bootstrap the strategy returns to get statistics of interest? Or should I create bootstrapped price series using bootstrapped returns from ...
Arun Lama's user avatar
2 votes
2 answers
502 views

Quantifying the impact of rates change on bond prices

How can I quantify the impact of a change in interest rates on bond prices? I know that in a classical textbook setting the answer would be to compute the modified duration of the bond and, to account ...
Peter's user avatar
  • 45
4 votes
1 answer
1k views

Parameters in Nelson-Siegel model and Nelson-Siegel-Svensson model

I am trying to determine the parameters for the Nelson Siegel and Nelson Siegel Svensson model and try to solve SE=$\sum_{i=1}^{n_{i}}(y_{t_{i}}-\hat{y}_{t_{i}}(X))^{2}$ where $y_{t_{i}}$ denotes the ...
Martin N.'s user avatar
1 vote
0 answers
90 views

How to analyse the resilience of banks during financial crises using linear regression and other statistical methods?

I am a student in finance and have to work on a project for the semester. I have to study the difference of resilience during financial crises between the 5 biggest US banks and the 5 biggest Canadian ...
Haseo1997's user avatar
3 votes
1 answer
185 views

Roll Critique - CAPM and mean variance tautology?

Wikipedia introduces the Roll Critique mean-variance tautology: Any mean-variance efficient portfolio $R_p$ satisfies the CAPM equation exactly: $$ E(R_i) = R_f + \beta_{ip}[E(R_p) - R_f] $$ A ...
nemui's user avatar
  • 131
2 votes
0 answers
72 views

Proving that the return from the butterfly spread is nonnegative [closed]

The butterfly spread satisfies the inequality c(X1) - 2c(X2) + c(X3) >= 0 Where call strikes satisfy X1<X2<X3 and X2 - X1 = X3 - X2. There is a “proof” that was provided here https://quant....
Jordan Man's user avatar
2 votes
2 answers
406 views

QuantLib: How to bootstrap Yield Curve using 3M futures - Python

I need to bootstrap a yieldcurve with 3M futures, using a cubic spline if possible. Using, for example 3M Euribor, how do I bootstrap the yield curve using python? I have a vector of dates and a ...
Afonso Batista's user avatar
5 votes
1 answer
501 views

How to find interesting open math problems in quantitative finance that I could publish articles about?

Which books on financial mathematics would you recommend for people with good background in probability, statistics and stochastic processes but without any background in financial mathematics? The ...
Botnakov N.'s user avatar
1 vote
0 answers
72 views

What is the closed-form solution for the PV of the following series? [closed]

I have the following exercise, where a closed-form solution is needed for the PV of the cash flows. The teacher's solution is the following: But I fail to understand how exactly we get to it in the ...
Delia's user avatar
  • 33
1 vote
0 answers
93 views

Questions on constructing WML factor (Fama French)

https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html We can see that the Winner and Loser portfolios are determined by the cumulative return from t-12 to t-2. To construct the WML ...
Yoosang  Lee's user avatar
1 vote
0 answers
52 views

Can I extend the private information model of Kyle in in a continuous analogue, e.g. the Ornstein–Uhlenbeck process?

Taking into account an old post of maths.stackexchange, I recall the following: On the one hand, we know that the Ornstein–Uhlenbeck process can also be considered as the continuous-time analogue of ...
Oliver Queen's user avatar
1 vote
2 answers
230 views

I can’t understand why the premium of two butterflies with same strike but different broadness are approximately the same

Consider the following premiums of calls option with different strikes. C90 = 57.35 C95 = 52.55 C100 = 47.3 C105 = 42.9 C110 = 38.25 In this case, the butterfly 90-100-110 cost 1 and the 95-100-105 ...
Alexandre Borel's user avatar
4 votes
1 answer
111 views

Discounted expectation of generic $\mathbb{C}^2$ function

Consider a standard geometric Brownian motion $V_t$ with drift $\mu<r$ and standard deviation $1$. It holds that the discounted expectation is $$E\left[\int_t^\infty e^{-r(s-t)} V_s ds | V_t \right]...
Luca Gi's user avatar
  • 327

1
2 3 4 5
9