Questions tagged [finance]
Questions related to the various aspects of financial mathematics. Topics include option pricing, arbitrage theory, market completeness and stochastic analysis.
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Calculating payments and APR for simple interest loans - different interest accrual methods.
I work for a small financial institution as an auditor. We do various small loans that are always simple interest. Currently, we calculate payments on loans using the =PMT() method in Excel.
There ...
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Finding duration of given payment
Question :A corporation bond with annual coupon rate 7,5% will mature at 30 june 2025.Find duration of the bond on 31 december 2023 given that the annual interest rate is 5,5%.Assume the par value is ...
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How to Compute the Derivative of Maximum Drawdown (MDD) with Respect to Portfolio Weights
I am working on a financial model and need to calculate the derivative of Maximum Drawdown (MDD) with respect to the portfolio weight vector (assume we fix it at the beginning and keep unchanged). The ...
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Is there a notion of approximation of continuous-time Markov processes by finite-valued Markov processes?
Recall that in practice, to simulate a Brownian motion on $[0,1]$, we usually use the interpolated process $X^n=(X^n_t)_{t\in[0,1]}$ between the jumps of a random walk $(S_k)_{k=1,...,n}$ with $n$-...
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Contribution of Growth Formula
The question I am trying to answer is:
Which store contributed ($\%$) most to the "National Share of Sales Growth" $(14,14\%)$. I would like the formula to calculate the "contribution ...
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How to solve for monthly interest rate given principal, number of payments, and total payment
The problem:
A lottery winner is given two payment options: Receive 131 million dollars in 25 yearly installments of equal size, the first payable immediately, or receive a single immediate payment of ...
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Analytical function from summation representing Dollar Cost Averaging
I would like to understand what is the math necessary to go from a summation representing the Dollar Cost Averaging (DCA) to the analytical function.
In DCA, a certain capital $C_0$ is invested ...
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Should I consider the price for "option pricing" problem?
I'm trying to solve the following problem from "Probability and Statistics" book by Morris H. DeGroot and Mark J. Schervish.
Suppose that common stock in the up-and-coming company A is ...
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No Arbitrage iff no generalized Arbitrage
Let’s consider a market in finite discrete time with trading dates $0,1,\dots,T$ probability space $(\Omega, \mathcal{F}, \mathbb{P})$, filtration $\{\mathcal{F_t}\}_{t \in \{0,1, \dots, T\}}$, $N$ ...
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How to formally justify fudge factor in this difference equation solution?
In Exercise $11$ from Section $3.3$ of Differential Equations With Boundary Value Problems by Polking, Boggess, and Arnold, we first develop the difference equation $P[n + 1] = (1 + \frac{I}{m})P[n],\ ...
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What formula would I use to calculate total income over $x$ years with a fixed salary increase rate.
I'm wanting to calculate how much total money I would have earned over x amount of years, but while accounting for increase in pay at the end of each year (or maybe even continuous?)
Lets say for ...
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How to find nominal annual rate of interest/discount?
1) at what nominal annual rate of interest, convertible four times a year will you quadruple your investment in $15$ years?
2) the annual nominal rate of interest compounded quarterly is $i^{(4)} ...
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Probability distribution of the future stock price
I have this exercise to do:
Consider a stock with an initial price of $40, an expected return of 16% per annum and a volatility of 20% per annum. Find the probability distribution of the future stock ...
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Financial based equation for Cash Flow analysis on Annuity ( Sequences and Series Analysis)
I have a particular Annuity type of question.
I am familiar with all the Cash Flow type of equations such as Present Value, Future Value for compound interest, and for Annuities and Mortgages etc.
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Mean and Variance of Geometric Mean Reverting Process
For the geometric mean-reverting process $dX_{t} = k(\theta - logX_{t})X_{t}dt + \sigma X_{t}dW_{t} $ it is possible to obtain the solution:
$log(X_{t}) = e^{-kt}log(X_{0}) + (\theta - \sigma^2/(2k))(...
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