Questions tagged [finance]
Questions related to the various aspects of financial mathematics. Topics include option pricing, arbitrage theory, market completeness and stochastic analysis.
2,647
questions
7
votes
0
answers
143
views
Show that no arbitrage implies the extension property in $L^p$
Let $(\Omega,\mathcal F,P)$ be a probability space, and let $X:=L^p$ denote the normed space of (equivalence classes) of $p$-integrable real random variables on $(\Omega,\mathcal F,P)$, where $1\leq p&...
- 4,827
0
votes
1
answer
372
views
Expected value of Ornstein-Uhlenbeck process
In the paper "The Impact of Jumps in Volatility and Returns" by Nicholas Polson, Bjorn Eraker, and Michael Johannes (2003), the authors state in footnote 6 on page 1273 that, given an ...
- 392
0
votes
0
answers
46
views
Derivation of $ \pi(\sigma) $
This is my first post on this website so please forgive me for any mistake or inappropriate use. I am taking a Master level Investments course, in which, amongst the rest, we are deriving $$
\pi(\...
1
vote
1
answer
72
views
Finding optimal way to pay a set of credit cards
Lets say we have two credit cards. Card $A$ has a balance of \$2000 and card $B$ \$3500. That is, $C_A = 2000, C_B = 3500$. The interest rates are $r_A = 0.20, r_B = 0.25$. What is the optimal way to ...
- 377
0
votes
0
answers
34
views
Seeking help with the application of Law of Large Numbers and Central Limit Theorem to calculate Investor Risk
I'm a newbie to the forum with zero financial or statistical skills - first time post...seeking some assistance and a solution..thanks in advance!
I am trying to create a investor calculator or at ...
- 1
0
votes
0
answers
35
views
European Option Volga Derivation
This should be a standard exercise involving high-school Calculus, but for some reason, my expression for the European option volga, does not match the one on Wikipedia. I would like to ask if, ...
- 5,450
0
votes
1
answer
88
views
Brownian motion X(t) is with probability 1 a continuous function of t
Here is an excerpt from "An Elementary Introduction to Mathematical Finance" by Sheldon Ross, 3rd edition:
I understand this is not meant to be rigorous, but I'm having trouble ...
- 303
0
votes
0
answers
24
views
Estimating Present Bond Value without YTM using yield curve rates
Suppose I have a bond where I know the par value, coupon rate, and maturity date as well as the daily Yield Curve Rates given here
How can I go about estimating the ytm needed to determine the present ...
- 21
1
vote
1
answer
104
views
Understand a FM question about a bond with varying interest rate. [closed]
Consider a coupon bond with maturity in $2$ years, with a coupon rate of $4.375\%$ (coupons are paid twice a year) and with a face value of $100€$. Let's say this coupon bond has a varying ...
- 1,141
1
vote
1
answer
143
views
Question about calculating the price of a coupon bond at different times: FM question.
Let's say we are working with a coupon bond with face value of $F = 100€$, maturity of $T = 5$ years and with $10€$ coupons paid anually. Also, consider we're dealing with a continuously compounded ...
- 1,141
0
votes
1
answer
54
views
How to interpret the value of money depending on the maturity of a bond? FM question.
Consider the following exercise:
Exercise. A financial institution issues bonds with maturities of $13$ weeks, $26$ weeks and $52$ weeks, at zero coupon, and with a discount value $B_1(0) = 98€$, $B_2(...
- 1,141
0
votes
0
answers
37
views
Loan Balance Formula for Cumulative Interest Paid?
I'm trying to find a formula to calculate the cumulative interest paid on a loan after x amount of time. I can do this with data science software but it has to amortize every loan for every customer ...
- 1
2
votes
0
answers
61
views
How can Capital Market Line portfolios be efficient when they're not feasible?
My course notes define
Suppose now that there are many different investments $A_1,\dots,A_n$ available. We can invest our one unit of currency by investing $t_i$ in $A_i$ for each $1 \leq i \leq n$ ...
- 2,281
1
vote
0
answers
20
views
Price sensitivity under Uniswap [closed]
Question. Under the uniswap pricing rule, what determines how much the price of an asset increases when you buy that asset?
Note. while this is a mathematical question, answering it requires an ...
- 653
0
votes
0
answers
37
views
How do Brownian/Wiener processes involve randomness?
My financial mathematics course notes have
A Brownian motion is a family of random variables $\{B_t|t\geq0\}$ on some probability space $(\Omega,\mathcal{F},P)$ such that: \begin{align}
(1) \; & ...
- 2,281