Questions tagged [finance-mathematics]
The finance-mathematics tag has no usage guidance.
281
questions
0
votes
1answer
68 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
28 views
Use AM-GM inequality to generalize price process
Consider the following 2 investing strategies.
Strategy $A$ buys $1$ share in every period.
Strategy $B$ invests a fixed amount of money in every period.
$B$ seems better because for the same ...
0
votes
0answers
35 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
98 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
0answers
26 views
Evaluating financial plans [closed]
I am solving the following problem:
30 y.o. Jack is working a manual job, earning only 8000USD yearly and
he isn't expecting any wage increase till his retirement at age 63.
However, he is ...
0
votes
2answers
61 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 ...
0
votes
1answer
43 views
How required yield affects price of the bond and how the durations changes
can somebody answer, those two theoretical questions?
How does the bond price depend on the desired yield (market interest
rates)?
How the duration changes if we have a shorter / longer
maturity and ...
1
vote
1answer
49 views
Accounting profitability [closed]
Can anyone please help me how to solve this problem?
Grocery Freshly want to open a new store. They expect an initial cost
of 30,000 to buy the property in which the store will be. After
...
1
vote
1answer
43 views
Differences in bull put spread option strategy
I am supposed to construct a profit and loss diagram for a bullish spread strategy: −1put($X_{1}$) + 1put($X_{2}$) and compare it to the profit and loss diagram for the strategy: −10put ($X_{1}$)+ ...
4
votes
1answer
86 views
How to determine components of Affine Term Structure for an Ohrnstein-Uhlenbeck process?
I wonder how I can determine the components $A(t,T)$ and $B(t,T)$ for the zero-coupon bond price process $p(t,T)=e^{A(t,T)-r(t)B(t,T)}$? The components are defined in the following link: https://en....
6
votes
1answer
161 views
Periodic functions when determining No Arbitrage price
Is it possible to value a T-claim which has a periodic component? For example a claim such as $X = cos(S(T))$.
We assume here that $S(T)$ is the stock price derived from the dynamics $dS(t)=rS(t)dt+\...
1
vote
0answers
35 views
Residual Income Valuation with Term Structure
I'm implementing a residual income model (RIM) to value stocks as described by Ohlson.
https://pdfs.semanticscholar.org/c0a5/4ef41311951fe406d15cd7d7ce19502cdc7c.pdf
The key to this model is ...
0
votes
1answer
70 views
Determining the No Arbitrage price of max[B(T), S(T)]
Following is given,
$dB(t)=rB(t)dt$
$dS(t)= (r-\delta)S(t)dt+\sigma S(t)dW(t)$
where, $r$ is the risk-free interest rate, $\delta$ the continous dividend yield $\sigma$ is the stock asset ...
3
votes
2answers
168 views
Stochastic Calculus problem with three processes? (Itô calculus)
Can someone help me solve this following Itô Calculus problem?
Let $Z(t):= [B(t)*X(t)]/S(t)$
We have the following dynamics of B(t), X(t) and S(t):
$dS(t)=\alpha S(t)dt+\sigma S(t)dW(t)$
$dB(t)=rB(...
0
votes
1answer
49 views
Deriving investment amount for one asset of a two asset minimum-variance portfolio
Suppose I bought $100 worth of stock A and I want to hedge it by shorting stock B, they have correlation of rho and respective standard deviations. How do I know how much of Stock B to sell? that's ...
0
votes
0answers
40 views
Span of a state price
Good morning,
I report here an equation that you can find in the following paper: "Portfolio Selection with Options and Transaction Costs" by Semyon Malamud (2014) page 10 - 11 (https://papers.ssrn....
0
votes
0answers
47 views
Classical Cramer Lundberg model - Ruin Theory Simple Question
I am trying to solve the following problem:
'An insurance company has an initial surplus of 150 and premium loading factor of 15%. Assume that claims arrive according to a compound Poisson process $(...
1
vote
1answer
86 views
0
votes
1answer
150 views
INTERPRETING PCA ANALYSIS
I am having little trouble figuring our which variables are the most important when I am using PCA .
What I am trying to do is see which variables explain the most variance when it comes to stock ...
1
vote
0answers
48 views
Another ZCB calculation
I am not getting the $f(t,t)dt$ term in the last equality when we have $df(t,T)=\alpha(t,T) dt +\sigma(t,T) dW$ and $f(0,t)=f^{*}(0,T)$. Instead I have an additional $\int_{t}^{T}f(0,u)du$ in the ...
3
votes
1answer
121 views
Zero coupon bond calculations
I am given the following forward rate dynamics $df(t,u)=\frac{\partial}{\partial u}(\frac{\sigma^2}{2})dt-\frac{\partial}{\partial u}\sigma dW$ and want to calculate the dynamics of the ZCB $p$ via ...
0
votes
0answers
20 views
How do you find a company average quality of income ratio?
Do you divide the weight average number of shares outstanding basic and diluted/by the net income? Or just add the current year and prior year quality of income ratio divide by two?
1
vote
2answers
91 views
Instantaneous change in value of portfolio
I am trying to figure out an intuitive explanation for the instantaneous change for the value of a portfolio (essentially I'm creating a self-financing portfolio to replicate a derivative payoff).
...
0
votes
0answers
16 views
capital recovery factor isolate interest
in the capital recovery factor formula:
CRF = i(1+i)^n / ((1+i)^n)-1
If we know CRF and n, is it possible to isolate the i? right now I am using excel to get ...
1
vote
1answer
116 views
Is my python solution good? : Global Minimum Variance portfolio with 'no-short sale' constraint
Question
Is my python code an answer (at least a close answer) to get the weight vector of the Global Minimum Variance portfolio problem? My codes are shown below after some explanations.
Details ...
4
votes
1answer
101 views
What the expectation of S^2 is from GBM? [closed]
I was at an interview and was asked to write down the SDE for GBM.
$$
dS = S\mu dt + S\sigma dX
$$
Then I was asked how I would compute the expectation of S^2. I didn't know where to start. Any ...
1
vote
3answers
208 views
How to calculate standard deviation of continuously compounded four-year stock returns?
Currently I am preparing for quant interview and I encounter the following question in Heard on the street.
Question: If the standard deviation of continuously compounded annual stock returns is $...
1
vote
0answers
94 views
2
votes
0answers
31 views
EMA with different resolutions
I am trying to understand something:
If I calculate an EMA over 5 days, using the hourly close, I have to go over 5 * 24 points.
If I calculate an EMA over 5 days, using the minutes close, I have to ...
0
votes
1answer
76 views
Interest rates compounded monthly [closed]
Suppose the quoted APR is $r_0 = x-1$ and interest is compounded monthly;
Am I correct in saying the formula for the monthly interest rate $r$ is:
$$r = (1+ (\frac{r_0}{m}))^m -1 $$
Is it also ...
1
vote
1answer
38 views
Moments of discrete Asset Price Model
Say if B is standard Brownian motion then:
$S(t) = S0e^{((𝜇- σ^2)/2)t+σB(t)}$
The mean of this SDE would be
$𝐄[𝑆(𝑡)]=𝑆_0𝑒^{𝜇𝑡}$
I know to do this you use the density function and ...
2
votes
2answers
134 views
How to derive Black-Scholes equation with dividend?
Question: The Black-Scholes equation without dividend is given by
$$\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2S^2\frac{\partial^2 V}{\partial S^2} + rS \frac{\partial V}{\partial S} -rV = ...
0
votes
1answer
39 views
How to deal with intermittent NA values in a price series when calculating returns
Let's say a have a price series for a share for the year 2000. On the 27th of July 2000, there is a missing value represented by NA. This was not a holiday or any other non trading day as other shares ...
1
vote
0answers
26 views
A fundamental question on optimal stopping time need clarification
I am currently studying optimal stopping time.Under this topic there is a basic concept which confuses me. I would appreciate some clarification.
So we define $\tau$ a stopping time, and $\phi (\tau,...
1
vote
2answers
106 views
Stock Volatility with Uncertain Probability
Suppose that the probability that determines the state of the economy is unknown. That is, you do not know whether the booms or recessions are more likely. Calculate the expected return and the ...
3
votes
1answer
51 views
Exposure/Factor Analysis on a loan portfolio?
I am working on performing factor analysis on a loan portfolio. This is my understanding so far, and I was hoping that some of the smart folks here might be able to chime and guide me through this ...
0
votes
0answers
26 views
Is it possible to price a double barrier option which one barrier is monitored continuously while another barrier discretely without using MCS?
I am thinking about pricing a down-and-in and up-and-out double barrier put option under Black-Scholes assumption. The upper barrier is monitored continuously and the lower barrier is monitored ...
2
votes
0answers
40 views
How to calculate the multiple integrals where the integral domain is based on the sum of normal distribution random variables?
The integral is shown below:
And how to use python to calculate pi (better if we don't need to code for each pi)?
0
votes
0answers
22 views
What NPV value to expect with X% success?
cross-posted from https://math.stackexchange.com/questions/3326309/what-value-to-expect-with-x-success
I'm trying to intuit the following statements based on the plot below, but I'm stuck on the ...
0
votes
1answer
58 views
Clarification on certain finance terms surrounding bonds
Whilst revising for my upcoming financial mathematics exam I've been struggling to get to grips with certain terms/ phrases used when studying Bonds. I am very new to Finance and get confused very ...
3
votes
2answers
112 views
How to Mathematically Prove Markets are Price-Discovering?
We all know that the Efficient Market Hypothesis is true if you're willing to make enough simplifying assumptions about the market participants. But where can I find a mathematical proof of this in ...
1
vote
1answer
84 views
Jensen’s Inequality for returns on short positions
this is puzzling me. Say you have an asset A, that on day t+1 returns 1%, and then on day t+2 returns 1% again.
If you invest $1 in A on day t (take a long position), then on day t+2 you have earned:...
0
votes
0answers
79 views
Stock prices and PCA
I'm trying to construct a portfolio using PCA based on a number of stocks. I was wondering what the best way to standardise the stock prices are.
Which method would be more appropriate? Standard ...
0
votes
0answers
20 views
Portfolio Values based on reference interest rates
How do I approach the following question?
A portfolio has 100 million invested in equities. It has also transacted an interest rate derivative issued by counterparty X, which the value is 0 if the ...
0
votes
1answer
244 views
Squared returns and volatility
Squared returns are considered pillars of GARCH/ARCH modelling and most used method for forecasting or studying volatility.
Can you tell me how to calculate it from simple stock price.
Is it better ...
0
votes
0answers
48 views
How Free Of Payment (FOP) trade works? How it impacts NAV and P&L?
I want to understand how the Free of Payment(FOP) trades work from accounting point of view. My questions are:
What data we collect while capturing FOP trade?
How it impacts NAV and P&L? e.g. say ...
1
vote
2answers
126 views
Find arbitrage opportunity in the given market model
Consider the following 3-period-market-model:
The discounted price of the risky asset $S$:
How can I find an arbitrage opportunity in this model?
I know that there would be no arbitrage if we ...
0
votes
1answer
130 views
Yield Curve Flattening Trade
Relatively simple question, but came upon it in class and have not been able to come up with an answer:
The two-year bond yield is equal to 4% while the 10-year one is equal to 10%. You want to put ...
3
votes
3answers
201 views
Getting sets of random correlated variables
For the training of a machine learning model I need to add additional features (macro variables), and these features are correlated. I need to run the model N times, and for each time I have to add ...
