Questions tagged [finance-mathematics]
The finance-mathematics tag has no usage guidance.
262
questions
0
votes
1answer
135 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
114 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
16 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
88 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
56 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 ...
3
votes
1answer
92 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
139 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
81 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
37 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
103 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
24 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
97 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
50 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
39 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
57 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
111 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
76 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
77 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
165 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
34 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
86 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
106 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
198 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 ...
8
votes
3answers
6k views
What mathematical theory is required for high frequency trading?
I am an applied math postdoc and I have been presented with the option of leaving academia to work in high frequency trading. I wanted to get a feel for the field and the theory underlying it so I ...
1
vote
1answer
43 views
How is hypothesis testing work in population sampiling? [closed]
I am learning the basics of quant trading from quantconnect's tutorial Confidence Interval and Hypothesis Testing. I understood the first part of the article but I dont understand "Hypothesis Testing"...
3
votes
1answer
73 views
How to comprehend this notation?
I learned mathematical finance from Bjork's Arbitrage Theory in Continous Time, and never once did I encounter the "quadratic variation"-thingy with the angle brackets.
So now that I am reading ...
1
vote
1answer
40 views
Is the undiscounted value process of a Euro call option under Bachelier model a Martingale? [duplicate]
Assume that $c_t$ is the UNDISCOUNTED price process for a European call option in Bachelier model. In Bachelier model call option pricing formula the formulas is discussed. The undiscounted value ...
1
vote
1answer
81 views
Modeling mortgage loan defaults
I have a machine learning model trained with a list of mortgage features that include macro variables where the field to predict (the label) is "Mortgage Defaulted" = 1 or 0 (Yes or No).
Now, I need ...
2
votes
0answers
105 views
Term structure equation in the Vasicek model
Consider the SDE $$dr_t = (b-ar_t)dt +\sigma dW_t, \text{with } a; b > 0.$$ Let $$F(t; r) = E(\exp(-\int_{t}^{T}r_sds)| r_t = r).$$ (F can be interpreted as price of a zero coupon bond with ...
2
votes
0answers
87 views
Quantitative Finance books for Practitioners [duplicate]
Currently searching for some books on real options and option pricing. However, the vast majority of the books are quite theoretical, and if someone has been taught these subject in class, half of it ...
3
votes
1answer
149 views
Finding optimal trading of option on a foward
Assume you have a option on a forward $F$ with a payoff: $\max(F_T - K, 0)$.
Assume also, that you have a bullish view on the forward in such a way that $E_{0}[F_T] > F_0 = E_{0}^{*}[F_T]$ (where ...
1
vote
1answer
56 views
Finding the extrinsic value of an option with conditions
Background:
Consider a spread option with the payoff $\max (P_{T} - HR\times G_T, 0)$, where $P$, $G$ are underlying prices and $HR$ is a constant.
Let's also assume, that the correlation ...
1
vote
2answers
200 views
Are there any quant strategies which do not involve simultaneous buying and selling of two or more assets?
Whenever I read about quant strategies it leads me to stratergies which involve simultaneous buying and selling of two or more assets. Pairs trading, arbitrage, market neurtal or headging all these ...
2
votes
1answer
181 views
Forward Start Spread Options
Question:
We have a spread option with payoff: $\max (P_{T} - HR\times G_T, 0)$, where $P$, $G$ are underlying prices and $HR$ is a constant.
At time zero only contract $G$ is available for ...
1
vote
1answer
92 views
How to calculate Spot Rate with interest rate [closed]
You are a foreign exchange trader specialized in the US dollar Swiss franc market (USD/CHF). One morning, you notice that the one-year dollar interest rate is 4%, while the one-year interest rate on ...
2
votes
1answer
106 views
Fair price of a coupon paying bond
Consider a coupon paying bond with a maturity of $3$ years, that pays coupon annually. Let $c$ be the coupon rate (percentage) and let $F$ be the face value. This means that the holder of the bond ...
1
vote
1answer
63 views
Is it possible to create an instrument on the amount of beds sold within the real-estate market
I have been doing some research on the PBSA (purpose-built student accommodation) market around the globe. The market is growing year on year there is an index on this market the cbre.
What ...
2
votes
0answers
180 views
Errata for Mark Joshi's Concepts and practice of mathematical finance
I am wondering if anyone has a PDF copy of the errata for Mark Joshi's book "Concepts and practice of mathematical finance"? It seems that Mark's website markjoshi.com is not accessible anymore. I ...
3
votes
2answers
139 views
Verifying two properties of the Clayton Copula
So I'm trying to verify the first two properties of a copula for the Clayton model. The first two properties being:
$C(u_1,…,u_d)$ is non-decreasing in each component, $u_i$
The $i^{th}$ marginal ...
1
vote
0answers
20 views
Show that the variance of the portfolio market portfolio is function of the betas of its consituents [closed]
Let us assume that the market portfolio consists of n assets.
Given that the return of the market portfolio can be written as $r_m = \sum_{j=1}^{n} w_jr_j$, we have that $\sigma^2_m = E(\sum_{j=1}^{n} ...
4
votes
1answer
60 views
How to prove that the expected squared error associated with the optimal combination weight is smaller than the minimum of 2 forecast variances?
I am looking at linear combination of two forecasts (Bates and Granger, 1969). I would like to understand how to prove that the expected squared error associated with the optimal combination weight is ...
2
votes
1answer
111 views
Convert Geometric Direct Alpha PME to Arithmetic Excess IRR (PME Alpha / Implied Private Premium)
As a followup to this old question, Private Equity: Direct Alpha vs Excess IRR, I have a new one.
In automating PME calculations, the Direct Alpha (DA) approach is computationally simpler and ...
