# Questions tagged [finance-mathematics]

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### 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. ...
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### 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 ...
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 ...
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 ...
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### 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 ...
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 ...
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 ...
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 ...
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### 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 ...
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 ($X_{1}$)+ ...
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....
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### Justify a backward differential equation

Regards of 4.5.1, how we get 4.5.5?
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 ...
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 ...
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 ...
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### 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?
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). ...
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 ...
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 ...
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 ...
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### 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 ...
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 ...
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 ...
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### 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)?
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### 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 ...
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 ...
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### 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 ...
84 views