# Questions tagged [finance]

Questions having to do with financial mathematics. This is not a tag about financing, which is not within the scope of mathematics defined by the help center: http://math.stackexchange.com/help/on-topic Please note that for questions in quantitative finance, quant.stackexchange.com is perhaps a better site.

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### What are some of the best books to learn Mathematics for Quantitative Finance and Machine learning?

I am finding it difficult to understand the math behind quantitative finance and machine learning. Can you tell what are the math concepts required to master these areas and also suggest some of the ...
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### How to use Itô's lemma to find expressions for mu and sigma?

if $𝑑S = \mu S𝑑𝑡 + \sigma S𝑑𝑧$ and $𝑑𝑐 = \mu_c 𝑐𝑑𝑡 + 𝜎_c 𝑐𝑑𝑧$ , how do i use Ito's lemma to find expressions for $\mu_c c$ and $\sigma_c 𝑐$? Thanks.
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### What kinds of mathematics are used to explain the theories of valuation?

Using economics as example, Marx "explained" to us "philosophically" what happens when capital is "created" from an initial value: D -> M -> D' (with D' > D) but even though „das Kapital“ is ...
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### Non-uniqueness in the $L^1$ martingale representation

Let $\xi \in L^1(P,\mathfrak F_T)$ on some probability space with measure $P$, supporting a Brownian motion, we consider the augmented filtration $\mathfrak F$ associated to $W$, and a time $T>0$. ...
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### What happens to the Black-Scholes pricing formula for a European Call Option when there is a rise in interest rates?

The topic The Black-Scholes pricing formula for a European Call Option C (S; t) is given by the picture. I'm puzzled about what will happen to the Black-Scholes pricing formula for a European Call ...
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### Acturial Studies: what is the formula for compound discount with simpe discount over the final fractional period?

What is the formula for compound discount with simple discount over the fractional period. I could not find the formula in my book and when I looked online the ones that had the formula where answers ...
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### Black-scholes model for binary options [closed]

Also check if the formula found satisfies Black-Scholes partial differential equation. Thank you!! enter image description here
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### Can a unit of currency be taken to n power? [duplicate]

I've been building a unit & rate library for a forex trading algorithm and I realized I didn't have an answer to this question: Can currencies be taken to the Nth power? Unlike physical units, ...
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### Show that the Value-at-Risk (VaR) at confidence level $c = 95\%$ is $\text{VaR} = 1$. [closed]

Suppose an asset has return $K = 1$ with probability $\frac{1}{2}$ and $K = −1$ with probabilty $\frac{1}{2}$. Show that the Value-at-Risk (VaR) at confidence level $c = 95\%$ is $\text{VaR} = 1$.
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### Actuarial theory of interest question with effective discount

I have spent several hours trying to solve this problem. $A$ and $B$ both open up new bank accounts at time $0$. The principle for $A$ (the amount deposited at $t=0$) is $100$. The principle of $B$ is ...
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### Method of images for Black-Scholes PDE

The paper. Let $\mathcal{L} = \partial/\partial t + \frac{1}{2}\sigma^2x^2 \partial^2/\partial x^2 + rx \partial/\partial x - r$ be the Black-Scholes operator. In the paper he mentioned about the "...
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### Find Swap Rate given Spot Interest Rate Curve

Question: Spot interest rate curve: $$\begin{array}{c|c} t & r_t \\ \hline 0.25 & 1.50\% \\ \hline 0.5 & 1.65\% \\ \hline 0.75 & 1.79\% \\ \hline 1 & 1.92\% \end{array}$$ I ...
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### Simple finance question [closed]

Is this statement correct? : Let's say I buy an apple for 1 dollar from a Mexican producer, pack it and export it at a cost of another dollar, and manage to sell it for 4 dollars to the prince of ...
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### Deferred social security break-even with discount factor

Zero Discount Solving for break-even for social security when not using discounted cash flows is simple. After full retirement age, an 8% increase is added to the base amount for each year of ...
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### Modeling Via ODE System

My Problem José invests $\$2500$of his$\$5000$ into an account with a $6\%$ annual interest rate, compounded continuously. If he continuously deposits an additional $3.5\%$ of his annual ...
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### Present value of varying annuities

I need help with the following questions. In order to answer these questions, I am only allowed to use two of the tables of values for $\ddot a_n , \bar a_n$ (continuous annuity) and $(I \ddot a)_n$ ...
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### Closed form for duration formula

so I was trying to prove this closed form for bond duration formula: D=1+$\frac{1}{r}$ + $\frac{T(r-c)-(1+r)}{c((1+r)^T-1)+r}$ where r- yield to maturity, c-coupon rate,T-time to maturity. I made some ...
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### How to find the derivative of a multi-factor brownian motion model of asset prices.

Does anyone know how to find the derivative for a multi-factor geometric brownian motion model ($\frac { dS_{i}}{S_{i}}$). I have seen solutions for the standard GBM model however I suspect that the ...
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### Does the American Put have a higher price than payoff

According to shreve the value of a put is equivalent to or greater than the possible payoff, before a stopping time with the condition that its value equals the intrinsic value. First what does it ...
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### Compound Interest Question from the textbook *Core Math for Advanced Level by Bostock and Chandler*

Good Day, I came across this question in a Form 6 Math textbook and it stomped me. I know it has to do with constructing the formula for compound interest and continuous interest but I think once I ...
Starting with the equation for continuously compounded interest, we can derive the differential equation. Let $A$ be the amount accumulated, $P$ be the principal amount and $r$ the rate. \begin{align*...