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.

Filter by
Sorted by
Tagged with
-1
votes
0answers
12 views

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 ...
0
votes
0answers
13 views

How to use Itô's lemma to find expressions for mu and sigma?

if $𝑑S = \mu S𝑑𝑑 + \sigma S𝑑𝑧$ and $𝑑𝑐 = \mu_c 𝑐𝑑𝑑 + 𝜎_c 𝑐𝑑𝑧$ , how do i use Ito's lemma to find expressions for $\mu_c c$ and $\sigma_c 𝑐$? Thanks.
0
votes
0answers
14 views

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 β€ždas Kapitalβ€œ is ...
1
vote
0answers
8 views

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 $T>0$. ...
0
votes
0answers
9 views

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 ...
0
votes
0answers
17 views

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 ...
0
votes
0answers
19 views

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
0
votes
1answer
25 views

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, ...
-1
votes
0answers
15 views

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 $K = βˆ’1$ with probabilty $\frac{1}{2}$. Show that the Value-at-Risk (VaR) at confidence level $c = 95\%$ is $\text{VaR} = 1$.
2
votes
1answer
37 views

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 ...
0
votes
0answers
28 views

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 "...
3
votes
1answer
44 views

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 ...
-1
votes
1answer
22 views

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 ...
0
votes
0answers
12 views

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 ...
1
vote
0answers
77 views
+50

Modeling Via ODE System

My Problem JosΓ© 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 ...
0
votes
0answers
20 views

Covariance of $X$ and $M$

I was wondering how we compute the covariance of $r$$x$ and $r$$m$. Here is the problem: We know that: For stock $X: E(r_x) = 0.21$, and $Stdev(r_x) = 0.15$. For stock $Y: E(r_y) = 0.15$, and $...
0
votes
0answers
24 views

I'm helping out a student with a business calculus question and his textbook does not help him solve this specific problem.

Kate is in the 27% bracket and has 21,000 dollars available for investment during her current tax year. Assume that she remains in the same tax bracket over the next 10 years, and determine the ...
1
vote
1answer
49 views

Proof of Expected value of Brownian Motion

Consider the following exercise: Let $T_{[-a,a]} = \inf \{t: B_t \notin [-a, a] \}.$ Show that $E[T_{[-a,a]}]$ $=$ $a^{2} \times E[T_{[-1,1]}]$. Please tell me if this reasoning is correct: $T_{[-a,...
1
vote
1answer
27 views

Properties of Brownian Motion (Expected value)

Consider the following exercise: Let $T_{[-a,a]} = \inf \{t: B_t \notin [-a, a] \}.$ Show that $E[T_{[-a,a]}]$ $=$ $a^{2} \times E[T_{[-1,1]}]$. Please tell me if this reasoning is correct: $T_{[-a,...
0
votes
1answer
37 views

Itô's formula and Integration by parts

Could someone please help with this question: By applying the generalized Itô’s formula to the 2-dimensional process $ {\{(Xt,Yt),t \ge 0 }\}$ with the function $ F(x,y) = xy $, show the integration ...
0
votes
0answers
17 views

Distribution of Itô Formula (Brownian Motion) [duplicate]

can you please help me with this question: Let $f: [0,T] \to \mathbb R$ be a deterministic function, with $\int_{0}^{t} {f^{2}(s)ds < \infty}$. Prove that $\int_{0}^{t} {f(s)dW_{s}$ has normal ...
0
votes
1answer
22 views

Brownian motion and expectation

I'm having trouble solving the following exercise: Let $T_{[-a,a]} = \inf \{t: B_t \notin \{-a, a\} \}.$ Show that $E[T_{[-a,a]}]$ $=$ $a^{2} \times E[T_{[-1,1]}]$. I don't see how I can solve this. ...
1
vote
0answers
24 views

Bank Interest in Terms of Convolution

Example 4 from an old set of MIT notes asks: Bank interest. On a savings account, a bank pays the continuous interest rate $r$, meaning that a sum $A_0$ deposited at time $u = 0$ will by time $...
1
vote
1answer
56 views

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 $(I \ddot a)_n$ ...
0
votes
1answer
32 views

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 ...
0
votes
0answers
18 views

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 ...
1
vote
1answer
23 views

Mean and Variance of Geometric Mean Reverting Process

For the geometric mean-reverting process $dX_{t} = k(\theta - logX_{t})X_{t}dt + \sigma X_{t}dW_{t} $ it is possible to obtain the solution: $log(X_{t}) = e^{-kt}log(X_{0}) + (\theta - \sigma^2/(2k))(...
1
vote
1answer
43 views

How to solve the Black-Scholes equation using Feyman-Kac with two underlying assets?

If we have the following Black-Sholes equation (PDE) for two independent stocks with the same volatility: $$f_t +\sum^{d=2}_{i=1}rs_i\frac{\delta F}{\delta s_i} + \sigma^2\frac{1}{2}\sum^{d=2}_{i,j=1}...
2
votes
1answer
61 views

How much bigger is the amount of security papers when comparing strategy X to strategy Y?

I'd like to ask the following question: Mr. X has a certain capital (10000 Dollars). He buys one security (from am company, say) now. The present value of one security paper is 10000 Dollars, but ...
0
votes
0answers
46 views

Equation with matrix exponential integral

For my thesis I came across an equation that involves a matrix exponential within an integral, i.e. $ \int_0^{\Delta t} e^{-Ks}\Sigma \Sigma'e^{-(K)'s}ds = Q$ Where K is non-symmetric with real ...
0
votes
1answer
10 views

Dividend growth model?

A company whose earnings and dividends are expected to grow at a rate of 3% per year. Next year's dividend is $0.65 per share. The market capitalization rate is 7%. How do I find the current price ...
0
votes
0answers
10 views

What formula do the majority of banks use for savings accounts?

I apologize if I'm asking this in the wrong forum or if it's already been answered and I missed it. I am a Software Engineer taking a Java course. Our final project it do write a Banking application ...
0
votes
0answers
10 views

Financial Mathematics Question relating to continuous investment and continuous interest

On 1 January 2014 an investor opens a bank account. The investor plans on depositing an amount of $20,000 continuously per year into the bank account for a total of five years. From 1 January 2019 ...
0
votes
0answers
16 views

Risk neutral for Black Scholes

In the Black-Scholes model, consider a forward contract on the asset S, expiring at time T. Let Ft be the corresponding forward price: how does this process evolve in the risk-neutral measure (i.e. ...
1
vote
1answer
39 views

Converge to a Dirac Delta Function [closed]

I was reading something when the author said that "x converges to a dirac delta function". Was wondering if someone could explain what it means. I work in IB and am unsure what this means. The exact ...
0
votes
1answer
27 views

accumulated value in geometric progression

In a general form, i know how to compute the PV of an annuity that follows a geometric progression. But how do i compute it when it's the accumulated value? let's say a payment of 100/ year with ...
0
votes
0answers
29 views

Stock price: Scaled Brownian Motion

Suppose that the share price of a given stock is modeled over time (measured in years) as the stochastic process $\{S(t), t β‰₯ 0\}$, with $S(t) = 100 + 10B(t)$, and $\{B(t), t β‰₯ 0\}$ is standard ...
1
vote
1answer
31 views

Layperson's explanation of what it means for something to become more and more like a Gaussian

Question: I was asked by a friend what it means for something to become more and more like a Gaussian and I was unable to come up with a satisfactory answer. Therefore my question is: How would you ...
0
votes
0answers
26 views

Black Scholes Model Put-Call Parity alternative proof

I have PDE like this: $f_t(t,x)=-\frac{1}{2}\sigma^2x^2f_{xx}(t,x)-rxf_x(t,x)+rf(t,x)$ and I have to find final condition $h(x)$ if function $f(t,x)=x-Ke^{-r(T-t)}$ satisfy this equation. So i ...
0
votes
1answer
39 views

accumulated value on the last payment of an annuity due

A $20$-year annuity-due makes payments of $100$ each year for the first $10$ years and then each subsequent payment decreases by $5$ for the next $10$ years. The effective annual interest rate is $9\%...
0
votes
2answers
38 views

Financial Mathematics Probability Question

It was crucial for our no arbitrage computations that there were only two possible values of the stock. Suppose that a stock is now at 100, but in one month may be at 130, 110, or 80 in outcomes that ...
0
votes
1answer
27 views

Determining Pricing Process of Futures Price

So I am studying Paul Glasserman's book on Monte Carlo in finance and I am currently working through Chapter 3 just to brush up on my risk neutral pricing processes (It's been a while). I have a ...
0
votes
1answer
22 views

Cost of the government

I am supposed to solve the following problem. The bank provides 1,000 dollars loans. Risk-free clients will repay the loan in full for a year, in addition to paying 4% interest. For a high-risk ...
0
votes
0answers
19 views

Showing CRR formula can be used to price call option: $Οƒ=15% R=6%$

Suppose that the volatility is 15% and that the annualized interest rate is 6%. Construct a binomial tree with 15 periods to value a 6- month instrument. Show that the Cox-Ross-Rubinstein formula ...
0
votes
0answers
26 views

Black Scholes theta at time t

I 'm trying to get the theta of a Call in the classical Black Scholes model. We have (classical result with usual notations) : $$C_t = S_tN(d_1) - Ke^{r(T-t)}N(d_2)$$ When deriving according to time,...
1
vote
1answer
31 views

Financial Mathematics Effective rate of interest

If you invest \$1000 , and you get paid \$500 in 5 years, \$1000 in 10 years, and \$1500 in 15 years and then get a final payment of \$2000 in twenty years, what is the effective annual rate of ...
0
votes
0answers
12 views

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 ...
0
votes
1answer
17 views

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 ...
0
votes
2answers
54 views

Modelling continuous compound interest with differential equations (Intuition)

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*...
1
vote
1answer
38 views

Conflicting Loan Amortization Formulae

When running a financial loan payoff simulation, I realized that my calculated monthly payment differed from the calculator offered by popular loan service Sallie Mae. I found two formulas for loan ...

1
2 3 4 5
…
41