Questions having to do with financial mathematics. Please note that for questions in quantitative finance, quant.stackexchange.com is perhaps a better site.

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3
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1answer
130 views

Altering a Lease Calculation to take into account an upfront payment

I am trying to find the interest rate of a lease if we know the monthly payment amount but have an advance payment. I have found a site with part of the calculation we need (Scenario 2 on the link ...
1
vote
1answer
45 views

Method to calculate the best way to repay two different loans given a set amount of money per month?

Given two (or more) loans of different balances and interest rates and a single amount of funds available per payment period, is there a way to calculate the best way to split the available funds to ...
0
votes
1answer
41 views

the intuitive difference between expected utility and utility of expected profit in a gambling game

What is the intuitive difference between expected utility and utility of expected profit in a gambling game ? Which one is the "usefulness of the game" to a player ?
0
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2answers
106 views

Compound interest with a compounding interest rate

I have an investment which pays 3% interest (r) annually but it also increases the interest rate every year by 5% (g). I re-invest all interest payments at the start of each year. How many years (t) ...
1
vote
1answer
188 views

Shape of utility function

I have read in a paper (http://www.public.asu.edu/~kirkwood/DAStuff/refs/risk.pdf) that the shape of the utility function depends on the attitude towards risk. My question is does not it also depend ...
0
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1answer
76 views

Discrete Fourier Transform Interpretation

Using Mathematica I took the Discrete Fourier Transform (DFT) of a vector whose entries are volumes of a particular stock. The power spectrum is plotted below: There are two questions that I have ...
1
vote
2answers
969 views

Deriving Geometric Brownian Motion's solution?

The Black Scholes model assumes the following underlying dynamics, known as Geometric Brownian Motion: $$dS_t=S_t(\mu dt+\sigma dW_t)$$ Then the solution is given: ...
3
votes
2answers
331 views

Partial Differential equations and applications- Reference request

I will be taking up a PDEs course next semester and would like to find some good references. The topics covered in the syllabus is given below. Partial differential equations: Conservation laws, ...
3
votes
1answer
186 views

What is the Most Efficient Way to Calculate the Internal Rate of Return?

I have built a program that prices financial assets and it does this in part by calculating the IRR. The problem is that it does not run as quickly as I would like it to. I currently use the ...
0
votes
0answers
168 views

Betfair Odds Percentage Movements & Hedging

I want to determine if the odds on Betfair have decreased by a certain percentage and then calculate the hedged profit when hedging on that percentage, but it's made tricky by the fact that decimal ...
0
votes
2answers
74 views

Bond valuation question

Trying to solve the following question, but I am a bit stuck. The 2IFM1 Corporation has two different bonds currently outstanding. Bond M has a face value of $\$20,000$ and matures in $20$ years. ...
0
votes
1answer
92 views

Actuarial Science - Amortization

Kevin takes out a $10$-year loan of $L$, which he pays by the amortization method at an annual effective interest rate of $i$. Kevin makes payments of $1000$ at the end of each year. The total amount ...
2
votes
1answer
88 views

Math Finance: Arbitragefree Pricing Q vs. P

I read that the Fundamental Theorem of Asset Pricing states, that a market is arbitrage-free if there exists a riskneutral equivalent martingale measure Q~P, under which the discounted asset price ...
2
votes
2answers
57 views

Solving $a_1x_1 + \cdots +a_nx_n = b$

I'm glad to ask my first question on the maths site! So here we go. I'm trying to set up prices right now and here is my problem : I know that my customer has a certain amount of money available. ...
1
vote
0answers
48 views

Matlab Optimization problem with Matrices

I'm trying to solve an optimization problem in Matlab. The expressions you will find below. Problem is it is all matrices, and I have no idea which solver to use for that. $w$ is of size $n \times 1$, ...
0
votes
2answers
118 views

Homework question compound interest

If $ \$ 6000$ are invested at 7% compounded continuously, what amount after 2 years? I know how to set it up but at one point I get lost $$A=Pe^rt$$ $$A=6000^{0.07}(2)$$ Somebody please help.
1
vote
1answer
468 views

Calculating FV and Payments for an inflation indexed savings (graduated annuity)

I have searched high and low but I can't seem to find the right calculation to work out exactly what I need. What I need is an equation. To work out the FV of an inflation indexed savings plan. The ...
1
vote
1answer
37 views

Is there any way to find compound interest easily?

What will be the compound interest on a sum of Rs. $25,000$ after $12$ years at the rate of $12%$ per annum?
0
votes
0answers
59 views

Finding criteria for a household financial budget falsification

I’m working on a financial problem about budget of households. Households in a state fill a form about their net budget in every year and our insurance company investigate their financial status and ...
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0answers
19 views

Finding the continuity of the mapping of a solution to a PDE to its partial derivative

Here is a modified version of the Black-Scholes PDE: $\frac{\partial \phi(t,S,i)}{\partial t}$ + $r_iS\frac{\partial \phi(t,S,i)}{\partial S}$ + $\frac{1}{2} \sigma^2_i S^2 \frac{\partial^2 ...
1
vote
0answers
115 views

Calculating VaR, CVaR

I am supposed to calculate the value at risk and expected shortfall of an asset with revenue given by a density function: $f(x)=0.5\exp{(-|x-0.05|)}$. My workings: If I understand it correctly, than ...
0
votes
1answer
58 views

How to find the expectation value?

Suppose that an insurer has an exponential utility function $u(x)=−2e^{-2x}$. What is the minimum premium $P^{-}$ to be asked for a risk X? After solving this we reached the following, So,only ...
0
votes
1answer
116 views

Fair Value Of a Call Option

I am dealing with the following question/information (which may not be complete): The price of the underlying asset is $100$. European call option with exercise price $150$ in a year. The price of ...
2
votes
1answer
42 views

the relationship between fractional difference and ACF of a time sequence

When reading the GARCH modeling part of book Analysis of Financial Time Series, I read the following statement. In specific, I do not understand how does the author ...
0
votes
2answers
90 views

Figuring out a growing monthly payment based on constraints

I'm working on a problem where I need to calculate the monthly payments for a loan given a few constraints. These payments grow at a constant rate every 2 years (24 months) and pay off the entire loan ...
0
votes
1answer
244 views

Derive the Black– Scholes formula for the European call option.

Consider the standard Black–Scholes model. Derive the Black– Scholes formula for the European call option. thanks for help.
0
votes
1answer
115 views

Including future value into calculation of interest rate

There is a discussion on this page regarding the back-calculation of the interest rate, given the other parameters of a typical finance calculation (present value, repayments and term length). Three ...
0
votes
2answers
203 views

How to rearrange this equation to solve for 'r' in closed form?

I'm taking a finance course, and I can't afford the financial calculator which can be used to solve this, so I would like to know how to solve this algebraically by hand (I don't care if it uses ...
2
votes
2answers
1k views

Calculating inflation rate

This is my maths problem (It is NOT homework help, just me trying to learn basics of this bit of maths): A car cost £14,000 in May 1994, the inflation rate then was 1.9%, but the current inflation ...
2
votes
1answer
53 views

Trying to calculate FV with annual & monthly fees

First question on here so please go easy if it's a stupid one! I have created a PHP based FV calculator for use on a client's website. This is the scenario: They offer returns of ...
-1
votes
1answer
77 views

Stochastic Finance I am having difficulty with my homework questions. Brownian Motion

A 2-dimensional process $(B_t^1,B_t^2),\ t \geq 0 $ is a standard 2-dimensional Brownian Motion if each $B_t$ is a standard Brownian motion and the $B_t^s$ are independent of each other. Let $ X_t = ...
1
vote
1answer
58 views

Recurrence On finance

A bank pays 6% interest at the end of each year on an account which initially starts with $2000. Find a recurrence relation for, the amount of money in the account at the end of year n if a) only ...
0
votes
1answer
17 views

To determine effective cost of investment

I have this problem,need of help on how to attempt it. If you pay for a certain investment with installments of GCD 1000 in early January and GCD 1000 in early July and then receive GCD 2000 in late ...
0
votes
1answer
31 views

Optimizing interest for a set of debt payments

Suppose I've got $n$ debts with principals $P_1, P_2, ..., P_n$, with corresponding interest rates $r_1, r_2, ..., r_n$, compounded monthly. Further, assume I have a constant $A$ dollars per month to ...
-2
votes
1answer
34 views

Calculate Interest

Peeta is saving to buy a new oven for his bakery that will cost \$8000. He has \$6,000 to invest at $5 \frac{1}{2} \%$ compounded semi-annually. How long will he need to wait for until he can afford ...
0
votes
1answer
52 views

Calculate expectation under risk neutral measure: $\mathbb{E_Q}(\max(S-1,0))$

I am busy with a numerical simulation and I want the calculate the following expectation under the risk neutral measure: $\mathbb{E_Q}(\max(S-1,0))$. $S$ is some variable that I calculated using ...
0
votes
4answers
57 views

what are the units for a rate of return?

My understanding of "rate" is more physics oriented. For example, distance/time is understandable for me and something I can explain. However, a rate of return: "The return, or rate of return, can ...
1
vote
2answers
68 views

Expected value of SinhX

A random variable X is distributed according to a normal distribution with mean u and variance d.How to evaluate the expected value of SinhX?Thanks
1
vote
0answers
73 views

Construct an arbitrage opportunity in a multi-period model

I am currently revising for my exam in Financial Mathematics, and I could not solve this question: For $T > 1$, consider a $T$-period model with a single risky asset and a bank account which pays ...
3
votes
0answers
214 views

Math for Future Value of Growing Annuity

Am I working this out correctly? I need to verify that my code is correct... $$1000 \cdot \left(\frac{(1 + 0.1 / 12)^{40 * 12} - (1 + 0.06 / 12)^{40 * 12}}{(0.1 / 12) - (0.06 / 12)}\right)$$ ...
1
vote
1answer
88 views

Interest Accumulation - Geometric Sequence

Hello I have just worked a question in which I get an answer different to the answer in my book. The question states: If a person deposits 500 at the end of each month for 20 years at an AER of ...
1
vote
0answers
78 views

Show that the risk-neutral probability of a European call option ending in money is N(d2)

Show that the risk-neutral probability of a European call option ending in money is N(d2). I was trying to using Risk-Neutral Valuation Formula, but how to show the result is N(d2)? Thanks
1
vote
1answer
48 views

Changing variables for a partial differential equation

If I have the following systems of PDE \begin{align} u_t+x^2u_{xx}-\dfrac{h_1(t)}{h_0(t)}e^{-(v-u)}-\dfrac{h_0'(t)}{h_0(t)}=0\\ v_t-\dfrac{h_0(t)}{h_1(t)}e^{-(u-v)}-\dfrac{h_1'(t)}{h_1(t)}=0, ...
1
vote
0answers
134 views

Expected value of multiplied and squared Wiener Process

Can someone help me how to calculate the following: $E0[z^2[2] \mathrm{Exp}[-2 z[2]] ]$ Where $z[2]$ is Wiener process. How to find exact expected value? I am new to this stuff and not sure how to ...
1
vote
1answer
159 views

Where to find Geman 1995's proof on Changes of Numaraire?

Geman, H., El Karoui, N., Rochet, J.C. (1995) published paper "Changes of Numeraire, Changes of Probability Measures and Pricing of Options", on "Journal of Applied Probability " vol 32, pg 443-458. ...
0
votes
1answer
534 views

Gremlins are investing in stock

Gremlin Industries will pay a dividend of \$1.80 per share this year. It is expected that this dividend will grow by 4% each year in the future. The current price of gremlins stock is \$22.40 per ...
0
votes
1answer
79 views

Girsanov's theorem and simulation of bond prices

Assume that we want to calculate the time $t=0$ price of a bond: $B(0,T) = E_P[\exp(-\int_0^T r_s ds)]$, where $r$ is the interest rate following the SDE $dr_t=k(\theta-r_t)dt+\sigma ...
1
vote
0answers
58 views

Why does the price term in Vega disappear for a European call option?

In my course, I have been asked to prove a number of statements about "the Greeks" from the Black-Scholes model for pricing a European call option with no dividends and a strike price of $K$. One of ...
-1
votes
1answer
304 views

Option Pricing, A Practitioners Guide, Martingale's, Drift Change and Radon-Nikodym

Im slightly confused about this section of the booklet regarding option prices byIain J. Clark. 1) Regarding the part of obtaining a martingale property we require that the last exponential term ...
3
votes
1answer
128 views

Why is that a risk averse consumer buys the optimum insurance when there is actuarially fair insurance?

I've asked the same question at the Quantitative Finance StackExchange. Consider the following example: "As a risk-averse consumer, you would want to choose a value of x so as to maximize expected ...