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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2answers
99 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
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1answer
127 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 ...
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1answer
70 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 ...
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2answers
613 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
258 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
139 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 ...
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0answers
141 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
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2answers
62 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. ...
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1answer
71 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
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1answer
72 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
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2answers
53 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. ...
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0answers
38 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 $n \times 1$, ...
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2answers
103 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.
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1answer
330 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 ...
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1answer
35 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?
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0answers
58 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 ...
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0answers
87 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
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1answer
57 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 ...
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1answer
92 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
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1answer
37 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
87 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
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1answer
162 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.
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1answer
48 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
148 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
806 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
49 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 ...
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1answer
69 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
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1answer
52 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 ...
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1answer
15 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
24 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
49 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 ...
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4answers
40 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
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2answers
64 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
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0answers
64 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
1answer
187 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
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1answer
72 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
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0answers
72 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
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1answer
47 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, ...
0
votes
0answers
111 views

Second Fundamental Theorem of Asset Pricing

It seems that there is a step missing in the proof of the second Fundamental Theorem of Asset Pricing in Shreve's Stochastic Calculus for Finance II: Does anyone know how to show the following: If ...
1
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0answers
100 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
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1answer
112 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
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1answer
356 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
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1answer
66 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 ...
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0answers
56 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 ...
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1answer
245 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
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1answer
97 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 ...
1
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0answers
43 views

On finance problem: saving money

First of all, sorry for my pour English. Consider the situation: I'd like to save an amount $P$ of money every month for $240$ months consecutively ($m_1,\ldots,m_{240}$). The gain with money is ...
0
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0answers
229 views

Put-Call-Parity of Asian Options

I could need some help with deriving the put-call-parity for asian options. Let $S_t$ be the price of the underlying asset at time $t$ and set $Y_t = \int_0^t S_t dt$. Then the payoff of an asian ...