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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Expected annual returns (financial maths)

An economy contains these three assets: Asset A has standard deviation of returns (per annum) of 25% and market capitalisation $600m Asset B has standard deviation of 20%, market capitalisation ...
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1answer
39 views

Math Finance Question NPV?!

A foundation announces that it will be offering one MIT scholarship every year for an indefinite number of years. The first scholarship is to be offered exactly one year from now (today is year $0$, ...
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0answers
43 views

Relations between Call and Put

I am trying to solve a question in finance but I am pretty much stuck and would need your help :) Suppose you know the following information about a market: Future is at 66 70 strike straddle is ...
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2answers
59 views

Calculating accumulated values for annuities

Having difficulty with this problem Find the accumulated value at end of four years of an investment fund in which 100 is deposited at the beginning of each quarter for the first two years and ...
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1answer
22 views

Determining outstanding balance using the prospective method

A loan is being repaid with 10 payments of 2,000 each followed by 10 payments of 1,000 each at the end of each half-year. Assume that the nominal rate of interest convertible semiannually ...
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0answers
22 views

Calculating ROI of Feature

I have the following figures: (x) Quote for new software feature: $10,000 (y) Employee Rate: $15.00/hour (z) Hours per Day to perform task manually: 2 (n) Number of working days in a year: 251 ...
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1answer
34 views

Financial mathematics annuities problem

I'm having trouble understanding the solution of this problem. Find the present value of a ten-year annuity which pays 400 at the beginning of each quarter for the first 5 years, increasing to 600 ...
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1answer
47 views

A sum of money amounts to Rs.49400 in 3 years and Rs.50400 in 5 years > at the same rate of simple interest.

A sum of money amounts to Rs.49400 in 3 years and Rs.50400 in 5 years at the same rate of simple interest. Find rate of interest per annum. This question was asked in Railway Exam. Source: ...
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24 views

Finding accumulated profit (Finance).

We need to find the accumulated profit at $t=5$ ( in years ) for the following project given that it is financed by a loan subject to interest $6.25\%$. Project : Initial outlay of $\$ 100,000$ , ...
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1answer
58 views

Outstanding balance and amount of interest

I'm having trouble with this problem: A loan is being repaid with level annual payments based on an annual e ffective interest rate of 8%. If the outstanding balance immediately after the 10th ...
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0answers
64 views

Exact match of assets and liabilities.

Liabilities of $1$ each are due at then ends of periods $1$ and $2$. There are three securities available to produce asset income to cover these liabilities, as follows: (i) A bond due at the end of ...
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1answer
58 views

SDE Integration: Normal-Mean Reverting Process - Question

I am trying to figure out how a particular SDE can be integrated. The SDE is the normal mean-reverting model: $dX_t = \theta(\mu - X_t)dt + \sigma dW_t$ (1) Where $W_t - N(0,t)$. So far, I have ...
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Distribution of stochastic process and Ito's lemma

Consider an arithmetic Brownian motion $X_t$ which follows $dX_t=\mu dt+\sigma dZ_t$ where $\mu$ and $\sigma$ are constants and $r$ is the discount rate. Assume an asset price $S_t=X_t^2$. I need to ...
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2answers
39 views

Amortization vs Sinking Fund Financial Mathematics

I'm struggling with this question A 20-year loan of 20,000 may be repaid under the following two methods: i) amortization method with equal annual payments at an annual effective rate of 6.5% ii) ...
2
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1answer
23 views

Get rate from Future Value of Annuity

$FV = \dfrac{(1+i)^t-1}{i}\cdot C$ What are the algabraic steps I need to rearrange to get i? The i divided by the i is specifically tripping me up. Many thanks!
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1answer
39 views

Exchange Rate Dynamics

Due to my project in mathematics I am trying to understand the dynamics of exchange rate. Consider the following: $$\dot{p}= \pi \ln (D/Y)= \pi[u+\delta(e-p)+(\gamma -1) y-\sigma r] \ \ \ \ \ \ \ \ ...
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2answers
95 views

Financial mathematics increasing annuities

I am having trouble solving this problem Julie bought a house with a 100,000 mortgage for 30 years being repaid with payments at the end of each month at an interest rate of 8% compounded monthly. ...
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1answer
21 views

Put-on-call option confusion

So the question asks: Given a 3-steps Binomial Tree model with $S(0) = 50$, $U = 20%,D = 􀀀20%$, and $R = 5%$. A European call option has the strike price $X = 40$ and maturity time $T = 3$. Also, a ...
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1answer
28 views

Prove that the following inequality holds: $P_E(\alpha X+(1+\alpha)X') \le \alpha P_E(X)+(1-\alpha)P_E(X')$

Prove that the price of the European put option is a convex function of the strike price in one-step binomial model. In other words, if $P_E(X)$ is the price of the European put option in one-step ...
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1answer
33 views

Minimum and maximum portfolio standard deviation

A portfolio consists of assets A and B which possesses the following expected return, risk and weights.\(a)What is the Maximum portfolio standard deviation.\(b) What is the minimum portfolio standard ...
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1answer
43 views

What is the return of the riskless asset in the market

A market consists of two risky assets and one riskless asset. Asset $1$ has a return of $5\%$ and a risk of $6\%$. Asset $2$ has a return of $15\%$ and a risk of $24\%$. The correlation between the ...
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0answers
15 views

Replication strategy of European call option

So the question asks: L et $S(0) = 120$ dollars, $u = 0.2$, $d = −0.1$ and $r = 0.1$. Consider a call option with strike price $X = 120$ dollars and exercise time $T = 2$. Find the option price and ...
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1answer
32 views

Finance mathematics doubt.

I don't understand the difference between the following two statements stated as : (1) The price rises by say $X\%$ during the time $t=0$ to $t=10$. (2) There is an inflation of $X\%$ during $t=0$ ...
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1answer
27 views

Sinking fund and differing interest and payment periods

I'm having trouble understanding this solution for a sinking fund question. A borrower takes out a loan of $2000 for two years. Construct a sinking fund schedule if the lender receives 10% ...
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1answer
31 views

What is a hedge ratio tree?

Determine the stock price tree, the call option tree, and the hedge ratio tree. I have to make three separate trees for a european call option, I know what a stock price tree and a call option tree ...
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1answer
27 views

Is the price of a European option at time $1$ equal to the payoff at time $1$ if expiration is time $2$?

$S(0)=150, u=1.2, d=.8, X(\text{strike price})=120, r=10\%$, expiration $T=2$ where $S(t)$ is price of stock at time $t$, $S_u$ is price of stock if it goes up at time $1$ and $S_{uu}$ is price of ...
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2answers
33 views

Showing that the square of Brownian motion, minus time, is a martingale

What exactly are we supposed to do to show what they have given is a martingale. If I try to follow through I'm getting a bit confused. In the third to last line I don't understand how they have ...
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0answers
26 views

How are Eurodollar futures prices calculated?

Whether the lecture notes are poorly written, or whether I'm just failing to understand them, I do not know. I'm currently looking at the following section, on Eurodollar futures: As you can see, ...
2
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0answers
34 views

Using reflection principle to find probabilities

I'm not able to answer these questions because firstly I don't understand the reflection principle properly. Secondly if someone could provide a visual explanation as to how this process works ...
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0answers
33 views

Interest rate calculation of non-constant monthly installments

I would like to calculate the interest rate $i$ of an annuity with $n$ payment periods. I have found a lot on this topic if the annuities $FV_t$ are constant (geometric series). In my case the ...
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1answer
27 views

If interest on drawings is charged at lets say 10% per annum and david made his drawings (monthly) which amounted to a

If interest on drawings is charged at lets say 10% per annum and david made his drawings (monthly) which amounted to a total of $50000 for the year. How much is he going to pay as interest on ...
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2answers
78 views

How many interest periods if you always pay double the interest [closed]

A loan of $12,500$ is made at an effective interest rate of $8.5\%$. Payments are made at the end of each interest period. Each payment equals twice the interest due until the borrower pays off the ...
2
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1answer
40 views

Why is Backward SDE more difficult than forward SDE?

I need to explain Backward Stochastic Differential Equation (BSDE) for some non-mathematicians. The audiences are most likely familiar with ODE/PDE as physicists. One concern is probably that why ...
2
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1answer
59 views

Simplifying Integral Expression w/ Antiderivative

I'm trying to simplify this formula here. For the most part, evaluating this expression is straightforward. However I am very confused about how to approach this last term in the expression. I want ...
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1answer
24 views

Forward Contracts.

Let $K$ be the forward price of a contract/asset agreed at time $t=0$ to be paid at $t=T$. Now, we say that the forward price $K$ is determined in such a way that the ' value of the forward contact ' ...
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2answers
84 views

How to find the price of the call option?

Assume we have a financial market consisting of a bond $A$, a stock $S$ and call options $f$ on the stock. Consider only two times $0$ and $T$ and only two possible outcomes for the value of $S$ at ...
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1answer
19 views

Calculate minimum growth rate required [closed]

I pay the following fees and taxes when trading a stock: 1% of the initial investment [when buying] 1% of the initial investment + profits [when selling] 25% tax on profits. What is the formula to ...
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3answers
30 views

Use the given rate of inflation to calculate the value of $100 in 1910, now.

problem: You have been told that the average rate of inflation between 1910 and 2016 is $3.8\%$. Using this information, calculate how much $100 in 1910 would be worth today. What I tried: This one ...
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2answers
42 views

How to calculate the interest rate in the below problem?

A loan of £12,000 is issued and is repaid in instalments of £300 at the end of each month for 4 years. Calculate the effective annual rate of interest for this loan. What I tried. The equation of ...
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2answers
29 views

Decreasing perpetuity problem

A perpetuity pays 1000 immediately. The second payment is 97% of the first payment and is made at the end of the fourth year. Each subsequent payment is 97% of the previous payment and is paid four ...
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1answer
56 views

Financial mathematics perpetuity problem

I'm having trouble solving this FM problem. For $3000$, Nick purchases an perpetuity-immediate paying $100$ at the end of each $6$ months period. For the same amount and for the same effective ...
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1answer
24 views

Pricing a digital put option using BS model

I'm not able to understand why we are working out probability sT is less than K. For example why could we not have done probability sT is more than K? I understand the steps after that but why ...
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1answer
34 views

Differential of Fisher-Weil Bond Price using discrete-time compunding

I would like to ask you if my calculations are correct regarding the differential of the price of a bond using a sequence of spot rates as discount factors. \begin{equation} P(i^S ) = \sum_{t=1}^{T} ...
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1answer
50 views

A level continuously paying annuity pay 1500 each month. Find the present value

Here is the full question: A level continuously paying annuty pays $\$ 1500$ each month for eight year. The force of interest is $\delta(t)=\frac{2t}{t^2+5}$ where time is measured in years. Find the ...
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0answers
46 views

Show that formula for European call option satisfies Black-Scholes equation and boundary conditions.

Can anyone please help me out with this question? Show that the formula for the European call option satisfies the Black Scholes equation, and that it satisfies the appropriate initial and boundary ...
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1answer
19 views

Replication in the multi-period binomial model.

For the solution: Just wanted to ask for $V_{3}(HTH)$ I get $S_{1}(H)$ and $S_{3}(HTH)$ to give me the same maximum value of $16$ so would it also be right if I used $S_{1}(H)$ nstead of ...
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2answers
38 views

Compound Interest Formula adding annual contributions

I'd like to know the compound interest formula for the following scenario: P = Initial Amount i = yearly interest rate A = yearly contribution or deposit added. n = the deposits will be made for 10 ...
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0answers
46 views

Pricing Function is convex

I am now reading Alternative Characterization of American Put Options by Carr et all (available at http://www.math.nyu.edu/research/carrp/papers/pdf/amerput7.pdf). There is a theorem called 'Main ...
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1answer
29 views

Potential arbitrage profit and proof

So the question asks: Consider 4 following European call and put options with the same maturity time: Call option with strike price $100$ sell for $45$ Call option with strike price $110$ sell for ...
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2answers
27 views

Annuities and interest conversion

I am having trouble understanding how to find the equivalent rate of interest per payment periods for annuities. For example, for this question: Find the accumulated value at the end of four years ...