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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30 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
35 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, ...
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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
39 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 ...
1
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1answer
30 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
81 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
88 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
21 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
32 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
44 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
30 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
57 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 ...
1
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1answer
27 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 ...
1
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1answer
36 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} ...
0
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1answer
51 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
53 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 ...
1
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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
42 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
50 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
30 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 ...
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1answer
19 views

IRR for Incremental Investment Doubt

I had a doubt in the following question's solution: Aren't the signs in the equation wrong? Shouldn't it be $-(6,000,000 - 400,000) + 15,000,000(P/F, i^*,15) - 400,000(P/A,i^*,14) = 0$ (using ...
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1answer
42 views

Derive an expression for the value of the asset as a function of time, V(t), t>=0

An investor deposits USD 300 in a bank account at time 0, reinvests all interest payments and also additionally continuously invests USD 300 per annum, until the total value of the deposits reaches ...
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2answers
24 views

Nominal annual interest

A bank offers the following certificates of deposit: $$ \begin{array}{c|lcr} \text{Term in years} & \text{Nominal annual interest rate(convertible semi-annually)} \\ \hline 1 & 0.05 \\ 2 ...
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1answer
18 views

Annuity and future equivalent values

I need some clarification on the formulas to use for these questions. Q1. If $\$30,000$ is deposited now into a savings account that earns $7\%$ per year, what uniform annual amount could be ...
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0answers
21 views

Intuition behind a market uncertainty represented by a filtered complete probability space?

What is the intuition behind a market uncertainty represented by a filtered complete probability space $(\Omega, F, P, {F_t})$, on which an m-dimensional standard Brownian Motion $W(t) = (W_1 (t), W_2 ...
2
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1answer
41 views

Financial Mathematics problem.

Consider a property developer who buys a property at time $0$ for $\$90,000$. He also spends $\$10,000$ at time $0$ to buy some materials he will use to develop the property. Ignoring Inflation , the ...
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1answer
21 views

Ordinary Annuity future value

I have a problem to calculate future value of this problem: "The parents of a newborn baby set up an account to cover the cost of college they deposited 1,500 every birthday in an account that pays ...
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0answers
35 views

Find the value of forward contract

The current spot gold price is $\$1788$ per ounce. The storage cost is $\$24$ per ounce per year, to be paid quarterly at the beginning of each quarter. Suppose the current $3$-month and $6$ month ...
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1answer
19 views

Need to find annual payment in 2 halfs of the payment period [closed]

A loan of $4000 is to be repaid over a period of 8 years. During the first years, exactly half of the loan principal is to be repaid (along with accumulated compound interest) by a uniform series of ...
0
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1answer
46 views

Finding implied interest rate from swap exchange

Suppose the current term structure of interest rates (0.5 year, 1 year, 1.5 year, 2 year maturities annualized with semi annual compounding) is (5.00%, 6.00%, 7.00%, 8.00%). A 2-year vanilla interest ...
0
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1answer
26 views

loan repayment involving added amounts

A bank charges $5\%$ interest p.a on loan. At the end of the year, the interest is added and then a fixed amount $R$ is paid off. If the amount borrowed is $1000$, show that the amount owed at the ...
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1answer
40 views

Financial mathematics - earning compound interest

This I assume is a very simple question but can't really wrap my head around it. So the question is: If 100 dollars is deposited at time t = 0 into an account earning 10% interest and $20 is ...
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1answer
32 views

how to prove that there is no arbitrage if the following inequality is satisfied?

The continuously compounded interest rate is $r$. The current price of the underlying asset is $S(0)$, and the forward price with delivery time in one year is $F(0,1)$. Short selling of the stock ...
0
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2answers
62 views

Simply this formula

Is there a way to write $\sum_{n=a}^b (Q+P(n-1)) v^n$ in terms of $\sum_{n=a}^b v^n$? So far I've gotten: (Q-P)$\sum_{n=a}^b v^n$ + P$\sum_{n=a}^b nv^n$. *I know the last term can be rewritten as ...
0
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1answer
32 views

Future value and simple interest

On a loan of $3,000 at an interest rate of 12% per year when half of the loan principal is repaid as a lump sum at the end of four years and the other half is repaid in one lump sum amount at the end ...
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0answers
38 views

what am I doing wrong when finding the weights of the market portfolio?

I need to find the weights of the market portfolio with three risky securities given the following information: $\mu_1=0.08$ $\sigma_{1}^{2}=0.0255$ $c_{12}=0.00225$ $\mu_2=0.1$ ...
1
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1answer
33 views

How do I calculate the delivery price for a forward contract?

How do I calculate the delivery price for a forward contract? In the time interval $[0,t]$ the interest rate is $r_1$ and in the time interval $[t,T]$ the interest rate is $r_2$. Determine the ...
0
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1answer
25 views

Sum of Present value [closed]

The sum of the present value of 1 paid the end of n periods and 1 paid at the end of 2n periods is 1. Find $(1+i)^{2n}$. Present value for n periods is given as $(1+i)^{n}$ and that of 2n follows the ...
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1answer
11 views

Compounded discount rate

The total amount of a loan to which interest has been added is $20000$. The term of the loan was for $4.5$ years. If the annual rate of interest was $6\%$ and interest was compounded annually, what ...
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2answers
16 views

Present value and discount function

What deposit made today will provide for a payment of $ \$1000$ in $1$ year and $ \$2000$ in $3$ years, if the effective rate of interest is $0.075$. Answer is $\$2540.15$ I have calculated $d=0.069$ ...
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2answers
53 views

Compound interest with penalty in withdrawal amount

Carl puts $10000$ into a bank account that pays an annual effective interest rate of $0.04$ for $10$ years. If a withdrawal is made during the first five and a half years, a penalty of $5\%$ of the ...
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1answer
19 views

Expectation equals to Black-Scholes Equation

Let $S_t$ be ageometric brownian motion with parameters $\sigma$ and $r$ and fix $T,K\in (0,\infty)$. How can I show that: \begin{align} \mathbb{E}[e^{-rT}max\{(S_T-K),0\}] & = ...
1
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1answer
32 views

How do you calculate the breakeven amount for two credit cards with different fees and rebates?

Credit Card (CC) M offers a rebate of cash back of $a$ dollars, with NO annual fee. CC S offers a rebate of cash back of $b$ dollars, but charges an annual fee of $f$. How much must I ...
0
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1answer
36 views

Empirical Formula for Financial problem

I have a financial problem, which is strictly related to math of course. The problem states that on the last year the steel market price was about $450$ \$, and a company, that sells steel, used to ...
2
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0answers
24 views

Under which conditions on $\sigma_1, \sigma_2$ and $\rho_{12}$ the minimum variance portfolio involves no short selling?

If $\rho_{12} \lt 1$ or $\sigma_1 \ne \sigma_2$ then $\sigma_{V}^2$ representing the variance of the portfolio with weights $(w_1, w_2)=(s, 1-s)$ as a function of $s$ attains its minimum value at ...