Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [finance]

Questions related to the various aspects of financial mathematics. Topics include option pricing, arbitrage theory, market completeness and stochastic analysis.

Mathematical finance, also known as quantitative finance, deal with finance and financial markets in a mathematical manner.

Some examples of mathematical finance are the fundamental theorem of asset pricing which provides the conditions for a market to be arbitrage-free and complete, and the Black–Scholes equation, which uses partial differential equations to describe the price of an option over time.

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2637 questions
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Optimal Compounding Interest Rate

I'm working in the crypto currency space. I have the ability to deposit some cash into an account and obtain interest from it. To get the interest, I have to claim it. I'd like compound the interest back into the account to increase earning…
Darthg8r
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NPV of a project

Consider the following project. Costs: $100,000, at time t = 0. $45,000, at time t = 4. Income: Three payments of $10,000, each one year apart, with the first payment at time t = 1. Four payments of $60,000, each paid every 4 years apart, with the…
brian24
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American call and put option relationship

If an American call option and an American put option both have the same strike price K and expire at time T, with no dividends, how can we find a relationship between their prices? I get that if they are both held till expiry, we can use the…
amalia peters
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I'm looking a compound interest formula.

Admittedly, I just finished physics and calculas but some of my more basic math skills escape me. I'm looking for a formula that will give me a total compounded value after x number of weeks. So for example lets say I start off with an initial…
Scott
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Finding present value without an intrest factor

I invest $\$750$ in an annuity for eight years at $6\%$pa with interest compounded annually. Find the present value of annuity to nearest dollar. Now, this can simply be solved using an interest factor table so $750 \times 6.2098$ However, I tried…
user71207
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Proving that for otherwise identical call options with different maturity T1 and T2, c2>c1

I'm currently stuck on trying to prove the following: use a 1-step binomial model, we have two otherwise identical call options with expiration $T_1$ and $T_2$. Prove that $c_1 ≤ c_2$. Here's the notations I've used: $S_0$ = spot price $u$ is when…
Anna Lavender
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Deferred Annuity not working

A simple financial math problem: Mack obtains $500\ 000$ repayable over $20$ years. If interest is compounded monthly at $9.25\%$ per annum, determine the monthly repayments if the repayment begins in $6$ months time. I used the formula: $$P_v =…
Daniel Feinstein
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Force of interest piecewise function to find nominal yearly interest

I have been given a question that asks to calculate the nominal yearly interest rate from the force of interest of the following piecewise function: I initially approached this question by doing the following. From this point onwards i solve for…
Jack123
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find the interest rate in the form of compound interest with recurring contribution

I have the following formula to find the final value of compound interest with recurring contribution: Where: S: is final amount T: my recurring value i: interest rate n: recurrence period what I want is to isolate i in this formula
Marcius Leandro
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Find an expression for $n$ in terms of $x$, $y$, and $z$.

At a certain rate of compound interest, $100$ will increase to $200$ in $x$ years, $200$ will increase to $300$ in $y$ years, and $300$ will increase to $1,500$ in $z$ years. If $600$ will increase to $1,000$ in $n$ year, find an expression for $n$…
Mahamad A. Kanouté
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Exposure At Default: Calculating the present value

In this numerical example, I can't figure out with which numbers (when using the PV formula) to calculate exposure at default (EAD) as shown in the table. The EAD is the value of the discounted future cashflows (CF) at the time of default. With my…
Dennis K.
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Can anyone show me how this was derived?

So here is all the slide says and I'm and trying to see the steps for derivation. Can someone please show me how this is derived? Essentially I'm trying to go from 1 to 2. Pi is the profit function. If 1.)$$v(t)=max \pi(t,b)=\pi(t,B(t))$$ why…
EhBabay
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Forward forward volatility

Given the spot rates for a zero coupon security maturing at time 1 and a zero coupon security maturing at time 2, (where time 1 < time 2), it is possible through bootstrapping, to calculate the forward rate for the period between time 1 and time…
user279687
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Market value of a bond between coupon payment

A 10,000 par value bond with coupons at 8%, convertible semiannually, is being sold 3 years and 4 months before the bond matures. The purchase will yield 6% convertible semiannually to the buyer. The price at the most recent coupon date,…
MinYoung Kim
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Yield rate as a nominal interest rate

Brown deposits $5000$ in a $5$-year investment that pays interest quarterly at $8\%$, compounded quarterly. Upon receipt of each interest payment, Brown reinvests the interest in an account that earns $6\%$, compounded quarterly. Determine Brown’s…
MinYoung Kim
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