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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Effective interest rate given two loan payment options...

Here's the full problem: You have two options to repay a loan. You can repay $\mathbb{$}6000$ now and $\mathbb{$}5940$ in one year, or you can repay $\mathbb{$}12000$ in $6$ months. Find the annual effective interest rate(s) i at which both options…
user146925
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Intuition behind American option pricing

The price of an American option is given by $V_n = \max\{G_n, \frac{1}{1 + r}(pV_{n +1}(H) + qV_{n + 1}(T)\}$, where $p$, $q$ are the risk neutral probabilities. I have two questions. How can one intuitively see that this must be the formula to…
user7348
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Bactracking to find compound interest

I'm trying to find what percentage 5000 dollars compounding monthly over 120 months will be if the final sum will be 7000 dollars. So: 7000=5000(1+r/12)^120 When working backwards to find r I always get the percentage = 0.2% but I did trial and…
shalorsar
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How much more than will you pay on a 30 year mortgage than if you paid it all up front?

There are hundreds of loan calculators online but none of them tell me this, Say I take out a 30 year mortgage on a 80,000 dollar house for 4% interest. How much more than $80k will I spend at the end of the 30 years? Assume the normal compounding,…
AnotherUser
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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?
Dinesh G
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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 $VaR_\alpha=F^{-1}(\alpha)$. Thus I need to…
Dahn
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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 the underlying asset in a year is $200$ with…
Dahn
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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
David
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Showing concavity of a function defined in terms of expectancy of another function

Suppose $ U : \mathbb{R} \to \mathbb{R} $ is concave, and that the random variable $ \epsilon $ has zero mean. Assuming that the function $ \phi : \mathbb{R} \to \mathbb{R} $, defined by $ \phi(\lambda) = \mathbb{E} U(\mu + \lambda \epsilon) $ is…
MartinP
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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 $1$ percent per month, that is, $i=0.01$. Starting…
Sigur
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Principal and Annuities

Suppose you want to accumulate $12\,000$ in a $5 \%$ account by making a level deposit at the beginning of each of the next $9$ years. Find the required level payment. So this seems to be an annuity due problem. I know the following: $ \displaystyle…
NebulousReveal
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Finding the compounding period

The future value of a 200 deposit in an account that earns 6.25% annual interest is $272.71 after 5 years. Determine the compounding period for this investment. This is what I have done: $272.71= 200 (1+ (0.0625/x))^x $ $1.36355= (1+…
Rose
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Price of Product

Suppose an item costs $ \$10$. The expected demand for 4 years are: $$ \text{1st year}: 5$$ $$ \text{2nd year}:10 $$ $$ \text{3rd year}:1 $$ $$ \text{4th year}:2 $$ The actual demand is: $$ \text{1st year}: 3$$ $$ \text{2nd year}:12$$ $$ \text{3rd…
finguy
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Check my math - Compound Interest

I recently calculated how long it would take to pay off a loan, and I would like to have someone check my math to make sure I'm doing it right. I used the formula below: (i = APR/12, b = total balance due today, p = monthly payment amount) n = ln((1…
Kyle Trauberman
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Acquisition + Rent payment calculations

I was reading some documentation which had an example scenario. In the scenario, they gave the following details Price = 150000 ownership buyer = 20% = 30000 bank = 80% = 120000 period = 30 years rent = 4.99% Using the above, apparently the…
oshirowanen
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