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.

If you don't think your question is suited for this site, try:

2637 questions
2
votes
2 answers

Solve for level payment with a twist

Reworded trying to clarify. Also corrected example to correctly state 4 years and 150 days. I'm struggling with how to solve for a level withdrawal that will reduce a starting balance amount to zero over n years and m days assuming interest rate x.…
brentj
  • 23
2
votes
1 answer

Mortgage calculating time for residual debt

I have a mortgage for C capital, with constant monthly payments, constant interest rate i (and constant duration in year D). I would like to know after how much time I reimburse $r$ dollars. For example: For a $10$ year $3$% mortgage, with $100…
Paolo
  • 123
2
votes
1 answer

Implying the risk-neutral distribution

This is a problem from the book Stochastic Calculus for Finance II: Continuous-Time Models by S, Schreve. Exercise 5.9 (Implying the risk-neutral distribution). Let S(t) be the price of an underlying asset, which is not necessarily a geometric…
Don P.
  • 313
2
votes
1 answer

Increasing annuity problem FM

Consider a situation where you took a loan for $\$15,000$ and you are paying back the amount at annual effective interest rate of $3\%$, $\textrm{# of periods = 25}$. Now, you make the first payment of $100$ and then the next payment is $200$.…
ATS
  • 133
2
votes
1 answer

Future Value AT TIME 12

The question states: $\$500$ deposited @ time $= 0$, and then $\$1000$ deposited @ time $=3$ for a total of $12$ years. I need to find the value @ time = $12$. Discount rate = $7.5\% $ So, my equation is -> $$500\times (1.075)^{12}+1000\times…
ATS
  • 133
2
votes
1 answer

Maximizing interest question

My initial investment is $\$100,$ and I earn $1\%$ interest per day. I can opt for any number of compoundings per day (if twice per day, then the interest rate per compounding period is $0.5\%,$ and so on), but I have to pay $\$0.01$ each time my…
thestar
  • 169
  • 11
2
votes
1 answer

Hedging a long position-one period

Consider a one period binomial stock model with $S_0=4$, $S_1(H)=8$ and $S_1(T)=2$. The interest rate is $25$%. Let's say I buy a call option for $1.20$ with strike price $K=5$ which expires at time $1$. I'm trying to figure out how to invest in…
Set
  • 7,600
2
votes
1 answer

WHY? Present Value of a growing annuity

I am doing an exercise (I don't know for how long now) that I just can't understand, worst, it's quite simple. opportunity cost for equity holders = $10\%$ Stock C is expected to pay a dividend of $\$5$ next year. Thereafter, dividend growth is…
trombo cide
  • 21
2
votes
0 answers

Convert the interest rate $j_{2}=9\%$ to $j_{12}$ equivalent

Convert the interest rate $j_{2}=9\%$ to $j_{12}$ equivalent $j_{m}:$ nominal (yearly) interest rate which is compounded (payable, convertible) $m$ times per year $\$1$ at $j_{12}=12i$ will accumulate to $(1+i)^{12}$; $\$1$ at $j_2=9\%$ will…
falamiw
  • 862
2
votes
1 answer

Inner mathematical workings of excels rate function or why is my manual APR calculation different?

I am trying to understand how the APR calculations we are using at work, but calculating it by hand is giving me different answers. The answer I am looking for to this question is either An explanation of the inner mathematical workings of excels…
CEH
  • 410
2
votes
1 answer

Arbitrage pricing for financial options

Are the following arguments valid for why $C(K_1) \geq C(K_2)$? There are several outcomes for the payoff. If $S
InvestingScientist
  • 433
2
votes
1 answer

Risk neutral probability for stock with continuous dividend

Setting: binomial tree with one step over time $\Delta t$. I'm trying to derive the risk neutral probability for a stock which pays a continuous dividend, say $\delta$. i.e. probability $p$ such that $$e^{r \Delta t} S_0 = S_u p + S_d(1-p)$$ where…
qp212223
  • 1,626
2
votes
1 answer

is possible to calculate Net Present Value with different discount rates per year?

The formular for NPV is: Net Present value formula $$\sum_{t=1}^n= \frac{Rt}{(1+i)^t}$$ where: Rt =Net cash inflow-outflows during a single period t i=Discount rate or return that could be earned in alternative investments t=Number of timer…
KmnsE2
  • 121
2
votes
1 answer

Which option is a better idea? Lottery Scenario.

I have a finance question and would appreciate if I could get some help on how to solve this one! The Question is the following: Imagine you won a lottery and you are given two choices to receive the prize. You can either receive 50,000 annually for…
Emon Hoque
  • 23
  • 2
2
votes
1 answer

FM question Financial math

A $10{,}000$ par value $10$-year bond with $8\%$ annual coupons is bought at a premium to yield an annual effective rate of $6\%$. Calculate the interest portion of the $7$th coupon. The solution (image) is the following: The book value at time…
musik lover
  • 33
1 2 3
…
52 53