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
1
vote
0 answers

Calculate sell(sales) price from margin and cost price

Slight finance question, trying to program the calculation of sell price when we have %margin and cost price. ((CostPrice / ((1 - %Margin) / 100)) * 100) / 100 This is what I am doing at the moment. Can someone confirm it is correct. I am having an…
Anicho
  • 111
1
vote
1 answer

Price of an option that pays $1$ when the stock hits $\$H$ for the first time

I am trying to understand the no arbitrage argument for to determine the price of an option that pays $1$ when the stock hits $\$H$ for the first time. The current price of the stock is $\$1$. The argument goes as follows. I can buy $1/H$ of the…
Johnny T.
  • 2,897
1
vote
1 answer

Basic concepts of Black Scholes formula

The Black Scholes formula gives the formula for European calls, for stock with no dividends, $$ c = S N(d_1) - K e^{- r (T-t)}N(d_2) $$ with $S$ the price of stock at time $t$, $T$ is the maturity date, $K$ is the strike price, $r$ is the risk free…
Johnny T.
  • 2,897
1
vote
0 answers

How to calculate years to gain 5 million net worth?

Givens: 20% annual growth 30k payments/year FV of Annuity$=P[\frac{(1+r)^n-1}{r}]$ $P=$ Periodic payment $r=$ Rate per period $n=$ Number of periods $5000 =…
adamaero
  • 127
1
vote
2 answers

Why can moving averages of the prices indicate the trend of a stock?

In technical analysis of stock trading, we can use the moving averages of the historical prices of a stock to indicate whether it is currently in the uptrend or downtrend. Let me exemplify the idea to focus my question. I may use a 10-day moving…
asinkxcoswt
  • 287
1
vote
1 answer

How can i prove that the duration of a bond with a zero coupon is equal to its maturity for discrete case compounded?

The duration of a bond is given by : $$ \frac{dP}{dy}\frac{1}{P} = - \frac{D}{1+y} $$ solving for D we have : $$D = -\frac{1}{P}\frac{dP}{dy}.$$ Now we know that the bond price formula is : $$P = \frac{c}{(1+y)^1} + \frac{c}{(1+y)^2}+\cdots +…
Homer Jay Simpson
  • 380
1
vote
1 answer

Compound Interest Including contributions

I am trying to discover the formula behind the calculations in this website(among others similar ones) https://moneysmart.gov.au/budgeting/compound-interest-calculator The formula for compound interest without any contributions is pretty simple, but…
Spyros
  • 113
1
vote
1 answer

Pay off for portfolio consisting of long call and short put both struck at K? Arbitrage construction?

I'm very new to financial maths. Please can I get some help on this question, thanks! Q: Write down the payoff of a put option with a strike of $K$. What is the payoff for a portfolio consisting of a long call and a short put both struck at $K$? Can…
user898975
  • 317
1
vote
1 answer

How can I calculate the % of balance paid in a month for a credit card user

In my credit card accounts dataset I have the current month end balance, previous month end balance, month end interest amount, and month end payment amount. How can I figure out the % of balance paid for each accounts using these values? Also, I…
new_commer1218
  • 13
1
vote
1 answer

How to obtain risk free profit via arbitrage on put-call parity?

I know that Put-Call parity allows us to find the fair price of a call/put for options with the same strike price and same expiry. In the example I am working on, I have a table showing values for Spot Price $S_0$, call price $c$, put price $p$ and…
rainingagain
  • 165
1
vote
0 answers

FM arithmetically increasing annuities

A fund is set up where each member will receive $100. Assume that 10 people will qualify at the end of one year and then 15 at the end of 2 years. [Making this an annuity immediate situation] So, this increase will go on till the number of…
ATS
  • 133
1
vote
1 answer

Pay off of investment while buying Stocks and options - An Elementary Introduction to Mathematical Finance by Sheldon Ross

I have just started the book -An Elementary Introduction to Mathematical Finance by Sheldon Ross. Please see the image (Pg 76): - Assuming the stock can only take either of the two prices: 200 or 50: then, according to me, when the stock price is…
MathMan
  • 8,974
  • 7
  • 70
  • 135
1
vote
1 answer

Call options convexity detail

here is an example I am studying to prepare for a quant interview: Nine months call options with strikes 20 and 25 on a non-dividend-paying underlying asset with spot price 22 are trading for 5.5 and 1, respectively. Can you find an arbitrage? I…
Andrea
  • 202
  • 1
  • 10
1
vote
1 answer

Calculate the yield rate on transaction

Problem:- 'A' is able to borrow $1000 from 'B' for one year at 8% effective and at the same time lend it to 'C' for one year at 10% effective. what is 'A's yield rate on this transaction? My answer:- I calculated NPV by calculating the future values…
Sujith
  • 11
1
vote
1 answer

Extra terms in continuously compounded superannuation

Adam opens a superannuation account with a deposit of $1000$ and intends to deposit money at a rate of $1000$ per year for the next 25 years. Interest is paid at the rate of $0.1$% pa, compounded continuously. If A is the amount after $t$ years,…
user71207
  • 1,543
1 2 3
…
52 53