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
17
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2 answers

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 consecutive years. F = final amount obtained. I…
user3323679
  • 171
16
votes
2 answers

Price of a European Call option is a convex function of strike price K

I'm trying to show that the price of a European call option (payoff function is $(S_1-K)^+$) in a no-arbitrage market is a decreasing and convex function of K. That it shall be decreasing makes sense; as $K$ increases, $S_1-K$ decreases and we make…
Marie. P.
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14
votes
7 answers

How the formula for EMI is derived

I was looking for a formula to calculate EMI (Equated Monthly Installments). I have some fixed known parameters like, Principal Amount, Rate of Interest and No. Of Installments. By googling, I came across the formula, $$Installment Amount = \frac…
Rumit Parakhiya
  • 243
12
votes
2 answers

Proof of the Black - Scholes pricing formula for European Call Option

I want to prove the following The price of a European call option with strike price $K$ and time of maturity $T$ is given by the formula $\Pi(t) = F(t,S(t))$, where $$F(t,s) = sN[d_1(t,s)]-e^{-r(T-t)}KN[d_2(t,s)]$$ $$d_1(t,s) =…
Teodor Fredriksson
  • 271
12
votes
2 answers

What's the math formula that is used to calculate the monthly payment in this mortgage calculator?

What's the math formula that is used to calculate the monthly payment in this mortgage calculator? I would like to know this math formula so that I can plug in the following values Mortgage Amount: $100,000 Rate Type: Fixed Interest Rate: 6% …
burnt1ce
  • 173
10
votes
3 answers

Proof of Continuous compounding formula

Following is the formula to calculate continuous compounding A = P e^(RT) Continuous Compound Interest Formula where, P = principal amount (initial investment) r = annual interest rate (as a decimal) t = number of years A = amount after time…
Tilak
  • 251
9
votes
4 answers

No-Arbitrage Principle

I hope you do not mind me asking a financial question in this section. I am having trouble understanding the concept of the no-arbitrage principle for a particular example in my notes: Suppose a share has price 100 at time $t=0$. Suppose further…
Delvesy
  • 749
7
votes
5 answers

Paying off a mortgage twice as fast?

My brother has a 30 year fixed mortgage. He pays monthly. Every month my brother doubles his principal payment (so every month, he pays a little bit more, according to how much more principal he's paying). He told me he'd pay his mortgage off in 15…
three-cups
  • 173
6
votes
1 answer

Why is there a difference between life-insurance and general (non-life) insurance mathematics?

I know that actuarial mathematicians specialize in either life or non-life insurance. My question is, what is the difference between these two fields mathematically? Why is there a need for specialization? Why isn't it the same mathematical theory…
menaci342
  • 163
5
votes
1 answer

Riskless Pricing of an European Option; How to calculate?

I don't know if this question could be asked/answered here but since there is a "finance" tag...I'll give it a shot. I am asked to show that the value of an option below obtained by 1. Risk-neutral 2. Risk-less portfolio argument are the same. I…
Melba1993
  • 1,111
4
votes
2 answers

Calculating credit card charges based on provided APR, balance amount and monthly payment amount?

Please first see the below sums and then the info below it to get a better understanding of my question: My input: Balance amount = $350 APR = 18% Monthly Payment Amount = $60 The output: Monthly Interest Amount = $5.25 Time to repay entire Balance…
Noob
  • 43
4
votes
4 answers

What is the reasoning for the Discount Factor formula?

I've previously come across dicount factors in my high school education but we had formula sheets so I never bothered actually learning it. In my university I have a business class in which we are now going over dicounted cash flows. Now that I'm a…
Emmanuel M. Smith
  • 143
4
votes
3 answers

Formula for calculating the total interest payable over the life of a loan

wondering if someone can help a non-mathematician out. I am looking for the formula for calculating the total interest payable over the life of a loan. Given that we know: P: Principal (amount) of loan R: The monthly repayments on the loan T: The…
cbp
  • 143
4
votes
2 answers

Put Options and Arbitrage

I came across the following problem on put options: A European put with strike price $100$ expiring in $1$ year has premium $ \$ 1$ and a European put with strike price $K$ expiring in $1$ year has premium $ \$ 2$. The continuously compounded risk…
Damien
  • 4,291
4
votes
1 answer

Calculating interest rate for a payment plan

I really should know this from high school so I'm a bit ashamed to ask... :) I've been offered several cars for lease and want to compare the offered interest rates. E.g. I have: Car: Ford Fiesta 1.0T Lease period: 36 months Price: 156619…
rickythefox
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