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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How do I calculate loan mortgage balance, interest, and payment, when I refinance a house and take out a new mortgage?

So I am actually confused with how to do loan mortgage problems in my textbook. I was wondering if someone can give me some insights to solving this problem: Problem: Ten years ago the Peter's bought a house, taking out a 30 year mortgage for…
Aurora Borealis
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SVI implied vol model parameterization

It would be nice if anybody could help me. I'm trying to understand the raw SVI parameterization of Gatheral. We have: $$\omega(k; \chi_R)=a+b \left\{\rho(k-m)+ \sqrt{(k-m)^2+ \sigma^2}\right\} $$ I'm not clear about what exactly is given to…
P.G.
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Find repayment amount on loan repaying a partial amount of the principal in a definite period of time.

I'm trying to calculate the Monthly payment amount on a loan where I want to be able to define the Principal amount that should be repaid and an Outstanding balance after the repayments. Example: 1749€ is the initial principal amount supposed to…
ALM83
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Find n such that $A(1+r)^n=2A$

Suppose that you deposit your money in a bank that pays interest at a nominal rate of 10% per year. How long will it take for your money to double if the interest rate is compound? Could you, please, check the correctness of my thoughts? The…
hellohowdoyoudo
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How to price a call-on-a-put option

I've started to try and find some more exotic options to try and price using general results about the Black-Scholes equation. One of the more interesting ones I came across is the call-on-a-put option with strike $K_1$ and expiry $T_1$. It gives…
asdf
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How to find amount of final payment

A man borrowed Rupees 20,000 at 6% C.I (compound interest) promising to repay Rupees 5000 at the end of first 4 years to reduce the principal and interest and to pay the balance at the end of the 5th year. Find the amount of his final payment. Here…
Raj Kumar Singh
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Question on delta approximation to VaR

Assume a market value of $ \$ 10000$.The daily change in the value of a portfolio is linearly dependent on two uncorrelated factors. The delta of a portfolio with respect to the first factor is $5$ and delta with respect to the second factor is…
Tosh
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Is the discount factor $v=(1+i)^{-1}$, where $i$ is an interest rate, always annualized?

So I was under the impression that the discount factor $v$ is always annualized. But as I work on this problem for an $n$-year bond, it seems not to be the case, as they arrive at this conclusion for the present value of some semiannual coupons…
ajnelson.alpha
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Macaulay Duration for coupon payment?

Sam buys an eight-year, 5000 par bond with an annual coupon rate of 5%, paid annually. The bond sells for 5000. Let $d_1$ be the Macaulay duration just before the first coupon is paid. Let $d_2$ be the Macaulay duration just after the first coupon…
llawliet_78
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Calculating Perpetuities

Sandy purchases a perpetuity-immediate that makes annual payments. The first payment is 100, and each payment thereafter increases by 10. Danny purchases a perpetuity-due which makes annual payments of 180. Using the same effective interest rate,…
uytt
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Determining Spot Rates

A three-year, 4%, par-value bond with annual coupons sells for $990$, a two-year, $1000$, 3% bond with annual coupons sells for $988$, and a one-year, zero-coupon, $1000$ bond sells for $974$. Determine the spot rates $r_1$, $r_2$ and $r_3$. This…
uytt
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Proof for Financial Mathematics

Assuming that the annual interest rate $r$ is constant, show that the present value of an infinite stream of annual payments of the form $C,Cg,Cg^2,\dots$ growing at a constant rate g, is given by the formula $$\frac{C}{1+r-g}$$ I don't understand…
MRT
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Call and put options in finance - general questions

Any help with those queries is greatly appreciated Question 1: How to understand call and put options? So far, I know that call option is a contract with an expiry date $T > t$ and a strike $K > 0$ in which: the holder (who has the long position)…
asdf
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Annual interest rate compounded monthly to monthly effective interest rate

I am given that the annual interest rate is $r=4\%$ and that it is compounded monthly. I have to find the monthly effective interest rate. If I wanted the annual effective interest rate, I would use the formula $r_e=(1+\frac{.04}{12})^{12}-1=.0407$…
Silvia Rossi
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Subtract simple interest from compound interest

Here's a question on compound interest and simple interest. The difference in compound interest and simple interest for 2 years on a sum of money is \$160. If the simple interest for 2 years be \$2,880, the rate percent is ____ ? How do I do it?
user53167
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