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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Finding the expected rate of return

Given the problem: The risk-free rate (per annum with semi-annual compounding) is 5%. You have a portfolio worth 10000 dollars today. Let X be the return of your portfolio in 6 months. Suppose the p.d.f. of X is given by $fX(x)$ = $\frac{x +…
user_123945839432
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How to calculate margin/addition

I'm passing trhough an issue that maybe is very simple for somebody has passed too. I have to calculate the margin of a sale, it goes good but the problem comes when I have a minus. Example Sale price without VAT: 300.00 Cost price without VAT:…
ndAR
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Show that question given a consistent market

Stuck on a "show that" question that is more interest rate related but I'll provide all the information needed below. Given a consistent market, show that: When $$A(0,t) = 1 + 0.05t, i_h(t)=\frac{(0.05)}{1+0.05t}$$ and that when $$A(0,t) =…
Jason Huang
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Finding yield rate for 2 bonds

An investor purchases two bonds with the following properties: Bond 1: Has a face value $1000 and is redeemable at par. Pays coupons annually at a rate of 8.1% annual and was purchased for 1117.19. Bond 2: Has a face value $1000 and is redeemable…
Alex Vincent
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Adjusting payoff diagram for call option

If the payoff for a 2 year European call option is (S2 - K) x I(S2>K) K is the strike price, which in this case is £90 I is the indicator function, so if S2>K then I(S2>K)=1, 0 otherwise S2 is the share price at time 2 S0 is the initial share…
F Erikssen
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Up and out barrier options clarification

Let $c_{uo}$(K, L) denote the price of a 1-year Apple European down-and-out call with strike $K$ and barrier $L$. Assume the spot price is $80$. Using only no-arbitrage, describe as many (in)equalities that can be derived comparing the five…
user_123945839432
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Question on effective rate of interest given rate continuous compounding

$\mathbf{\text{(i) Given r= $0.12 $ annually compounded, find the monthly}}$ $\mathbf{\text{repayments on a $ 1 000 000$ Dollar loan to be repaid completely in 5 years}}$ $\mathbf{\text{Solution}}$ Finding equivalent rate of monthly…
Tosh
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Refinancing a loan with penalty

Jeremy purchases a piece of construction equipment worth $26000 by paying 12% down and the balance with quarterly payments over 15 years at quarterly rate of 11% (i = 0.11/4). If he wants to refinance the loan, there is a penalty equal to one…
Alex Vincent
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Refinancing a loan with skipped payments.

Sam takes out a bank loan for \$19500 that he will repay with 11 quarterly payments at $j_{12} = 5.75%$. Sam has some financial troubles come up and is unable to pay the 7th and 8th payments. The bank allows Sam to skip these payments and then…
adamvincent
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American Put option problem

A stock XYZ is trading at $\$11.70$ today. Consider an American $put$ option on 1 share of XYZ with strike $K$ = 12 and expiration in $T$ = .25 years. The put is selling today for $\$1.46$. Assume the risk-free rate is $1\%$. Times goes by and 1…
user_123945839432
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How to find nominal annual rate of interest/discount?

1) at what nominal annual rate of interest, convertible four times a year will you quadruple your investment in $15$ years? 2) the annual nominal rate of interest compounded quarterly is $i^{(4)} = 0.08$. what is $d^{(2)}$, the equivalent nominal…
Allie
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Arbitrage trade using oil forwards

The price of oil is currently $\$100$ per barrel. The contract size is one barrel. The forward price for delivery in one year is $\$130$. You can borrow money at $7\%$ per annum with annual compounding. Assume the cost of storing one barrel of oil…
user_123945839432
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How to solve a hard annuity question, changing payments

I am having a lot of confusion trying to work out this problem because it seems like a lot is going on all at once. I am looking for someone to please help. A man would like to buy an annuity of $15$ years, that provides $30$ semi annual payments.…
PersonaA
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Clarification on finance math

Given the problem: A bank account pays interest with continuous compounding at the rate of 6% per annum. What is the value of an initial deposit of $700 after 3 months? after 1.7 years? From what I understand, the formula is $$A=Pe^{rt}$$ My…
user_123945839432
  • 379
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Percentage of capitalization

After how many years the deposited sum of K-euros will triple itself if the interest percentage of capitalization is 12%, the capitalization is annual.
Milingona Ana
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