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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American Call Spread early exercise

It is generally agreed that it is not optimal to exercise the call option, $C_t = (S_t-K)^+$ early. My question is this, can anyone help in proving or disproving if the American call spread, $C_t = (S_t-K_1)^+ - (S_t-K_2)^+ $ can have an early…
Aloagbaye Momodu
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Interest rate, bond problem

I am trying to solve the following problem: Debtor issued a bond on 20 000€ (including interest rate) with maturity rate of 8 months and interest rate of 8% per annum. Month later, the creditor sold the bond to a different person, who discount …
Daniel P.
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Consider a non-dividend paying stock subject to risk-free force of interest

Consider a non-dividend paying stock subject to risk-free force of interest, r = 0.045 as well as volatility, σ = 0.24 and time horizon three months, i.e., T = 1/4 for a stock with current price S0 = $45. Recall that dSt = St(rdt + σdBt) where…
James M
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Recommendation of financial mathematics books for beginner

I am a PhD student in pure mathematics. However, I start to learn financial mathematics by myself and plan to apply one more PhD course in this major 2 years later. Could you please recommend some text book for beginner? Thank you for your consult…
Trần Linh
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Put Options and Arbitrage Proof

I am trying to prove that if $P$ is the price of a European put option to sell a security whose current price is $S$ with strike price $K$, then $P\le K$ must be true. My first instinct with this is to do a counter proof that shows that if on the…
batman
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How to calculate Net Present Value?

So I have this question : Your boss asked you to evaluate a project with an infinite life. Sales and costs project to$ \$1,000 $ and $\$500$ per year, respectively. (Assume sales and costs occur at the end of the year, i.e., profit of $\$500$ at…
Sara Saletti
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Finding Equity Of A Home Bought Using A Mortgage.

Let's say I buy a house using a mortgage where the following information is true: The house's original price was $100,000. A down payment of 20% was required. I get a 30 year mortgage with a 4.5% interest rate. The house's value appreciates 3% per…
Seth Connell
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Annuities, lottery and interest rate

I am having trouble doing this question. Mary Jones won $\$4,000,000$ in a state lottery. She will receive a cheque for $\$200,000$ now and a similar one for each year for 19 years. To provide these 20 payments, the State Lottery Commission…
T. Smith
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How do I solve for n (number of periods) in a loan repayment formula?

Where A = payment Amount per period P = initial Principal (loan amount) r = interest rate per period n = total number of payments or periods How can I rearrange the formula to solve for n?
Caleb Macdonald Black
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Formula for calculating total interest that will be paid over non-fixed loan

I am trying to calculate the lifetime interest paid on a credit account. I know that I can enter it into a spreadsheet and take the sum of the interest, but is there a formula to calculate such a value when you know the balance, minimum, and…
Forklift
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Calculating monthly payments of a savings plan

The question reads: A savings plan requires you to make payments of £250 each at the end of every month for a year. The bank will then make six equal monthly payments to you, with its first payment due one month after the last payment you make to…
jpatrickd
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Required amount to invest now in a trust fund (difficulty with discount rate)

The parents of three children aged 1, 3, and 6 wish to set up a trust fund that will pay 25k to each child upon attainment of age 18, and 100k to each child upon attainment of age of 21. Assume that the trust fund will grow at nominal annual…
xim
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Capital after interest per month and additional deposits per month

Person A has 1000€ on the bank with 5% interest per month. He also puts 50€ per month to his bank account before he receives the interest. How much does he have after 12 months? My calculation 1000*((1.05^12)+50)
user645673
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Convert flat interest rate to effective interest rate

My bank currently has promotion on personal loan on flat interest rate which is 3.80%. And there are some minor remarks Terms and Conditions apply. Effective rates vary from 7.07% p.a. to 7.15% p.a. for tenures from 2 – 5 years. Based on the…
karfai
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Value of the last installment.

The price of a TV set is ₹20,000 to be paid in 20 installments of ₹1,000 each. Rate of interest=6% p.a The first installment is to be paid at the time of purchase, then what will be the value of the last installment covering the interest as…
ANANYA AKHOURI
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