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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Determining Total Assets, Total Liabilities From a Financial Statement with Missing Values

I at a loss trying to figure out the total assets and liabilities from what is given. K-Os Corporation Beginning of year Total assets $66,410 Total liabilities 31,080 …
Victoria
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How do I approach this proof to show that P (T, K) is non-decreasing function of T without making any model assumption

Let P (T, K) be the price of a Put option with maturity T and strike K, and assume that the interest rate is zero, i.e., r = 0. By no-arbitrage pricing rule, show that P (T, K) is non-decreasing function of T without making any model assumption,…
Statnerd
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How to compute a contract price from an original price by adjusting the taxable total while accounting for the tax being part of the contract price

I'm not sure how to best describe this in the title, so I will do my best here: Let's say we have an order that prices out to $48,967.00 - but we have a few categories that make this up: taxes, delivery, products, labor, and installation. To make it…
Brandon Ragland
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Optimal weights/Tobin separation

I'm having troubles understanding the following: I understand given, let's say 5 stocks and their historic data, how to compute the efficient frontier of optimal assets. However, when I introduce Tobin separation the confusion starts. Given a…
Nuts
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Derivation of $ \pi(\sigma) $

This is my first post on this website so please forgive me for any mistake or inappropriate use. I am taking a Master level Investments course, in which, amongst the rest, we are deriving $$ \pi(\sigma) = \frac{\alpha(\bar{W})}{2} $$ We started from…
Giuseppe Siragusa
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Question #2: Finding the probability of a decline higher than 9%

Expected monthly price change=E(x) = 0.60% Average monthly volatility = 9.40% I am looking for the probability that gold will decline by more than 9% in the next month. According to the formula for z score: X - E(X) / σ the equation would be=…
Mhuncho
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When to equate FV(deposits) = FV(withdrawals)

So I have this question: Starting from her 30th birthday (t = 0), Miss Saver deposited some money each year in a savings account for the next 35 years. The first deposit of $1000 was made on her 30th birthday, she made 35 deposits in total, and…
user19825372
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Using convexity to determine arbitrage opportunity with two put options

I have seen questions involving the convexity of the price of put options as functions of strike price. https://quant.stackexchange.com/questions/50308/how-to-take-advantage-of-arbitrage-opportunity-of-two-options and…
Zonova
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Calculating the "average" exchange rate from multiple transactions

One day I purchase €$N_1$ at an exchange rate of £1 = €$R_1$, for a cost of £$\frac{N_1}{R_1}$ The next day I purchase €$N_2$ at an exchange rate of £1 = €$R_2$, for a cost of £$\frac{N_2}{R_2}$ How do I calculate the "average" exchange rate, i.e.…
jonnybolton16
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Suppose that interest rates are always positive. Then the present value of a cash flow is at most its time value at t=2.

Suppose that interest rates are always positive. Then the present value of a cash flow is at most its time value at t=2. Is this true or false? I think it is false. My reasoning is because the present value of a cash flow at a certain point in time…
user19825372
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Help with Effective Rate of Discount- Theory of interest

I am just beggining Financial Mathematics. One of my assignment questions are as follows: (Q) Find the amount of interest earned from the principal of $1000 during the fourth period If the effective rate of discount is dn = 0.02n + 0.005 for n =…
Suraj
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Is the stochastic process of the volatility of a stock market square integrable?

I am taking a course in financial mathematics(Ito-Integrals, Black-Scholes,...) and there is something that is not immediately clear to me. When constructing our stock price model, the integral $\int_0^t \sigma_s\;dW_s$, $\sigma_t$ being the…
Josh.K
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No arbitrage in a 1-period market.

Let $(\Omega, \mathcal{F}, \mathbb{P})$ a probability space. Consider a random variable $R \in \mathbb{L}^1$ such that $\mathbb{E}[R] > 0$ and $\mathbb{P}( R < 0) >0$. Define a 1-period market with riskless asset $S^0_0 = 1$, $S^0_1 = 1$ and risky…
leobgg
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Question about proving the existence of an arbitrage opportunity

I have this lemma in front of me an dI have hard time understanding the reasoning behind a statement in the proof. Lemma: If there exists a self financing stragegy $\phi$ (not necessarily admissible) with $V_{0}(\phi)=0, V_{T}(\phi)\geq 0$ and…
Omer
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Connection between law of one price and and pricing of ECC (finite market)

knowing that the payoff of a ECC at maturity T is given by $C_T = max(S_T-K,0)$ can we deduce by the law of one price that $C_t = max(S_t-K,0)$ given that K is the strike price? In particular, why do make the effort and find pricing strategies for…
Anton2107
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