# Questions tagged [finance]

Questions related to the various aspects of financial mathematics. Topics include option pricing, arbitrage theory, market completeness and stochastic analysis.

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### Calculating the exact inverse of a transaction fee with a linear volume-based fee structure

Let's say we have a volume-based fee structure that takes a 5% fee of a transaction from \$0, and a 2% fee at \$1000, with the intermediate amount being a linear interpolation of these two points - ...
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### On the operational process of fractional and delay Brownian motions (FGBM/GDBM) governing respective market scenarios

I have some knowledge about the fabrication of a stochastic differential equation (SDE) governing asset price ($S(t)$) dynamics (This answer helped me up to some extend). For instance, the Geometric ...
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### How to calculate Excel's Yield function for coupons more than 1? [closed]

Below is the actual process for calculating the Bond yield for coupons > 1. Reference : YIELD If there is more than one coupon period until redemption, YIELD is calculated through a hundred ...
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### Testing predictability of a predictor of expected weekely returns on the stock market

say I have a T daily observations for the last ten years on a new predictor $x_t$ which I think is a predictor of the expected weekly return on the stock market, $r_{t,t+5} = r_{t+1}+...+r_{t+5}$, ...
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### What is the formula for cumulative compound interest? [closed]

I would like to start with a principal amount (P) in year 0, then add compound interest (C) to it for year 1, and then add that total value to the starting amount. So for example: P=1000 C=2.5% For ...
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### Partial derivative of a matrix product w.r.t. a vector

What is the partial derivative of $$w^T\beta \cdot \Sigma \cdot \beta^Tw$$ with respect to $w$? Dimentions: $w$ is a $N \times 1$ vector ("asset weights") $\beta$ is a $N \times K$ matrix ...
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### Valuing Call Option Expiring Tomorrow given final stock prices

Here is the original question: At the end of the day, a stock will be 100 with prob. 0.6 or 50 with prob. 0.4. What is the stock trading for right now? Value an ATM Euro call option expiring at the ...
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### Looking for an equation to separate Compound interest from a given amount [duplicate]

Maths newbie here. I am trying to make a formula to discern the monthly payments required to achieve a target amount over a given time with a given compounding interest rate. The information I have is ...
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### Properties of an American Derivative Security Process

$$\newcommand{\cbkt}{\left\{{#1}\right\}} \newcommand{\rbkt}{\left({#1}\right)} \newcommand{\sqbkt}{\left[{#1}\right]}$$ I am self-learning basic stochastic calculus using Shreve's books. ...
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### A put option and a call option with identical exercise price are both marketable or neither is.

I am doing Exercise 1.13 in Introduction to Mathematical Finance: Discrete Time Models by Pliska. Exercise 1.13 Suppose the interest rate $r$ is a scalar, and let $c$ and $p$ denote the prices of a ...
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### How to do this financial math (Exam FM) question from first principles (summation)

A perpetuity costs 77.1 and makes end-of-year payments. The perpetuity pays 1 at the end of year 2, 2 at the end of year 3, ...., n at the end of year (n+1). After year (n+1), the payments remain ...
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### Financial Calculation with compound interest: Determine how much a person will need to have saved in year 0 of retirement based on monthly withdrawals [closed]

I am trying to come up with a formula to determine how much a person will need in retirement. So every year, they will take their inflation-adjusted withdrawals out of their retirement savings, and ...
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1 vote
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### why can we add accumulated values in example shown below?

Can you explain to me why we're able to add the accumulated amount of 1000 invested for 5 years to the additional accumulated value of 1000 they invested after 3 years?
1 vote
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### Price a SWAP contract in no arbitrage market

We have a single period, arbitrage free market with riskless rate of return $r$. A swap contract operates in the following way: At $t = 0$ the buyer pays the seller amount $q$. The seller agrees to ...
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### How is the Dybvig (1981) asset pricing kernel in return space derived?

Coval and Shumway ("Expected Option Returns", Journal of Finance, 2001) cite to a working paper by Dybvig (1981), which does not appear to be available online. Dybvig shows that, under Black-...
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### What's the math formula that is used to calculate maximum mortgage amount like in this calculator? [closed]

What's the math formula that is used to calculate maximum mortgage amount like in this calculator? Visual Reference: Take a look at these images to see which tool I'm specifically referring to: ...
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### Taylor Expansion for the Return averaged over k periods? [closed]

this is my first question here. I need help to understand the Taylor Expansion which gives the (2.2.5) equation (see the pictures). Thanks (pictures from: Schmidt - Quantitative Finance for Physicists....
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### Betting on the outcome of a semidecidable computation

If my neighbor Colin insists that Bruce Willis will be the winner of the 2024 U.S. presidential election we can bet on it, and (barring some very strange outcomes) there is some well-defined future ...
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### Finding the Rate of Decrease to End Up at Goal Number [closed]

I'm trying to find the Rate of decrease at which 1,262 is multiplied by every day (16 times in total) and added to the Base number of 17,584 in total 16 times to get to the goal number of 24,000. I've ...
Suppose that the interest rate $r$ is a random variable. Given a future value $FV$, the expected present value is $\mathbb E (\frac{FV}{1+r})$. Given a present value $PV$, the expected future value is ...