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 to tell whether put or call is more expensive using put-call parity?

Using the following example can someone explain to me why the put is more expensive in part a and why the call is more expensive in part b? $$C_E-P_E=S(0)-X \cdot \frac{1}{1+R}$$ where $X$ is the strike price. Assume that the stock price is governed…
idknuttin
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Determining outstanding balance using the prospective method

A loan is being repaid with 10 payments of 2,000 each followed by 10 payments of 1,000 each at the end of each half-year. Assume that the nominal rate of interest convertible semiannually equals $i^{(2)} = 10%$. Find the outstanding loan…
minpreet khaling
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Calculating ROI of Feature

I have the following figures: (x) Quote for new software feature: $10,000 (y) Employee Rate: $15.00/hour (z) Hours per Day to perform task manually: 2 (n) Number of working days in a year: 251 (a) Hours per day to perform task after feature is…
manumoomoo
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Finding accumulated profit (Finance).

We need to find the accumulated profit at $t=5$ ( in years ) for the following project given that it is financed by a loan subject to interest $6.25\%$. Project : Initial outlay of $\$ 100,000$ , proceeds at the end of each of the next 3 years…
User9523
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Financial mathematics increasing annuities

I am having trouble solving this problem Julie bought a house with a 100,000 mortgage for 30 years being repaid with payments at the end of each month at an interest rate of 8% compounded monthly. If Julie pays an extra 100 each month, what is the…
user270494
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Minimum and maximum portfolio standard deviation

A portfolio consists of assets A and B which possesses the following expected return, risk and weights.\(a)What is the Maximum portfolio standard deviation.\(b) What is the minimum portfolio standard deviation? $$ \begin{array}{c|c|c|c} Asset &…
Tosh
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What is the return of the riskless asset in the market

A market consists of two risky assets and one riskless asset. Asset $1$ has a return of $5\%$ and a risk of $6\%$. Asset $2$ has a return of $15\%$ and a risk of $24\%$. The correlation between the returns of the two assets is $- 1$. $A)$ Find the…
Rob B
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Replication strategy of European call option

So the question asks: L et $S(0) = 120$ dollars, $u = 0.2$, $d = −0.1$ and $r = 0.1$. Consider a call option with strike price $X = 120$ dollars and exercise time $T = 2$. Find the option price and the replicating strategy. So the solution is: The…
Betty
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Finance mathematics doubt.

I don't understand the difference between the following two statements stated as : (1) The price rises by say $X\%$ during the time $t=0$ to $t=10$. (2) There is an inflation of $X\%$ during $t=0$ to $t=10$. Aren't these the same ? Can anyone…
User9523
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What is a hedge ratio tree?

Determine the stock price tree, the call option tree, and the hedge ratio tree. I have to make three separate trees for a european call option, I know what a stock price tree and a call option tree is but what information do I need to find to create…
idknuttin
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Decreasing perpetuity problem

A perpetuity pays 1000 immediately. The second payment is 97% of the first payment and is made at the end of the fourth year. Each subsequent payment is 97% of the previous payment and is paid four years after the previous payment. Calculate the…
gdasm
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Pricing a digital put option using BS model

I'm not able to understand why we are working out probability sT is less than K. For example why could we not have done probability sT is more than K? I understand the steps after that but why we were supposed to start with that first step is…
user134785
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Potential arbitrage profit and proof

So the question asks: Consider 4 following European call and put options with the same maturity time: Call option with strike price $100$ sell for $45$ Call option with strike price $110$ sell for $40$ Put option with strike price $100$ sell for…
Betty
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what am I doing wrong when finding the weights of the market portfolio?

I need to find the weights of the market portfolio with three risky securities given the following information: $\mu_1=0.08$ $\sigma_{1}^{2}=0.0255$ $c_{12}=0.00225$ $\mu_2=0.1$ $\sigma_{2}^{2}=0.0025$ $c_{13}=-0.0036$ $\mu_3=0.06$ …
idknuttin
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How do I calculate the delivery price for a forward contract?

How do I calculate the delivery price for a forward contract? In the time interval $[0,t]$ the interest rate is $r_1$ and in the time interval $[t,T]$ the interest rate is $r_2$. Determine the delivery price $F(0,T)$ for a forward contract on an…
idknuttin
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