Questions having to do with financial mathematics. Please note that for questions in quantitative finance, quant.stackexchange.com is perhaps a better site.

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2answers
63 views

How to rearrange this equation to solve for 'r' in closed form?

I'm taking a finance course, and I can't afford the financial calculator which can be used to solve this, so I would like to know how to solve this algebraically by hand (I don't care if it uses ...
0
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0answers
68 views

I want the solution of Bjork Arbitrage Theory in Continuous Time

I am working on Financial Mathematics and also work on Bjork Arbitrage Theory in Continuous Time sometimes I have problem in the Exercises. Does any body know about solution of this book ?
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2answers
64 views

Calculating inflation rate

This is my maths problem (It is NOT homework help, just me trying to learn basics of this bit of maths): A car cost £14,000 in May 1994, the inflation rate then was 1.9%, but the current inflation ...
2
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1answer
36 views

Trying to calculate FV with annual & monthly fees

First question on here so please go easy if it's a stupid one! I have created a PHP based FV calculator for use on a client's website. This is the scenario: They offer returns of ...
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1answer
50 views

Stochastic Finance I am having difficulty with my homework questions. Brownian Motion

A 2-dimensional process $(B_t^1,B_t^2),\ t \geq 0 $ is a standard 2-dimensional Brownian Motion if each $B_t$ is a standard Brownian motion and the $B_t^s$ are independent of each other. Let $ X_t = ...
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1answer
35 views

Recurrence On finance

A bank pays 6% interest at the end of each year on an account which initially starts with $2000. Find a recurrence relation for, the amount of money in the account at the end of year n if a) only ...
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1answer
10 views

To determine effective cost of investment

I have this problem,need of help on how to attempt it. If you pay for a certain investment with installments of GCD 1000 in early January and GCD 1000 in early July and then receive GCD 2000 in late ...
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1answer
10 views

Optimizing interest for a set of debt payments

Suppose I've got $n$ debts with principals $P_1, P_2, ..., P_n$, with corresponding interest rates $r_1, r_2, ..., r_n$, compounded monthly. Further, assume I have a constant $A$ dollars per month to ...
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1answer
31 views

Calculate Interest

Peeta is saving to buy a new oven for his bakery that will cost \$8000. He has \$6,000 to invest at $5 \frac{1}{2} \%$ compounded semi-annually. How long will he need to wait for until he can afford ...
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1answer
28 views

Calculate expectation under risk neutral measure: $\mathbb{E_Q}(\max(S-1,0))$

I am busy with a numerical simulation and I want the calculate the following expectation under the risk neutral measure: $\mathbb{E_Q}(\max(S-1,0))$. $S$ is some variable that I calculated using ...
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4answers
28 views

what are the units for a rate of return?

My understanding of "rate" is more physics oriented. For example, distance/time is understandable for me and something I can explain. However, a rate of return: "The return, or rate of return, can ...
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0answers
112 views

Which math courses should I take to prepare myself for Masters in Financial Mathematics?

I am an Applied Mathematics (BSc.) student that is graduating soon. Apparently, I need to take one more elective course (but I can also fit in two more electives if I want to) before I can graduate. I ...
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2answers
55 views

Expected value of SinhX

A random variable X is distributed according to a normal distribution with mean u and variance d.How to evaluate the expected value of SinhX?Thanks
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0answers
11 views

Computing the probability that a stock process is more valuable than the bond process

I am currently revising for my exam and I cannot really deal with the following problem (I am a beginner in terms of stochastic processes): $W_t$ is the standard Brownian motion. Consider a stock ...
1
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0answers
37 views

Construct an arbitrage opportunity in a multi-period model

I am currently revising for my exam in Financial Mathematics, and I could not solve this question: For $T > 1$, consider a $T$-period model with a single risky asset and a bank account which pays ...
3
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1answer
99 views

Math for Future Value of Growing Annuity

Am I working this out correctly? I need to verify that my code is correct... $$1000 \cdot \left(\frac{(1 + 0.1 / 12)^{40 * 12} - (1 + 0.06 / 12)^{40 * 12}}{(0.1 / 12) - (0.06 / 12)}\right)$$ ...
1
vote
1answer
25 views

Interest Accumulation - Geometric Sequence

Hello I have just worked a question in which I get an answer different to the answer in my book. The question states: If a person deposits 500 at the end of each month for 20 years at an AER of ...
1
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0answers
50 views

Show that the risk-neutral probability of a European call option ending in money is N(d2)

Show that the risk-neutral probability of a European call option ending in money is N(d2). I was trying to using Risk-Neutral Valuation Formula, but how to show the result is N(d2)? Thanks
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0answers
39 views

Simple Stochastic Control Problem

Consider $dX_t = \pi_t X_t dt + \pi_t X_t dW_t, X_0 = x$, where $W_t$ is a standard brownian motion, and $\pi$ is some real valued process. Let T>0. How can we calculate $P[X_T\geq 2x]$, where ...
1
vote
1answer
43 views

Changing variables for a partial differential equation

If I have the following systems of PDE \begin{align} u_t+x^2u_{xx}-\dfrac{h_1(t)}{h_0(t)}e^{-(v-u)}-\dfrac{h_0'(t)}{h_0(t)}=0\\ v_t-\dfrac{h_0(t)}{h_1(t)}e^{-(u-v)}-\dfrac{h_1'(t)}{h_1(t)}=0, ...
1
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0answers
23 views

financial mathematics: n financial assets in p states of the world.

Suppose there are two dates, $0$ and $1$. Suppose the world will be in one of $p$ states at date $1$, but the true state of the world at date $1$ is unknown at date $0$. Let there be $n$ financial ...
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0answers
54 views

Second Fundamental Theorem of Asset Pricing

It seems that there is a step missing in the proof of the second Fundamental Theorem of Asset Pricing in Shreve's Stochastic Calculus for Finance II: Does anyone know how to show the following: If ...
1
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0answers
41 views

Expected value of multiplied and squared Wiener Process

May someone help me how to calculate the following thing: E0[z^2[2] Exp[-2 z[2]] ] Where z[2] is Wiener process. How to find exact expected value? I am new to this stuff, not sure how to do this. ...
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1answer
33 views

Where to find Geman 1995's proof on Changes of Numaraire?

Geman, H., El Karoui, N., Rochet, J.C. (1995) published paper "Changes of Numeraire, Changes of Probability Measures and Pricing of Options", on "Journal of Applied Probability " vol 32, pg 443-458. ...
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0answers
25 views

Proposition from Oksendal Stochastic Calculus

I am reading Oksendal's Malliavin Calculus with applications to Finance and there is a part that I do not understand. First we have a proposition which is fine: If $\zeta_1$,$\zeta_2$,... are ...
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0answers
41 views

Financial Mathematics - Security Market Line and CAPM

not sure if this is the correct place to be posting this but I couldn't find a relevant stack exchange site (albeit this is part of my financial mathematics university course.) I have to write a ...
0
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0answers
44 views

Application of Ito's formula

I recently learned about Ito's formula and integral and now i have to do the following exercise, but I actually don't really know, how to start: Apply Ito's formula to prove that $$Z_t=exp(\sigma ...
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0answers
46 views

Black-Scholes derivation assumption contradiction

In many books and derivations of the Black-Scholes PDE one sees that $$\Pi=V-\Delta F \Rightarrow d\Pi=dV-\Delta dF$$ which implicitly assumes that $d\Delta=0$. Somewhere down the road one then ...
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0answers
30 views

Calculate breakeven point for business

I have a question with which I am somewhat stuck. Specifically I need to calculate the break-even figure for the following scenario. Peter is a business consultant. As well as providing ...
0
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0answers
23 views

Parameter estimation using characteristic function

Is it possible to do parameter fitting using log-returns data & the characteristic function(CF) in Matlab? I have been trying it on the Variance Gamma Scaled Self-Decompasable (VGSSD) model CF for ...
0
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1answer
69 views

Gremlins are investing in stock

Gremlin Industries will pay a dividend of \$1.80 per share this year. It is expected that this dividend will grow by 4% each year in the future. The current price of gremlins stock is \$22.40 per ...
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0answers
45 views

Girsanov's theorem and simulation of bond prices

Assume that we want to calculate the time $t=0$ price of a bond: $B(0,T) = E_P[\exp(-\int_0^T r_s ds)]$, where $r$ is the interest rate following the SDE $dr_t=k(\theta-r_t)dt+\sigma ...
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0answers
35 views

Why does the price term in Vega disappear for a European call option?

In my course, I have been asked to prove a number of statements about "the Greeks" from the Black-Scholes model for pricing a European call option with no dividends and a strike price of $K$. One of ...
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0answers
8 views

Tangency portfolio in multiple periods model (Finance)

This might be a bit specific, but i'm stuck at this "little" problem. I've got a little problem now that i'm writing my BA thesis in dynamic asset allocation. It might be a very specific question, but ...
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1answer
102 views

Option Pricing, A Practitioners Guide, Martingale's, Drift Change and Radon-Nikodym

Im slightly confused about this section of the booklet regarding option prices byIain J. Clark. 1) Regarding the part of obtaining a martingale property we require that the last exponential term ...
3
votes
1answer
55 views

Why is that a risk averse consumer buys the optimum insurance when there is actuarially fair insurance?

I've asked the same question at the Quantitative Finance StackExchange. Consider the following example: "As a risk-averse consumer, you would want to choose a value of x so as to maximize expected ...
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0answers
34 views

On finance problem: saving money

First of all, sorry for my pour English. Consider the situation: I'd like to save an amount $P$ of money every month for $240$ months consecutively ($m_1,\ldots,m_{240}$). The gain with money is ...
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0answers
46 views

Put-Call-Parity of Asian Options

I could need some help with deriving the put-call-parity for asian options. Let $S_t$ be the price of the underlying asset at time $t$ and set $Y_t = \int_0^t S_t dt$. Then the payoff of an asian ...
2
votes
1answer
35 views

Arbitrage opportunity for call price set on avarage

I have the following problem. Let C(K) be the market price of a Option Call with respect to the strike K. Let $C(100) = \frac{C(110)+C(90)}{2}$, then show that there exists an arbitrage opportunity. ...
0
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1answer
51 views

Finding the mortgage interest rate

Given the principal and term payment and number of terms, how can I calculate the interest rate of this mortgage? Been searching the internet for formulas, but to no avail. What is being calculated ...
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0answers
14 views

Partial differential of sharpe ratio of a portfolio with n ( =4 )equities with respect to the allocation for each equity.

Sharpe ratio is the mean of the daily returns from the portfolio divided (minus a constant )by the standard deviation of the return from the portfolio. Daily return of the portfolio is calculated by ...
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0answers
23 views

How can I show that $u=e^{\sigma\sqrt{\Delta t}}$ in the binomial option pricing model

Given that $e^{r\Delta t}(u+d)-ud-e^{2r\Delta t} = \sigma^2\Delta t$ I would like to show that $u=e^{\sigma\sqrt{\Delta t}}$ I know I must somehow use Taylor's approximation $e^x = 1 + x + ...
1
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0answers
176 views

What do two number on top of each other in square brackets mean?

Im currently going through "Universal Portfolios with Side Information" by Cover and Ordentlich [96]. Near the end of the paper, they provide a formula for calculating weights of a Universal Portfolio ...
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1answer
34 views

What is present value of the carbon expense for five years?

Suppose I have computed the cost of carbon per mile for my car at 0.009 per mile. Assume that the interest rate is 5% and that I drive the car 20,000 miles per year. What is present value of the ...
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2answers
45 views

Loan repayment calculations when interest compounding frequency does not match repayment frquency

Is there a formula for calculating loan repayments where interest is compounded daily, but repayments are made only monthly, for instance? I would like to be able to calculate the repayment amount ...
0
votes
1answer
34 views

Annual Interest Rate

Your credit card has a balance of $6100 and an annual interest rate of 1%. You decide to pay off the balance over two years. if there are no further purchases charged to the card, a. how much must ...
0
votes
1answer
52 views

Calculating Upside Potential

I have a story problem in my finance class. I can't figure out how to determine if my math is correct or not. The problem is: You purchase stock for 0.015 (one and a half cent) per share. You ...
0
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2answers
30 views

perpetuity valuation

A perpetuity paying 1 every 6 months has present value of 20. A perpetuity paying X every 2 years has the same present value. Assuming equal effective annual rates, what is X? I know X is 3.71 from ...
2
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2answers
86 views

Understanding basic stochastic differential equations

This is from a physics course in economics, the literature provides a bare minimum of mathematical explanations. I am trying to understand how to work with stochastic differential equations given in ...
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1answer
46 views

How can I calculate in Excel the price of something with inflation

I live in Argentina, and we have 30% anual rate of inflation. I am paying a car also, in a plan of 84 payments. Each payment has a 27.7% of "Administrative Costs". For example, for a ...