All Questions
Tagged with finance solution-verification
38
questions
-1
votes
1
answer
28
views
Finding the effective annual rate of interest (no constant)
A deposit of 10,000 is done. During first year, the bank credits an annual effective interest rate of $\text {i}$. During the second year, the bank credits an annual effective interest rate of $\text {...
- 561
0
votes
0
answers
111
views
Is this the correct proof of Proposition 10.23 in Björk's ''Arbitrage theory in continuous time''?
I want to prove Proposition 10.23 from Tomas Björk's ''Arbitrage theory in continuous time'' in the snippet below.
My attempt: For simplicity, assume everything is one-dimensional, with one risky ...
- 135
1
vote
1
answer
104
views
Understand a FM question about a bond with varying interest rate. [closed]
Consider a coupon bond with maturity in $2$ years, with a coupon rate of $4.375\%$ (coupons are paid twice a year) and with a face value of $100€$. Let's say this coupon bond has a varying ...
- 1,141
1
vote
1
answer
143
views
Question about calculating the price of a coupon bond at different times: FM question.
Let's say we are working with a coupon bond with face value of $F = 100€$, maturity of $T = 5$ years and with $10€$ coupons paid anually. Also, consider we're dealing with a continuously compounded ...
- 1,141
0
votes
1
answer
54
views
How to interpret the value of money depending on the maturity of a bond? FM question.
Consider the following exercise:
Exercise. A financial institution issues bonds with maturities of $13$ weeks, $26$ weeks and $52$ weeks, at zero coupon, and with a discount value $B_1(0) = 98€$, $B_2(...
- 1,141
0
votes
0
answers
143
views
Minimum Variance, Tangency Portfolio, and Efficient Frontier
There are 3 assets $S_1$, $S_2$ and $S_3$. $S_1$ has a mean return of $0.17$ and standard deviation of $0.2$, $S_2$ has a mean return of $0.13$ and standard deviation of $0.4$ and $S_3$ has a mean ...
- 189
2
votes
0
answers
204
views
Prices in a lottery with given utility problem
Suppose a person has a Bernoulli utility function $u(\cdot)$ and an initial wealth $w_0$. A lottery $L$ offers a payoff $A$ with probability $p$ and payoff $B$ with probability $q$, where $q = 1-p$. ...
- 1,271
0
votes
0
answers
89
views
How much loan you owed after 20 years
Statement: Paying down a mortgage: you took a $\$200000$ home mortgage at an annual interest rate of 3%.suppose that the loan is amortized over a period of 30 years and let P(t) denote the amount of ...
- 115
2
votes
2
answers
148
views
Using $(I^{(m)}a)^{(m)}_{\bar{n}|}$ to solve for the present value of an annuity where payments increase monthly
I've seen this answer and I understand the methodology, but I am wondering why my original solution using a different method did not work.
This is the sample problem in my study guide for Exam FM:
...
- 23
1
vote
1
answer
176
views
Black and Scholes option pricing
I have to solve the following problem in the Black and scholes model: find the price at anty $t\in[0,T)$ for an option whose payoff at the maturity is:
\begin{equation}
0 \ \ \ \text{if} \ S_T<K_1\\...
- 664
1
vote
0
answers
107
views
Force of transition and probabilities
Suppose that a model has four states: $0, 1, 2,$ and $3$, and the only possible transitions between these states is $0\rightarrow 1$, $0\rightarrow 2$, and $0\rightarrow 3$. For $t\geq 0$, $\mu_{x+t}^{...
- 189
1
vote
1
answer
282
views
Life insurance transition matrix (actuarial)
Suppose that a life insurance coverage waives premium upon disability of the insured. You model
the coverage as a homogeneous Markov chain with three states: active, disabled, and dead.
The annual ...
- 189
3
votes
1
answer
277
views
Duhamel's Principle Intuition
I am trying to understand Duhamel's Principle by applying it to some simple problems. I am thinking of $P(t)$ as expressing a bank account balance at time $t$, to try to gain an intuition for Duhamel'...
- 1,922
0
votes
1
answer
507
views
$\$9000$ is invested in a account offering $3\%$ per year, compounded continuously, how fast (in dollars/yr) is the balance growing after $4$ years?
If $\$9000$ is invested in a savings account offering $3\%$ per year, compounded continuously, how fast (in dollars/yr) is the balance growing after $4$ years? (Round your answer to the nearest cent)
...
- 1,502
-1
votes
1
answer
71
views
Annuity & Perpetuity problem
Suppose Joe has been paying $600$ from his monthly salary at the end of every month for the past $n$ years. After $n$ years of payments, he retires having purchased a perpetuity-due plan that begins ...
- 1,271