Questions tagged [self-study]
A routine question from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for self-study questions.
73
questions
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36 views
Optimizing Portfolio Return by Targeting Variance
I understand Markowitz and targeting returns to minimize our variance. I know this optimization problem well and its constraints. However when the reverse scenario is to be considered I get very ...
2
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1answer
45 views
(Self-study) Futures, bonds, and arbitrage
I'm currently self studying futures, so I'm sorry if this questions comes off a bit stupid. I'm currently reading a book by Walsh, J.B. Knowing the Odds: An Introduction to Probability.
I quote this ...
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1answer
38 views
the relationship between VaR(0.05) and mean?
What is the meaning of the difference between the quantile of prob=0.05 and mean for a sample form a specific distribution?
In other words, I would like to understand the relationship between ...
-2
votes
1answer
59 views
Most liquid index options?
I need to work with option prices in my master's thesis. Specifically, I investigate index options (S&P 500). Which kind of options could you recommend to use? I have seen that there are options ...
0
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1answer
64 views
Should he choose long position or short position? [closed]
On July 2, 1997, a a company is worry about the value of its Yen income over the next few weeks and makes a decision to hedge its risk by taking a position in the futures market. Right now, a futures ...
0
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1answer
82 views
calculation of theoretical value of futures contract [closed]
we form a stock index by using only two stocks in the index.
One of the stocks is the Stock-A. The current selling price of the stock-A is 103 dollars and the second stock is the stock-B. The current ...
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2answers
69 views
How can I calculate returns for three investment strategy?
Assume that the price of DF stock went from a price of $104 on March 2 to 146 on April 1.
With a current stock price of 146, there is a call option available on the DF stock with an exercise price ...
0
votes
1answer
37 views
Calculate 6 month- return for an investment [closed]
Assume that the price of DF stock went from a price of $104 on March 2 to 146 on April 1.
With a current stock price of 146,
Invest all of your amount 14,600 in the DF stock (buy 100 shares)
...
0
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1answer
71 views
Question about the writing a call option on an existing portfolio of stocks [closed]
My question is Please discuss about the following statement
“ the advantages and disadvantages of writing a call option on an existing portfolio of stocks”
Note that
I read an article nearly ...
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0answers
29 views
Positive carry with negative yielding bonds when repo is negative
Could someone please explain to me how positive carry is achieved when the repo rate is negative?
For example I can see the German repo rate is -0.57% and the 2 year German bund is -0.78%. So to ...
1
vote
0answers
89 views
Difference between spread duration & IR duration for a fixed rate bond
I am struggling to comprehend the difference in impact between spread duration & IR for a fixed rate bond when yields move.
I know that both measures would be the same for a fixed rate bond but ...
2
votes
2answers
214 views
Black-Scholes-Merton formula and option pricing
If the distribution is skewed to the right,Black-Scholes overprices out-of-the-money puts and in-the-money calls. It underprices in-the-money puts and out-of-the-money calls.
How?
Stock price log-...
2
votes
2answers
225 views
Carry & roll - question regarding the repo transaction
Could someone please explain the carry and roll trade that a lot of traders are doing with negative euro debt?
I read an example that they borrow in the repo market then buy a longer dated bond to ...
1
vote
1answer
248 views
How does buying a CDX and then taking a short CDS position generates alpha? [closed]
Can someone please explain to me how buying a CDX and then taking a short CDS position generates alpha? I am so confused.
1
vote
3answers
1k views
Interpolating the swap curve
Does anyone know how I can calculate the swap rate in between main tenors for specific dates? For example: what is the implied swap rate in 1 year, 60 days time.
Is there an easy way to do this in ...
2
votes
1answer
98 views
Is the Non-discounted Bachelier call option price a Martingale? [duplicate]
My math finance professor once said someting that I can't make sense of. Hope you can answer:
For a foward process the non-discounted price for a European call option under Bachelier is
$$C_t = \...
1
vote
0answers
57 views
What should I learn/know before reading Investments by Bodie Kane Marcus?
I hope this is the appropriate place to post this. If not, I would really appreciate if someone could redirect me to the right site.
I've been seeing a lot of recommendations for the book, ...
3
votes
1answer
155 views
Introduction of a stochastic discount factor in martingale pricing
The example below is taken from Björk (2009). Let Radon-Nikodym derivative be
$$L=\frac{dP}{dQ} \;\; \text{on} \; \mathcal F$$
or written analogously
$$P(A) = \int_AL(\omega)dQ(\omega) \;\; \text{for ...
6
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1answer
628 views
Tick Imbalance Bars - clarification on T index
I have been trying to learn quant related things on my own. I recently picked up a book called "Advances in Financial Machine Learning" by Marcos Lopez De Prado. I am having difficulty understanding ...
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2answers
2k views
Tick Imbalance Bars - Advances in Financial Machine Learning
I would really appreciate if any of you can clarify the following questions. I have been struggling to understand it on my own.
$b_t=\begin{cases}b_{t-1}, & \text{if}\ \Delta p_t = 0 \\ \frac{|\...
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vote
2answers
1k views
Relationship between CML and SML
I am referring to the book Sharpe et al. (1998), Investments, 6th Edition. I am trying to wrap my head around some lines from the book, pertaining to Security Market Line.
It reads:
Earlier it was ...
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votes
1answer
252 views
Probability and statistics in Quantitative Finance
Certain types of traders attempt to repeatedly buy and sell the same asset for a profit over a short time period, such as high-frequency “market makers”. For example, if you can repeatedly sell a ...
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1answer
218 views
Measure of a Brownian motion = normal distribution?
Consider some model where the process increments are normally distributed, e.g. Vasicek:
$$dr(t) = \left(\theta - ar(t)\right)dt + \sigma dW(t).$$
We usually say that $W(t)$ is a Brownian motion ...
2
votes
1answer
167 views
Risk neutral modelling of a stock
Suppose a stock $S$ follows
$$dS(t) = \alpha(t)S(t)dt + \sigma(t)S(t)dW(t),$$
where $W(t)$ is a Brownian motion under $P$. Also suppose there is a short rate process $r(t)$. My question would be is ...
2
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1answer
78 views
Characteristic function and distribution of a random variable
This is exercise 4.3 in Bjork, Arbitrage Theory in Continous Time.
$$
X_t = \int^t_0 \sigma(s)dW_s
$$
$\sigma$ is a deterministic function and $W_t$ is brownian motion.
I am asked to find the ...
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vote
2answers
94 views
Bootstrap zero curve source of information
I'm trying to understand the bootstrap methodology to construct a zero curve from a par curve in detail. I'm looking for a good source of information, preferably with a detailed example, that ...
1
vote
3answers
117 views
Need help to interpret the definition of a diffusion process
https://studentportalen.uu.se/uusp-filearea-tool/download.action?nodeId=1134155&toolAttachmentId=218130
In these lecture notes at page 15 and 16 I am looking at the definition of diffusion ...
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votes
1answer
180 views
Self finance conditions - proof check
Find expressions for the process $\psi=(\psi(t),\ 0\leq t\leq T)$ , so the portfolio $(\phi,\ \psi)$ is self-financing when:
(1) $\phi(t)= \int_{0}^{t}S_{s}ds $
(2) $\phi(t)=S_{t}$
where $\phi(t)$ is ...
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votes
2answers
363 views
Show a process is Martingale
$$Z(t)=(\frac{S(t)}{H})^p$$where $S$ has a standard Black-scholes Dynamics for a stock, $H$ is a postive constant and $p =1 - \frac{2r}{\sigma^2}$. How can I show that $Z(t)/Z(0)$ is a postive Q-...
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vote
2answers
101 views
Is a wiener proces measurable? (exercise from Bjork)
I will claim $$E[W(T) \vert F_t] = 0$$ for $t<T$. Anyway, in an exercise in Bjork the results requires that $$E[W(t) \vert F_t] = 0$$ But why? Isn't $W(t)$ measurable at time $t$ and hence not ...
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0answers
2k views
How to derive the Greek theta from Black-Scholes solution formula?
Which are the steps to compute the theta greek from the BS solution:
$$c(t, x) = xN(d_+(T-t,x)) - K e ^{-r(T-t)}N(d_-(T-t,x))$$
with:
$$ d_\pm (T-t, x) = \dfrac{1}{\sigma \sqrt{T-t}} \left[ \ln \...
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1answer
5k views
Z-Spread vs Discount Margin
I'm comparing two types of discounting: Z-Spread and Discount Margin.
Reading the article by O'Kane Credit Spread Explained I found Z-Spread is used for fixed rate notes meanwhile Discount Margin, ...
2
votes
1answer
294 views
What is a notation '1' in risk neutral probabilities paper?
I'm reading the paper by Zhao et al (2008) and have a problem with used definitions in the text on the page 1535.
First, we generate a sample, $R$, of a given size from the distribution (21). Let $\...
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3answers
212 views
A more mathematically rigorous explanation for why in the B-S model, the expected return on a call goes down as the stock price goes up
A problem asks whether the following statement is true assuming the Black-Scholes Framework:
The expected return on a call option goes up as the stock price goes up.
The solution is:
The statement ...
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vote
1answer
87 views
Is it possible to approach finding the risk premium of this derivative using Ito's Lemma?
I understand the author's intended solution to the below problem, but I thought I would see if I could solve this using first principles and Ito's Lemma instead for practice.
Let $V(S(t), t) = e^{rt}\...
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1answer
100 views
Is there a quick way to see why this claim $C(S, t)$ on $S$ does not satisfy the Black-Scholes PDE?
I'm self-studying for an actuarial exam on financial economics and encountered the below practice exam problem.
An exam problem should typically take 5-6 minutes to complete, so I'm wondering if ...
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1answer
102 views
Why is the statement “the volatility of a $T - t$-month prepaid forward on asset X is $\sigma$” the same as “the volatility of asset X is $\sigma$”?
I'm self studying and I'm having trouble with understanding the equivalent formulations of the volatility $\sigma$ of an asset $X$, as in the below problem.
In the below the problem (and the first ...
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1answer
46 views
Valuing a claim on $S^a$: This exercise/solution appears to have a mistake
The below exercise and solution was found in "Models for Financial Economics" by Abraham Weishaus. My issues are:
In this problem, $S(t)$ does not satisfy the Black-Scholes framework because ...
0
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1answer
112 views
Simulating a stock price with Monte Carlo - Why my solution isn't equivalent to the author's
I am self-studying and I am working on the following problem:
My solution is different and I'm arriving at a different answer:
The parameters of the lognormal random variable $S_t/S_0$ are: $$m = \...
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1answer
1k views
Proving that the $\Delta$ of a call on a futures contract under the B-S model is $N(d_1)$
The author of my textbook says that the $\Delta$ of a call on a futures contract is $N(d_1)$ and not $e^{-rT}N(d_1)$. I wasn't convinced, so I tried to prove this.
Let $F = F_{0, T}(S) = S_0e^{(r - \...
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1answer
340 views
Why doesn't the overnight profit on a delta-hedged porfolio include interest on the initial selling/buying of the option?
I am self-studying and encountered the following passage from my textbook on the market maker's overnight profit on a delta-hedged portfolio:
I don't understand why their isn't a factor of $(e^{r/365}...
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0answers
331 views
How do we know that the instaneous rate of return on this option, $\gamma$ is negative?
I am self-studying models for financial economics and encountered the following problem:
I don't see how the author can conclude that $\gamma = -0.62$. Let's rearrange the second to last equation: $$\...
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1answer
73 views
Why would a principal 'insist on a name' at the original price
A Dealing Certificate practice question
What is a principal doing if he 'insists on a name' at the original price?
Answer:
He refuses the broker's compensation and demands that the transaction is ...
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0answers
295 views
How to calculate an option porfolio cost and payoff function?
There are call and put options on the same underlying asset, with the same expiry, $T$, and with strikes $K_c=(k_c^1, k_c^2, \ldots, k_c^m)$ and $K_p=(k_p^1, k_p^2, \ldots, k_p^m)$, $S_t$ is a price ...
0
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1answer
82 views
Is it possible to calculate the call-put parity for an option's portfolio?
Let's say I have designed an option's portfolio. The portfolio includes long as well as short positions in European-style put and call contracts based on the same underlying asset with different ...
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vote
2answers
2k views
Trading liquidity risk
I am trying to understand trading liquidity risk $\cdots$ "Trading liquidity risk occurs when an entity is unable to buy or sell a security at the market price due to a temporary inability to find a ...
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1answer
593 views
How to derive the formula for risk-neutral probability for a Standard Binomial Tree (Forward Tree)
Consider a standard binomial tree. Let $u = e^{(r - \delta)h + \sigma\sqrt{h}}$ and $d = e^{(r - \delta)h - \sigma\sqrt{h}},$ where $\delta$ is the continuously compounded dividend yield, $h$ is the ...
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1answer
166 views
Calculating the annual return on an option using a replicating porfolio
I am self-studying and encountered the following problem:
My idea was to calculate the price of the put using a replicating portfolio, then use the formula:
$$Pe^{\gamma h} = S\Delta e^{\alpha h} + \...
0
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2answers
589 views
Understanding the payoff of currency options
I am self-studying for an actuarial exam and I am having a hard time understanding what happens when a currency option pays off.
Consider the below problem. The payoff at $C_u$ would be $\max(x_u - ...
3
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1answer
1k views
Understanding the relationship between the Black-Scholes formula and a replicating portfolio
I'm self-studying and I'm considering the below example. The specific example is not especially relevant, but I included it for reference.
I'm trying to understand the relationship between a ...
