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.
78
questions
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75 views
Show that portfolio's percentage contribution to loss (PCL) equals PCR (risk)
I came across this question during self study on a quantitative book (Question 3.6 on Page 75 of Quantitative Equity Portfolio Management: Modern Techniques and Applications By Edward E. Qian, Ronald ...
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1answer
61 views
Characterizing distribution of a stochastic intergal
characterize the distribution of $\int_0^T f(t)Z_tdt$. In
particular, verify that it is a Gaussian distribution and compute its moments.
1
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1answer
153 views
issue with benchmarks in “standard securities calculation methods”
I wonder if anyone is using the benchmark cases in "Standard securities calculation methods" issued by Securities Industry Association (Vol 1, 3rd ed.) to calibrate their implementations for ...
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1answer
91 views
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58 views
Risk free rate application to option pricing
We have $S_o = 50, u = 1.0606, d = 1/u, K = 54.50,$ risk free rate $r = 0.1$ per week, maturity in 9 weeks, given a binomial tree (3 steps)with the probabilities given by $q = (1+e^{r(T-t)}/u-d)$, no ...
2
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1answer
83 views
Martingale Binomial Tree Process
3 step binomial tree process with $S_0=4,u=2,d=0.5,r=0.25.$ Determine the probability p and q such that the stock price process is a martingale (i.e. $E[S3]=S_0)$
I know P = 1/3 and Q = 2/3 but having ...
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39 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
49 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
44 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 ...
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1answer
120 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
65 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
146 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
75 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 ...
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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
76 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
144 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
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2answers
288 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
366 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
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1answer
382 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.
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3answers
2k 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
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1answer
115 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
$$C_t = \...
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0answers
66 views
What should I learn/know before reading Investments by Bodie Kane Marcus?
I hope this is the appropriate place to post this. If not, I would really appreciate if someone could redirect me to the right site.
I've been seeing a lot of recommendations for the book, ...
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1answer
185 views
Introduction of a stochastic discount factor in martingale pricing
The example below is taken from Björk (2009). Let Radon-Nikodym derivative be
$$L=\frac{dP}{dQ} \;\; \text{on} \; \mathcal F$$
or written analogously
$$P(A) = \int_AL(\omega)dQ(\omega) \;\; \text{for ...
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1answer
797 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
3k 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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2answers
2k 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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1answer
260 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
268 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
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1answer
176 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 ...
3
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1answer
89 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
107 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
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3answers
137 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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1answer
232 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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2answers
404 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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2answers
110 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, ...
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1answer
296 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
228 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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1answer
88 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
104 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
112 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 ...
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1answer
114 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 = \...
1
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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
387 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
416 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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376 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
84 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 ...
