# 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.

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### 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-...
134 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 ...
73 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 ...
57 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.
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### Calculating European call option, the Bjork way

We have a 3 period binomial tree with values: ...
54 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 ...
66 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 ...
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 ...
48 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 ...
41 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 ...
79 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 ...
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 ...
105 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 ...
98 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 ...
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### 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 ...
3k views

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### 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 ...
379 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-...
107 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 ...
294 views

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 $F = F_{0, T}(S) = S_0e^{(r - \... 1answer 103 views ### Is there a quick way to see why this claim$C(S, t)$on$S$does not satisfy the Black-Scholes PDE? I'm self-studying for an actuarial exam on financial economics and encountered the below practice exam problem. An exam problem should typically take 5-6 minutes to complete, so I'm wondering if ... 1answer 108 views ### Why is the statement “the volatility of a$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$, as in the below problem. In the below the problem (and the first ... 1answer 46 views ### Valuing a claim on$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)$does not satisfy the Black-Scholes framework because ... 1answer 113 views ### Simulating a stock price with Monte Carlo - Why my solution isn't equivalent to the author's I am self-studying and I am working on the following problem: My solution is different and I'm arriving at a different answer: The parameters of the lognormal random variable$S_t/S_0$are: $$m = \... 0answers 372 views ### How do we know that the instaneous rate of return on this option, \gamma is negative? I am self-studying models for financial economics and encountered the following problem: I don't see how the author can conclude that \gamma = -0.62. Let's rearrange the second to last equation:$$\... 1answer 365 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}...
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 ...