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.
89
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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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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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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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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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134
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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: $$m = \...
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1
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Proving that the $\Delta$ of a call on a futures contract under the B-S model is $N(d_1)$
The author of my textbook says that the $\Delta$ of a call on a futures contract is $N(d_1)$ and not $e^{-rT}N(d_1)$. I wasn't convinced, so I tried to prove this.
Let $F = F_{0, T}(S) = S_0e^{(r - \...
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Why doesn't the overnight profit on a delta-hedged porfolio include interest on the initial selling/buying of the option?
I am self-studying and encountered the following passage from my textbook on the market maker's overnight profit on a delta-hedged portfolio:
I don't understand why their isn't a factor of $(e^{r/365}...
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0
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How do we know that the instantaneous rate of return on this option, $\gamma$ is negative?
I am self-studying models for financial economics and encountered the following problem:
I don't see how the author can conclude that $\gamma = -0.62$. Let's rearrange the second to last equation: $$\...
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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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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 ...
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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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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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778
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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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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} + \...
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2
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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 - ...
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1
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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 ...
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1
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Clarification on this author's solution for this problem on lognormal stock distribution
I am self-studying from a manual on financial economics, and I am trying to completely wrap my head around this solution:
I'm trying to fill in the in-between steps of this solution based on first ...
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Is this a poorly written example, or could volatility in fact be negative?
I'm self-studying and I encountered the following example. It seems to suggest that volatility is negative in this example. I was under the impression that volatility can never be negative, both from ...
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341
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Monte Carlo Accuracy - Antithetic Variate Method
I'm self studying for an actuarial exam and I am curious about a property of the antithetic variate method for increasing the Monte Carlo price accuracy (i.e. For every random draw of $z$, also ...
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Why are the greeks for the underlying stock 0 with the exception of delta?
In my textbook that I am self-studying from it is given that (assuming the Black-Scholes framework):
$\Delta_{stock} = \partial S / \partial S = 1$
All other Greeks for the underlying stock = 0
I ...
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How does this statement about the price of a prepaid forward on a stock follow?
I am self-studying for an actuarial exam on financial economics. This statement in the following problem/solution seems to imply that the prepaid forward price on a stock is the same as the prepaid ...
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2
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538
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What's the explanation for the formula for the volatility of a stock / volatility of the continuously compounded return of a stock?
I am self-studying for an actuarial exam, Models for Financial Economics.
It's stated as a given in my manual that $\sigma$ is the volatility of the stock, $\sqrt{\text{Var}(\ln(S_t/S_0))}$ and that ...
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143
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Is there an error in this problem on pricing an asset using the true probability of an up move?
I'm self-studying for an actuarial exam and I encountered the following problem:
The true probability of an up move, $p$, must satisfy: $$p = \frac{e^{{(\alpha - \delta})h} - d}{u - d},$$
where $\...
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Calculating the price of a call and put using multinomial trees and risk-neutral probabilities
I am self-studying for an actuarial exam and I encountered this example. The books shows one method of solving using a replicating portfolio, and then shows this solution involving risk-neutral ...
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4
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Self study references for a Mathematician
I just finished my undergraduate (BSc) degree in Pure Mathematics & Applied Mathematics. I am starting my postgraduate degree in Pure Mathematics in a month's time.
I am considering pursuing a ...
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Option analysis
Assume zero dividend and that the strike price for a European call option on a stock at a fixed maturity T and strike price K is given by C(K).Suppose that $C(K)=e^{-k}$ for all $K\geq 0$ ,then, I ...
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Modelling the Cost of Risk
I would like to read something about the cost of risk. Could anyone recommend some reference about how it is calculated or modelled?
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Risk Manager must-know list
What are the products, concepts, and models a risk manager must know? I'm not looking for an exhaustive list, but rather a general list as the one in Paul & Dominic's Guide To Quant Careers:
...
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354
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Equivalent Definitions of Self-Financing Portfolio
Consider a multi-period model with $t=0,...,T$. Suppose there is a bond with $B_0=1$ and $B_t=(1+R)^t$ and a stock with $S_0=s_0$ and
$$
S_{t+1}=S_t\,\xi_{t+1},
$$
with $\xi_t$ iid random variables....
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Understanding the necessary and sufficient conditions for rational early exercise of a call option
I am self-studying for an actuarial exam, and I encountered the following in my text:
The author states that if $PV_{t, T}\text{(Divs)} < K(1 - e^{-r(T - t)})$, early exercise is not rational.
...
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Difficulty understanding put-call parity for currency options
I am self-studying for an actuarial exam on models for financial economics. I am having difficulty thinking about the put-call parity for currency options, specifically how use the notation. Here is ...
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Problem solving using the put-call parity
I am self-studying for an actuarial exam on financial economics. I encountered this problem, and I am having difficulty seeing why the statement underlined is true:
How do we know that $P(60) - C(60) ...
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Computing $\gamma$ and $\mu$ at the efficient frontier
Consider the condition which the weights of any portfolio belonging to the efficient frontier satisfy:
\begin{equation}
\gamma\boldsymbol{wC} = \boldsymbol{m} - \mu\boldsymbol{u}\end{equation}
...
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Where am I making a mistake in my calculation of profit on a short-sale?
I am studying financial math and here is a problem and the solution from the author:
Here are my calculations:
The short sale is $200\cdot24.82 = 4964$. Now half of this amount will be taken for a ...
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0
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285
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stochastic calculus and multidimentional itos lemma
I am considering a number of assets (N) in a portfolio. each asset follows a geometric Brownian motion process therefore the stochastic differential equation is dS(i) = S(i)μdt + S(i)σdX(i).
The ...
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Derive OIS rate from IRS rate and Fed Funds/Libor basis spread
For example I have 7Y interest rate swap rate and 7Y Fed funds/Libor basis spread. What is the step-by-step procedure to derive OIS rate from these two?
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Expected Utility
We know that under certainty, any increasing monotone transformation of a utility function is also a utility function representing the same preferences. Under uncertainty, we must restrict this ...
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Financial theory
Ok guys, I'm studying from Danthine and Donaldson - Intermediate Financial Theory. The book itself doesn't have a lot of worked examples, and I'm lacking the basics for understanding some concepts ...
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Implicit relation between risk and reward
I want to differentiate w.r.t. $\sigma^2$ the following equation
$u'(Y)\mu$ + $\frac{u''(Y)}{2}$$(\sigma^2 + \mu^2) = 0$
where we can consider $\mu$(reward) as an implicit function of $\sigma^2$(risk) ...