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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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 ...
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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
168 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} + \...
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1answer
640 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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2answers
696 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 - ...
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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 ...
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1answer
69 views

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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1answer
281 views

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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2answers
238 views

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 ...
2
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1answer
445 views

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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1answer
171 views

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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2answers
297 views

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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2answers
121 views

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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4answers
3k views

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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1answer
139 views

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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4answers
2k views

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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1answer
190 views

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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1answer
104 views

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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0answers
80 views

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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1answer
329 views

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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1answer
266 views

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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1answer
75 views

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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1answer
121 views

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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1answer
142 views

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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1answer
1k views

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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0answers
248 views

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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2answers
208 views

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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0answers
81 views

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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