improved by replacing with at date
replacing with what?
50 Matching Annotations
- Dec 2024
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book.derivative-securities.org book.derivative-securities.org
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?sec-s_fundamentalconcepts
huh?
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as pd.
We can maybe use code format here
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Equation 6.24 is e
we haven't defined equation 6.24 yet
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the random variable the mean of which we want to estimate is
The mean of the random variable of which we want to discuss is*
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SS
we should also something like mean_terminal_stock_price or something more explicit or even S_hat
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timate for the stock price as the dicsounted expected value of the terminal stock price
Should be \(S_t(m,i)\) we should also explain m here. The mth subdivision?
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inout
input*
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we would generate a standard normal Zi and compute logSi(T)=logS(0)+(r−q−12σ2)T+σTZi,logSi′(T)=logS(0)+(r−q−12σ2)T−σTZi. Given the first terminal price, the value of the derivative will be some number xi and given the second it will be some number yi. The date–0 value of the derivative is estimated as
Why does \(\log S_i(T)\) have the same randomness as \(\log S_i^{'}(T)\)? Do we need \(Z_i^{'}\) for the second simulated price?
also it might help to write \(x(S_i(T)) \) and \(y(S_i^{'}(T)) \) in the mean estimation for clarity.
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## Antithetic Variates in Monte Carlo
Think this is missing sub-heading format?
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two
too*
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000
10,000 counting zeros without the commas is a pain
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The black scholes fromula= 4.759422392871532
We've already the Black-Scholes function. Based on how compile.py works, we should be able to just recall it from the previous section and use it in the above block.
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norm = stats.norm
this can be defined/declared outside the function. It's static
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# <!-- norm = sp.stats.norm -->
shouldn't be here
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cp
these variables are confusing. We should be more explicit about what these mean (e.g., cp to call_price and cc,cc1 to call_payoff_1, call_payoff_2)
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Section 6.3 and~???. Of
missing section link
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Monte Carlo and B
in general the previews from hovering the cursor over the links is missing
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Chaps.~??? and~???.
missing citation here
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and variance σ2T, where
Is nu supposed to be \(\mu\) ?
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book.derivative-securities.org book.derivative-securities.org
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blem~??? for
What is this referencing? 2.1?
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- Nov 2024
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book.derivative-securities.org book.derivative-securities.org
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where now B∗ denotes a Brownian motion when V is the numeraire. This is equivalent to
@Mark they should know Girsonov Thm before this point
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Close observation of the right hand side we see this is the drift term of Ito expansion for C if we work in the risk neutral measure.
what is 'this' referring to?
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thw
the*
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Calculations in Python
We can really get a lot out of interactivity here
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delta
you should stick with either 'delta' or \(\delta\) not switch between
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ion function N is the normal density function nd defined as
nd(d)?
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left-hand side,
lefthand side of what?
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^[T
what's going on with the brackets here
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consider
dont need an extra 'consider' here
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number Equation 4.2
the number in *
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on the volatility coefficients and on B and B∗ to distinguish the Brownian motion driving S from the Brownian motion driving Y and to distinguish their volatilities are not needed here
this is grammatically confusing
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There is no other risky asset price Y in this model, so the subscripts we used in Section 3.10
what about the subscripts
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book.derivative-securities.org book.derivative-securities.org
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``
we can take these out
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it
dont need the 'it' here
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ns, n=1. G
is n paths or subdivisions?
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The code below simulates n=10000 paths with m=1000 time steps. There are some features of the simulation which will prove useful late
before we used m as the number of paths. Inconsistency here @mark
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have
should have brackets to indicate what's included in summation
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dividend
dividends
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One input the is number n=10000 of time periods
One input is the number...
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value
values*
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ts, to a deterministic model, for example, in a model predicting the position of a falling object.
The model of noise was developed by Ito to account for random disturbances to a deterministic model, such as unpredictable wind gusts in predicting the position of a falling object.
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book.derivative-securities.org book.derivative-securities.org
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h price num(t). We w
"num" might be a little too generic. It could just be me but this looks off-putting
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under different
Under different measures? Different probabilities?
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are
are is not grammatically correct here
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are
are is not grammatically correct here
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The expected future (date–T) value equals the current (date–0) value, so the random variables (C/R and S/R or C/S and R/S) are
are martingales?
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called a
called a martingale?
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called a
called a what? Are we missing a word here?
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asset as the
as the what? As the numeraire?
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