46 Matching Annotations
  1. Last 7 days
    1. 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*

    2. SS

      we should also something like mean_terminal_stock_price or something more explicit or even S_hat

    3. 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?

    4. inout

      input*

    5. we would generate a standard normal Zi and compute log⁡Si(T)=log⁡S(0)+(r−q−12σ2)T+σTZi,log⁡Si′(T)=log⁡S(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.

    6. ## Antithetic Variates in Monte Carlo

      Think this is missing sub-heading format?

    7. two

      too*

    8. 000

      10,000 counting zeros without the commas is a pain

    9. 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.

    10. norm = stats.norm

      this can be defined/declared outside the function. It's static

    11. # <!-- norm = sp.stats.norm -->

      shouldn't be here

    12. 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)

    13. Section 6.3 and~???. Of

      missing section link

    14. Monte Carlo and B

      in general the previews from hovering the cursor over the links is missing

    15. Chaps.~??? and~???.

      missing citation here

    16. and variance σ2T, where

      Is nu supposed to be \(\mu\) ?

  2. Nov 2024
    1. 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

    2. 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?

    3. thw

      the*

    4. Calculations in Python

      We can really get a lot out of interactivity here

    5. delta

      you should stick with either 'delta' or \(\delta\) not switch between

    6. ion function N is the normal density function nd defined as

      nd(d)?

    7. left-hand side,

      lefthand side of what?

    8. ^[T

      what's going on with the brackets here

    9. consider

      dont need an extra 'consider' here

    10. number Equation 4.2

      the number in *

    11. 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

    12. There is no other risky asset price Y in this model, so the subscripts we used in Section 3.10

      what about the subscripts

    1. ``

      we can take these out

    2. it

      dont need the 'it' here

    3. ns, n=1. G

      is n paths or subdivisions?

    4. 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

    5. have

      should have brackets to indicate what's included in summation

    6. dividend

      dividends

    7. One input the is number n=10000 of time periods

      One input is the number...

    8. value

      values*

    9. 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.

    1. h price num(t). We w

      "num" might be a little too generic. It could just be me but this looks off-putting

    2. under different

      Under different measures? Different probabilities?

    3. are

      are is not grammatically correct here

    4. are

      are is not grammatically correct here

    5. 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?

    6. called a

      called a martingale?

    7. called a

      called a what? Are we missing a word here?

    8. asset as the

      as the what? As the numeraire?