XlsxEdit Library First User
I got my first active user on Xlsx Edit who opened issues :) another mini milestone achieved.
I will implement his feature requests.
2026 · August
C++ Programming for Financial Engineering
Finished my C++ Exam and I got an average >90% yay!
A new Baruch certificate with distinction!
Final message on my thoughts
Probability Theory and Statistics Recap
Chapter 7: Expectation and Variance (discrete)
Expectation
Variance: $\mathrm{Var}(X)=\mathbb{E}[(X-m)^2],\qquad m=\mathbb{E}[X].$
Chapter 8: Continuous distributions
Uniform distribution: $X\sim\mathcal{U}([a,b])$
Exponential distribution: $f(x)=\lambda e^{-\lambda x}$
Normal distribuiton: $f_{m,\sigma}(x)=\frac{1}{\sqrt{2\pi\sigma^2}}\exp\!\left(-\frac{(x-m)^2}{2\sigma^2}\right).$
Chapter 9: Joints, Marginal and Asymptotics
Joint density: X,Y random variables and double integral for probability
Marginal density: We integrate over one variable so only the other is left
Independence: Joint heights factor into product of marginal heights
Chapter 10: Statistics
MLE
Hypothesis testing
Confidence intervals
Recap
17.08 finished recap and went through exam
Quote on talent and insecurity
You're saying this because you're insecure.
You keep saying that I'm different, but those words are looking down on me more than anyone. Are you saying those words because you know how much effort I've put in and how I've lived?
All you're doing is disregarding your own effort. Doing it to yourself. By categorizing it all under the word talent.
If you're weak, family can become a burden and a weakness. For truly strong people family becomes their true strength.
The older you get the less confidence you have. You rely on experience instead. What looks like confidence is just familiarity.
Probability Theory and Statistics Recap
Started recapping probability theory and statistics which I had in 4th semester of ETH.
Chapter 1: Probability spaces and Events
Chapter 2: Laplace Model and counting
Laplace means probability have same chance so problem turns into occurences / total set
Chapter 3 Conditional Probability & Bayes
Conditional Probability: $\mathbb{P}[A\mid B]=\frac{\mathbb{P}[A\cap B]}{\mathbb{P}[B]}.$
Law of total probability: $\mathbb{P}[A]=\sum_{i=1}^n \mathbb{P}[A\mid B_i]\,\mathbb{P}[B_i]$ when B are partition of $\Omega$.
Bayes: $\mathbb{P}[B_i\mid A]=\frac{\mathbb{P}[A\mid B_i]\,\mathbb{P}[B_i]}{\sum_{j=1}^n \mathbb{P}[A\mid B_j]\,\mathbb{P}[B_j]}.$ Given the outcome what is probability of hypothesis.
Chapter 4 Independence
$A$ and $B$ are independent when $\mathbb{P}[A\cap B]=\mathbb{P}[A]\,\mathbb{P}[B].$
Multiple events: Every subcollection needs to be independent
Random Variables: independent and identically distributed
Chapter 5 Random Variables
Measurable map, grouping of events with different payoff (function).
Continous:
- CDF (cumulative distribution function)
- PDF (probabiliry density function)
Discrete:
- CDF
- PMF (probabiity mass function)
Chapter 6 Discrete distributions
Bernouille: one yes/no trial
Binomial: n independent Bernouille trails
Geometric: Bernoille untill first success
Poisson: Approximation of Binomial for rare events, large n small p, $\lambda=np$, $\mathbb{P}[N=k]=e^{-\lambda}\frac{\lambda^k}{k!},\qquad k=0,1,2,\ldots.$
Insecurity about why breakup
Post Breakup Thoughts
C++ For Financial Engineering HW
Level 9 — exact BS, perpetual American, Monte Carlo, SD/SE, Excel COM, and explicit FDM puts.
Level 9 Homework
Group A
Implementation of European Option Pricing with Black-Scholes Model
Put Call Parity relationships
Matrix Pricer to price multiple options
Option Sensitivities aka Greeks
Parameters
- $T$ expiry, $K$ strike, $\sigma$ volatility, $r$ risk-free rate, $S$ spot
- $b$ cost-of-carry: $b = r$ (stock), $b = r - q$ (dividend), $b = 0$ (futures), $b = r - R$ (FX)
- $N(x)$ standard normal CDF, $n(x)$ standard normal PDF
Black–Scholes (European call / put)
$$ d_1 = \frac{\ln(S/K) + (b + \sigma^2/2)T}{\sigma\sqrt{T}}, \quad d_2 = d_1 - \sigma\sqrt{T} $$
$$ C = S e^{(b-r)T} N(d_1) - K e^{-rT} N(d_2) $$
$$ P = K e^{-rT} N(-d_2) - S e^{(b-r)T} N(-d_1) $$
Put–call parity
$$ C + K e^{-rT} = P + S $$
(so $P = C + K e^{-rT} - S$, and $C = P + S - K e^{-rT}$)
Greeks (exact)
$$ \Delta_C = e^{(b-r)T} N(d_1), \quad \Delta_P = e^{(b-r)T}\bigl(N(d_1) - 1\bigr) $$
$$ \Gamma = \frac{n(d_1)\, e^{(b-r)T}}{S\,\sigma\sqrt{T}} \quad\text{(same for call and put)} $$
Greeks (divided differences)
$$ \Delta \approx \frac{V(S+h) - V(S-h)}{2h} $$
$$ \Gamma \approx \frac{V(S+h) - 2V(S) + V(S-h)}{h^2} $$
Group B
Perpetual American Option Pricing
Perpetual American call
$$ y_1 = \tfrac{1}{2} - \frac{b}{\sigma^2} + \sqrt{\Bigl(\frac{b}{\sigma^2} - \tfrac{1}{2}\Bigr)^2 + \frac{2r}{\sigma^2}} $$
$$ C = \frac{K}{y_1 - 1}\left(\frac{(y_1 - 1)S}{y_1 K}\right)^{y_1} $$
Perpetual American put
$$ y_2 = \tfrac{1}{2} - \frac{b}{\sigma^2} - \sqrt{\Bigl(\frac{b}{\sigma^2} - \tfrac{1}{2}\Bigr)^2 + \frac{2r}{\sigma^2}} $$
$$ P = \frac{K}{1 - y_2}\left(\frac{(y_2 - 1)S}{y_2 K}\right)^{y_2} $$
Group C Monte Carlo Simulation
GBM paths via Euler–Maruyama; European call/put by averaging discounted payoffs; sweep NT / NSim on Batches 1, 2, 4.
MC pipeline
- Simulate a path of the underlying.
- Get stock price at $t = T$.
- Payoff at $T$; repeat $M$ times (
NSim). - Average the payoffs.
- Discount to $t = 0$.
Euler–Maruyama step
$$ X_{n+1} = X_n + k\,r\,X_n + \sqrt{k}\,\sigma\,X_n\,Z, \quad Z\sim N(0,1) $$
($k = T/N$, $N$ = time steps)
Takeaways
NSimcuts statistical noise;NTcuts Euler time-discretization bias — both needed.- Coarse mesh (
N=10) leaves a bias floor even with millions of paths. - Short maturity:
NSimoften matters more thanN; long $T=30$ needs much largerNTandNSim. - Realistic match to exact BS is order $10^{-3}$, not exact equality.
Group D Advanced Monte Carlo
Added generic SD / SE on the vector of discounted path payoffs (Statistics.hpp), wired into TestMC / RunMC; reported SD/SE vs NT / NSim on Batches 1–2.
$$ \mathrm{SE} = \mathrm{SD}/\sqrt{M} $$
($M$ = NSim)
Takeaways
- SD ≈ payoff dispersion for that option; stays roughly flat when
NorNSimchange. - SE shrinks like $1/\sqrt{\mathrm{NSim}}$;
NTbarely affects SE. - Once
Nis large enough, absolute error vs exact is often on the order of SE (MC noise, not Euler bias). - Larger SD (e.g. Batch 2 call) → larger SE at the same
NSim→ harder to match exact.
Group E Excel Visualization
Ran Duffy Excel demos (TestSingleCurve, TestTwoCurve, TestMultiCurve) on Windows via Parallels + Office 365 (path / #import / Boost / IntDir fixes for Mac→VM). Then TestExactMeshExcel: mesh of $S$, exact BS prices from Group A into a vector, charted in Excel.
Takeaways
- Excel Automation (COM) is Windows-only.
- Pattern: mesh in $S$ → price each spot → send vectors to ExcelDriver → chart.
Group F Finite Difference Methods
Explicit Euler on the Black–Scholes PDE (European put); TestBSPDE1 + Excel. Batches 1–4 with mesh $S_{\max}=2K$, $J=2K$, $N=9999$.
Main pieces
ParabolicPDE.hpp— IBVP callbacks ($\sigma$, $\mu$, $b$, $f$, BCL, BCR, IC)Mesher.hpp— uniform grids in $S$ and $t$FDM.hpp— one explicit Euler time stepFDMDirector.hpp— meshes + IC + time loop to $T$- Excel helpers — plot the solution
Takeaways
- Batches 1–3: FDM puts within ~$10^{-3}$ of exact BS puts.
- Batch 4 ($T=30$): same $N$ → explicit Euler unstable (time step too large vs domain); need larger $N$ (or a stabler scheme) for a useful price.