Derivatives
Value at Risk
While the Greek letters view portfolio risk from multiple angles and generate numerous risk measures, the VaR (Value at Risk) metric is an attempt to express portfolio risk […]
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Understand stock price as a forecast
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Derivatives
Finite Difference Methods
The finite difference method, beyond finance, is actively used in physics and engineering fields, such as: The method involves breaking down a continuous differential equation into a system […]
Derivatives
Monte Carlo in Option Pricing
The main advantage of the Monte Carlo simulation method over binomial trees is that it can be used to price options whose payoff depends not only on the […]
Derivatives
American Options – Binomial Trees
One method used to value an American option is the construction of a binomial tree. I have written about this before (Binomial Trees), so here I will focus […]
Derivatives
Volatility Smile
It turns out that the option price calculated using the Black–Scholes–Merton (BSM) model differs from the price formed in the real market. The reason is that the market […]
Derivatives
Portfolio Insurance with Synthetic PUTs
The presence of a risk-free asset portion in a portfolio can insure its value with almost the same precision as purchasing put options. The value of a diversified […]
Behavioral Finance
Fuled by Randomness
📘 Fooled by Randomness — Nassim Nicholas Taleb🎯 Core Idea🎲 We systematically confuse luck with skill📉 Randomness explains far more success and failure than we admit🧠 We invent […]
Derivatives
The Greeks – Vega (V)
Here is a clear, accurate translation into English, keeping the financial meaning intact: Vega (V) Vega is the rate at which the value of an options portfolio changes […]
Derivatives
The Greeks – Gamma (Γ)
Also, the relationship between the option price and the underlying price is not linear. Gamma determines the degree of curvature of this relationship. It is the second derivative […]
Derivatives
The Greek Letters
📈 As we saw, Delta Hedging is a very effective tool for hedging the risk of a sold option.⚖️ When a portfolio becomes Delta Neutral, changes in the […]
Derivatives
The Greek Letters – Δ (Delta)
Trading options requires risk hedging.Suppose an investment fund uses the Black-Scholes-Merton model to calculate the value of a call option and then sells it in the market at […]
Derivatives
Black-76 Model – Futures Options
Black’s brilliant model was originally developed for pricing European futures options (“The Pricing of Commodity Contracts,” Journal of Financial Economics, 3 (March 1976)). Later, it turned out to […]
Derivatives
Valuation of American Futures Options
Valuation of American-Style Futures Options using Binomial Trees American-style futures options are valued using binomial trees. The difference between a futures option and a stock option is that […]
Derivatives
Futures Options
A futures option is the right, but not the obligation, to enter into a futures transaction at a predetermined futures price, by a predetermined date. The final date […]
Derivatives
Stock vs Bonds
📌 Why Long-Term Stock Guarantees Are More Expensive Than They Look I recently came across a fascinating “Business Snapshot” in John Hull’s classic textbook Options, Futures, and Other […]
Derivatives
Portfolio Insurance with Index Option
A diversified portfolio’s value can be insured using options written on a corresponding index (e.g., the S&P 500). If we assume that the portfolio closely replicates the index, […]
Derivatives
Employee Stock Options
Microsoft was one of the first companies to grant stock options to all employees. Later it was estimated that thanks to this decision, more than 10,000 employees became […]