It’s been an eventful couple of days, with Options, Futures, and other derivatives taking center stage in my learning. While I’m still grasping everything, reading through and identifying key themes and points of interest has been incredibly rewarding. Just a note: The formulas included in this article are purely for interest sake, I do not claim to and do not understand it fully.

I’ve delved deeper into options trading and pricing. As mentioned previously, I’ve explored both European and American options. A key distinction is that a European option can only be exercised on its expiration date, whereas an American option can be exercised at any point up to and including the expiration date, which significantly increases its complexity.

I’m starting to develop an intuitive understanding of various option pricing methods. The Binomial Option Pricing Model stands out as quite straightforward. Its core idea is that, in a simplified theoretical world, an option’s value can only move up or down over a given period. While the actual application is more complex, this foundational concept makes intuitive sense. The formula for a single-period binomial model is:

\(C = \frac{(pC_u + (1-p)C_d)e^{-r\Delta t}}{1}\)

where:

• C = Current option price
• Cu​ = Option price if underlying asset goes up
• Cd​ = Option price if underlying asset goes down
• p = Probability of an upward movement
• r = Risk-free interest rate
• Δt = Time period

Then there’s the revolutionary Black-Scholes Model. Derived using complex calculus, this model provides a precise formula to determine an option’s theoretical value by plugging in various market variables. Before its development, there wasn’t a definitive way to price options, making it a groundbreaking advancement in finance. The Black-Scholes formula for a European call option is:

\(C = S_0 N(d_1) – Ke^{-rT} N(d_2)\)

And for a European put option:

\(P = Ke^{-rT} N(-d_2) – S_0 N(-d_1)\)

where:

• C = Call option price
• P = Put option price
• S0​ = Current stock price
• K = Option strike price
• r = Risk-free interest rate
• T = Time to expiration (in years)
• N(x) = Cumulative standard normal distribution function
• \(d_1 = \frac{\ln(S_0/K) + (r + \sigma^2/2)T}{\sigma\sqrt{T}}\)
• \(d_2 = d_1 – \sigma\sqrt{T}\)
• σ = Volatility of the underlying asset

I also learned about the different avenues through which options are traded. Similar to stocks on the NYSE, options are traded on dedicated options exchanges, many of which are accessible through the NYSE, along with other markets. Additionally, options can be traded “Over-the-Counter” (OTC), which is often done to bypass certain exchange-imposed restrictions.

Moving on to futures contracts, they share similarities with options but are generally more straightforward and have stricter rules. Essentially, a futures contract is a binding agreement to buy or sell a specific asset at a predetermined price on a future date. Both parties must agree on crucial details such as the quality, quantity, and delivery terms of the underlying asset. The basic concept is a commitment to a future transaction.

This week also involved dedicating significant time to a speech I’m preparing, which I’ll share more about after I’ve delivered it.

For now, have a brilliant day! I’ll be back with another update tomorrow.