Part 1: Dionysus

Part 1: Dionysus#

Call option price is analogous to the difference between the base-case & clinical-scenario; i.e., logHR. In clinical medicine, we’ve kept our cumulative distribution functions non-parametric, at least for our base-case (62,000 citations: Google Scholar)

\[ C(S, t) = S_0 \mathcal{N}(d_1) - X e^{-r(T-t)} \mathcal{N}(d_2) \]

where:

\[ d_1 = \frac{\ln(S_0/X) + (r + \sigma^2/2)(T-t)}{\sigma \sqrt{T-t}} \]
\[ d_2 = d_1 - \sigma \sqrt{T-t} \]

Here, \(C\) is the call option price, \(S_0\) is the current stock price, \(X\) is the strike price, \(r\) is the risk-free interest rate, \(T\) is the time to maturity, \(\sigma\) is the volatility of the stock, and \(\mathcal{N}(\cdot)\) is the cumulative distribution function of the standard normal distribution.

       1. Chaos
               \
  2. Frenzy -> 4. Unpredictable -> 5. Algorithm -> 6. Binary
               / 
               3. Random-Walk

Efficient-Market Hypothesis#

Null 1, 2, 3#

  • Voir: Random brownian motion as seen in digital information from Bloomberg Terminal; \(\text{H}_0:\) logHR=0

  • Savoir: Compute may find patterns than Eugene Fama’s mind couldn’t

  • Pouvoir: \(\mu | \text{X}\beta\) ; \(\sigma | t\); two overlayed multivariable Kaplan-Meier’s

Sing O Muse 4#

  • Unpredictable: Estimates conditional on factors millions of orders of magnitude more than human mind “tameth”; no wonder there’s been gnashing of teeth

Alternative 5, 6#

  • Identity: Some quants, programmers, and algorithms have produced better returns than the null-hypothesis over decades

  • Achievements: Using super-human AI capabilities of machines to handle \(N^N\) parameters, Jim Simmons is the best way to summarize this

Table of Contents#

Contents