American Option Pricing with Machine Learning

American Option Pricing with machine Learning

Below we model American Call valuation by using Machine Learning. Dense-Lattice-Model-generated American Options have an almost precise relationship with arguments/attributes described below. Thus, we can in the abstract say "TRUE" value if Black Scholes (1973) BS assumptions are met. Broadie and Detemple (1996) obtained the “TRUE” value of American options by elaborating a 15,000-step benchmark binomial model for Cox, Ross and Rubinstein (1979). Using probabilistic methods, Amin and Khanna (1994) proved that the discrete-time models converge to the corresponding continuous-time models. This is important, as it provides a roadmap for establishing "TRUE" benchmarks. (This is mostly not applicable when we consider Market Option Values - then "TRUE" is better viewed as a market/social construct and somewhat fraught with noise). Here we explore initially how off the shelf-machine learning techniques can be applied to uncover the true theoretical value revealed by 15,000 step Cox, Ross and Rubintein (1979) mesh. We try to gauge the extent to which very basic machine learning techniques can predict American Option Values and with what level of accuracy. In previous research Shang and Byrne (2019) (https://jod.pm-research.com/content/27/1/92.abstract) developed intelligent lattice search to expedite CRR estimation which will be central here for generating our estimate of true. We will try to assess the performance of standard machine learning techniques and tentatively glean robustness of models. We would hope this presents a vista to piecemeal experientially reduce error by exploring a range of ML estimation techniques and tweaking appropriately to approximate "TRUE" using a data science approach. We impose laboratory conditions by assuming the Black Scholes assumptions hold. What we have set up below is purely a pilot to see if an off-the-shelf machine learning approach can be tuned/trained to retrieve / predict True American Option Values for Puts and Calls and with a view to ultimately develop ml strategies that yield improved accuracy with an eye on computational cost.

Model Attributes/Arguments include

S Stock Price

T Maturity

r risk free rate

b cost of carry (r - q)

q dividend yield

v volatility

PC Put or Call

AmericanTrue American value at 15,000 steps for Cox Ross and Rubinstein

EuropeanTrue Black Scholes

AER American/European Ratio

StrongWeak Strong or Weak (here all weak)

InOut In the Money or Out of the Money

In the following two videos we set out the relationship between American and European Options and under what circumstances valuations diverge.