# Independent Study
My second year of the program focused on my independent study. It is titled *Optimal Stochastic Control of Net Credit Multi-Leg Options Strategies*. I am grateful to be advised by [Prof. Tim Leung](https://sites.google.com/site/timleungresearch/).
My research employs numerical solutions to optimal stopping problems in strategies involving the buying and selling of multiple options simultaneously, on the same underlying stock. In particular I am looking at the net credit varieties of the [iron condor](https://en.wikipedia.org/wiki/Iron_condor) and [iron butterfly](https://en.wikipedia.org/wiki/Iron_butterfly_\(options_strategy\)). I seek to answer the question:
> If you allowed yourself to adjust this strategy only *once* during its its lifetime, when should you do it, and by how much?
This question is answered by setting up a [variational inequality](https://en.wikipedia.org/wiki/Variational_inequality) using a [Snell envelope](https://en.wikipedia.org/wiki/Snell_envelope) to compare the expected value of action vs. inaction. This is done rigorously by employing a [stochastic volatility model](https://en.wikipedia.org/wiki/Heston_model) under the conditions of [American options](https://en.wikipedia.org/wiki/Option_style#American_and_European_options) that consider the possibility of early exercising.
Do I get to call myself a principal investigator?
The greatest part of the experience was being able to share in the work with bright undergraduate students who volunteered to assist in the research. You-Ruei Hsu, Patricia Dao, and Thomas Zeng contributed greatly by assisting in the literature review and setting aside time for me to explain it to them as I was working on it, serving as a much needed sanity check.
As much as we could, we met twice a week this year for study. It started with an initial primer on options strategies, then understanding the research process and what it means to produce novel work. Because the work is centered around a retail investor strategy, I had a fun tangent teaching them how to use [thinkorswim](https://www.schwab.com/trading/thinkorswim/desktop) to do conduct equity research and construct theoretical strategies and paper trade.
