Methodology: Dynamic programming, convex optimization, system analysis, numerical methods and data visualization based on cutting-edge research papers. Numerical computations were carried out using the Matlab software.
Empirical base of research: Price and volatility data from the Russian futures and options market; high-frequency trading data from the Russian stock market.
Results of research:
- We obtained an incomplete market model in a deterministic setting. The model assumes discrete time, no transaction costs, but allows some trading restrictions. We derived a no-arbitrage condition for the model in terms of model parameters. Within this model, we state the superhedging problem for a general contingent claim. When the trading restrictions are absent or non-binding this problem is equivalent to finding the minimal concave hull of the payoff function in a neighborhood of the current underlying price determined by the set of possible future prices. Active trading restrictions result in more complex solutions with less evident geometric interpretations.
- We studied the properties of the obtained contingent claim pricing procedure with respect to the payoff function, price dynamics, and trading restrictions.
- We obtained recurrent equations for superhedge prices of the most common financial options and their combinations: European options, American options, binary options, lookback options, and combinations.
- We implemented an approach to compare the marginal requirements and applied it to the developed approach as well as the margining methods currently in use by the Moscow Exchange. The results can be used to infer the practical parameter values for our model.