1. Take a sequence of standard binomial lattices for a GBM stock price process each with (boundary) nodes at S=100. The originating node could be S(0)>100,
1. What are sequence of binomial lattices, suitable norm to the continuous model (that should be standard),??
2. I can't visualise what's going on
3. I can't see the maths/numerics. BTW what does the continuous model look like? SDE, PDE, analytic, whatever?
inter os atque offam
say S(0)=110. Each sequence member has decreasing time step size. A typical convergence notion for lattice to continuum models is weak convergence of measures.
2. Visualize a reflecting GBM process with reflection at S=100, starting at, let's say S(0) = 110. On the lattice, visualize a binomial lattice process with reflection at a lower level.
3. For the transition density, reflecting GBM has standard BS pde generator (no killing term) with standard zero derivative bc for reflection at a level. For an option value function, standard BS pde with zero derivative bc. However, a caveat is that the option values may be ``illegitimate" in the presence of arbitrage opps. The transition density should be fine, as well as expectations under the "physical" process. The simplest setup might be a world with zero physical drift and zero interest rates.
The main point is the implications of a trading strategy (on the lattice) that buys the stock whenever it reaches the barrier. If you bought the stock with borrowed funds, this is obviously an arbitrage opp in each lattice world. But, can it be shown rigorously that it converges to an arbitrage opp in the continuum limit? (The author of the paper at issue believes "no". bearish & I believe "yes").