the Heston stochastic volatility model

The development of mathematical finance, much like the processes it aims to study, has had a particularly jumpy history. A major leap came in 1973, when the Black-Scholes option pricing model was published and mathematically understood. The essential idea is to model the underlying asset $S_t$ of an option as a geometric brownian motion, with a stochastic differential equation (SDE), given by $$ dS_t = \mu S_t \ dt + \sigma S_t \ dW_t, $$...

August 1, 2021 · 7 min

the Freeman method

Just about a year ago today, I began working on implementing an algorithm my undergrad research advisor had devised to speed up the Metropolis algorithm, in the regime where the acceptance probability is very low, which is the case in lattice simulations of quantum gravity. Quantum Gravity Physics has experienced its most rapid advancement when theories are unified: electromagnetism $\leftarrow$ electricity + magnetism + light general relativity $\leftarrow$ special relativity + curved space-time (gravity) quantum field theory $\leftarrow$ quantum mechanics + special relativity + electromagnetism + matter + nuclear forces And hopefully soon…...

June 9, 2021 · 3 min