Geometric Brownian Motion.pdf
Black-Scholes Formula.pdf
PDSV/PDSVH/PDSV-OIM/PDSVH-OIM
Butterfly arbitrage
Log OU process
Which one is your volatility — Constant, Local or Stochastic?
As an upgrade/alternative to LV model, a stochastic volatility (SV) model can produce a more realistic forward volatility surface, where the smile is almost self similar, compared to LV models which flatten out the forward volatility curve and vanish the smile. LV models assume that skew in the future will be what we see the forward skew today in local vol, whereas SV models assume the skew in the future is similar to the skew today. That’s why SV model is likely to overprice options, whereas the LV and BS models tends to underestimate options.