Feynman-Kac formula connects the solution to a SDE to the solution of a PDE. For example, the Black-Scholes formula is an application of Feynman-Kac. Let satisfies the following SDE driven… Gaussian mixture model (GMM) is a probability model for a mixture of several Gaussian distributions with possibly different mean and variance. For example, we can model the 100m race time… Ito’s formula is one of the fundamental tools in stochastic analysis. If the reader is interested in a proof of it, section 5.2 of Le Gull’s Brownian Motion, Martingales, and… The derivation of the Black-Scholes-Merton formula is very clearly organized in section 4.5 of Shreve’s Stochastic Calculus for Finance II Continuous-Time Models. It is the most intuitive and clearest way that the… Implied Volatility Option price in the Black-Scholes-Merton formula can be seen as a function of volatility if interest rate and strike price are known. Market quote of option price gives… Denote the stock price at time by for . is a stochastic process adapted to a filtration . is the one-dimensional standard Brownian motion. We assume satisfies the following stochastic…Feynman-Kac Formula
Gaussian Mixture Model
Ito’s Formula
Derivation of Black-Scholes-Merton Formula
Volatility
Geometric Brownian Motion
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