Black Scholes PDE Black Scholes Greeks.

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Presentation transcript:

Black Scholes PDE Black Scholes Greeks

Stock Equation

Self Financing

Replicate an Option

Rewriting terms

Black-Scholes PDE

Call Options

The Greeks (Delta)

Delta Hedging Delta Hedging is to re-balance the portfolio of the option and stock continuously so that you always have a new delta of zero. Of course this is not practical to hedge continuously and so instead we hedge periodically. Example) suppose S = $100, C=$10 and Delta = 0.6 and you sold Call options on 2000 shares. You can hedge your position by buying 0.6 * 2,000 = 1200 shares. The gains (losses) on the call options would offset the gains (losses) of the stock.

The Greeks (Gamma)

Gamma Neutral portfolio

Greeks (Vega)

Greeks (Theta)

Greeks (Rho)

Relationship between Greeks

Relationship between Θ and Γ