3.0.Background - Options
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Define Call & Put Option
- Call option: gives the option buyer the right to buy an asset for a given price at some date.
- Put option: gives the option buyer the right to sell an asset for a fiven price at some date.
American vs European option
American option can be exercised any time, while european can only be exercised on the expiration date.
Factors that affect the price of an option
- Current stock price
- Exercise price or strike price
- Time to expiration
- Risk-free rate
C + Ke-rT = P + S
- C = N(d1) - N(d2)Ke-rT
- d1 = [ln(S/K) + (r + ½σ²)T] / σ√T
- d2 = [ln(S/K) + (r - ½σ²)T] / σ√T
- d2 = d1 - σ√T
- Special case when K = Se-rT, C ≈ 0.4S σ√T
- Geometric Brownian Motion: dS = μSdt + σSdz
- dG = [(δG/δS)μS + (δG/δt)μS + ½(δ²G/δS²)σ²S²]dt + (δG/δS)σSdz
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