Black-Scholes and Binomial Option Pricing Models Outline

A. Concept
- Stock price can go up or down over a specific period
- Simplistic assumptions: linear discrete outcomes
B. Process
1. Define time period (e.g., three months)
2. Possible outcomes (e.g., stock rises to $60 or drops to $40)
3. More detailed model:
  - Multiple periods (e.g., monthly)
  - Combinations of outcomes (e.g., four possible outcomes after three months)
4. Assign probabilities to outcomes and discount back
C. Complications and Limitations
- Limitations of only allowing a few possible outcomes
- Complexity increasing with more nodes and time frames

A. Continuous Stock Price Variation
- Introduction of continuous variation over discrete nodes
- Normal distribution of stock prices vs. discrete outcomes
B. Mathematical Basis
- Use of differential equations
- Comparison to physics (e.g., heat diffusion)
- Nobel Prize awarded for these contributions

A. Call Option Pricing Formula
- Formula: (C = S N(d_1) - K e^{-rT} N(d_2))
  - Where:
    - S = Current stock price
    - K = Exercise price
    - r = Risk-free rate
    - T = Time until expiration
    - N(d_1), N(d_2) = Normal distribution functions
B. Components of the Formula
- Intrinsic Value vs. Speculative Value
- Impact of volatility and time
C. Black-Scholes-Merton Model
- Addition of dividend yield ( Y)
- New formula adjustment: (C = S e^{-Y T} N(d_1) - K e^{-rT} N(d_2))

A. Validity for European-style options
- Differences with American options
- Conditions allowing American options to behave like European options
B. Use of Put-Call Parity
- Understanding value of put options based on call options
C. Importance of Market Equilibrium
- Arbitrage and market efficiency considerations