W2: option valuation

• binomial option pricing model - pricing options based on the assumption that the stock's return can only take on 2 values
• risk-neutral valuation:

  • ρ - probability that stock price increases
  • (1 - ρ) - probability that stock price decreases
• binomial option pricing model:

  • Δ - number of stocks to purchase
  • β - initial investment in bonds
• Black-Scholes option pricing model - technique for pricing european style options when the stock can be traded continuously
• the Black-Scholes model shortens the time period so that there are only 2 possible share price movements because it's unrealistic to have only 2 movements over the long-term
• replicating portfolio of call option:

  • stock - long position
  • bond - short position
• option delta (Δ) - change in price of the option given a $1 change in stock price
• assumptions of risk-neutral valuation:

  • market participants are risk neutral
  • financial assets have same cost of capital → risk-free rate
• binomial option pricing model:

  law of one price states that today's price of the call option must equal the current value of the replicating portfolio