SUMMARY:
• Lecture 2 title slide (slide 1)
• reminder of Dan's plight and Alice's offer (slide 2)
• reminder of Alice's hedging strategy (slide 3)
• reminder of the three equation in three unknowns; goal is to avoid systems of equations; key point; the tricky idea of the risk-neutral world (slide 4)
• introduce a 70-30 real-world model and find expected values of the Euro and bank (slides 5-6)
• real-world risk-aversion; imaginary risk-neutrality (slide 7)
• reminder of the 60-40 weightings; change from 70-30 to 60-40 and recalculate expected value of Euro and bank (slides 8-11)
• equality of expected value of Euro and bank; risk-neutrality (slide 12)
• expected value, in the risk-neutral world, of various portfolios (slides 13-15)
• risk-neutral calculation of Alice's price (slide 16)
• coin-flippers got price! (slide 17)
• explanation of why risk-neutral calculation agrees with calculation by solving three equations (slides 18-20)
• reminder of Fred and Cathy's two-month option (slide 21)
• risk-neutral calculation of Cathy's price (slide 22)
• comparison to coin-flipping game (slide 23)
• explanation of why direct calculation of price from payoff agrees with working back month-by-month (slide 24)
• remainder of lecture: terminology and pricing of a stock option (slide 25)
• second act of Lecture 2 title slide (slide 26)
• description of Harry's plight and Gail's offer; the spot price; the strike price or excercise price; discussion of the underlying (the stock) and the derivative (the option) (slide 27)
• other underlying markets and derivative markets (slide 28)
• the risk-neutral probabilities for Gail's option (slide 29)
• template of prices and hedging parameters (slide 30)
• the share price in the template (slides 31-32)
• the ending portfolio value in the template, a.k.a. the "contingent claim"; the payoff function as the transition between the underlying and the derivative (slides 33-35)
• month-by-month calculation of the derivative price using the risk-neutral world (slides 36-38)
• starting over and planning direct calculation of the option price (slide 38)
• the direct calculation (slide 39)
• discussion of what happens with an N-step option; The Central Limit Theorem and the Black-Scholes Option Pricing Formula (slide 40)
• a review of pricing via the template, working back month-by-month, and they by the direct calculation (slide 41)
• the missing boxes in the template; the hedge parameters; let's go get hedge (in the next lecture) (slide 42)