Math 582 Financial Derivatives

For Stochastic Calculus

Young man, in mathematics you don’t understand things. You just get used to them.”

• Probability

  • Conditional Expected Value

• Binomial Security Pricing Model

• Stochastic Process

  • Stochastic Calculus
  • Quadratic Variation

• No-Arbitrage (=Law of One Price)

• Forwards

  • Futures

• Options (Finance)

  • Black Scholes European Option Pricing Formula
    • Risk-Neutral Assumption and Risk-Neutral Derivation of BSM
    • Binomial Option Pricing Model derivation of BSM
  • Greeks (Option)
  • Delta and Gamma Hedging
  • Warrants (Finance)
  • Merton Jump Diffusion Model

• Payoff: the gross outcome of an investment or trade. The amount you earned from that trade, regardless of commissions, extraneous costs, etc.

• Profits: the gross outcome of an investment or trade, including commissions, extraneous cost

  • → the distinction happens in Options (Finance). Payoffs don’t consider the option premium, while the profits do.

• Return: short for “rate of return”. The percentage of profit (not payoff!) per original investment. Quoted in percentage (%) or log-returns.

• #task 582: Why expectation is zero? here

• TW2 Q1(g) & Q2(a)#task

• TW3 Q4 & Q5 & Q6#task

• TW: Solving the BSM PDE (second derivatives)#task

• TW8#task

• #task understand Warrants (Finance)

• #task Understand gamma hedging

• #task understand Risk-Neutral Derivation of BSM

• #task Understand Merton Jump Diffusion Model

• #task Understanding Quadratic Variation