Math 581 & 582 Mathematical Finance, Derivatives

For Stochastic Calculus

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

Mathematical Background §

• Probability
  • Conditional Expected Value
• Stochastic Process
  • Stochastic Calculus
  • Quadratic Variation

Basic Concepts in Money §

• Time Value of Money
  • Present Value Calculations
  • Future Value Calculations
  • Interest Rate
  • Banker’s Rule

Basic Finance §

• Amortizing Securities
  • Annuity
  • Perpetuity
  • Bond Price
• Portfolio Theory
  • Dividend Discount Model
  • CAPM Model
    • Market Beta
  • Measuring Security Performance
• Binomial Security Pricing Model
• No-Arbitrage (=Law of One Price)

Derivatives §

• 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

• Forwards

  • Futures

• 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.