Exotic Options and Complex Derivatives › Key Parameters
Michael BrenndoerferDecember 5, 20252 min read
Quantitative FinanceAll chapters Part 6 of 15Numerical Methods for Derivative Pricing
Exotic Options and Complex Derivatives › Key ParametersOne section · Sections in this chapter9 / 10 ↓
Sections in this chapter10
Reading tools Definitions & inline links
Choose your expertise level to adjust how many terms are explained. Beginners see more tooltips, experts see fewer to maintain reading flow. Hover over underlined terms for instant definitions.
Article links
Make inline references clickable
Key parameters for exotic options vary by type.
Asian Options:
- S₀: Current stock price. Higher prices increase call option values.
- K: Strike price. Determines the threshold for in-the-money payoff.
- T: Time to expiration. Longer durations increase option value.
- r: Risk-free rate. Affects discounting of expected payoff.
- σ: Volatility. Higher volatility increases option value.
- Average type: Arithmetic or geometric. Arithmetic averages lead to higher option values.
- n: Number of averaging points. More frequent averaging reduces sensitivity to extreme values.
Barrier Options:
- S₀: Current stock price. Starting point for the price path.
- K: Strike price. Determines payoff if option survives.
- H: Barrier level. The price that triggers knockout or knock-in.
- T: Time to expiration. Longer periods increase barrier-crossing probability.
- r: Risk-free rate. Affects both drift and discounting.
- σ: Volatility. Higher volatility increases probability of hitting barriers.
- Barrier type: Down-and-out, up-and-out, down-and-in, or up-and-in.
Lookback Options:
- S₀: Current stock price. Starting point for tracking extrema.
- Sₘᵢₙ or Sₘₐₓ: Historical minimum or maximum, relevant for options with existing history.
- T: Time to expiration. Longer periods increase likelihood of larger extrema.
- r: Risk-free rate. Affects discounting and drift.
- σ: Volatility. Higher volatility increases value significantly for lookback options.
- Strike type: Floating or fixed. This determines whether the strike or payoff reference changes.
Digital Options:
- S₀: Current stock price. Determines probability of finishing in-the-money.
- K: Strike price. The threshold for the discontinuous payoff.
- Q: Cash payout amount for cash-or-nothing digitals.
- T: Time to expiration. Affects probability calculations.
- r: Risk-free rate. Used for discounting.
- σ: Volatility. Affects the probability of crossing the strike.
Compound Options:
- S₀: Current stock price. Affects both compound and underlying option values.
- K₁: Strike of the compound option (cost to acquire the underlying).
- K₂: Strike of the underlying option.
- T₁: Expiration of the compound option.
- T₂: Expiration of the underlying option (must be > T₁).
- r: Risk-free rate. Affects both stages of the option.
- σ: Volatility. Impacts both decision points.