Overview of Financial Risks and Regulatory Frameworks › Key Parameters
Michael BrenndoerferDecember 19, 20251 min read
Quantitative FinanceAll chapters Part 10 of 15Risk Management and Financial Risk Controls
Overview of Financial Risks and Regulatory Frameworks › Key ParametersOne section · Sections in this chapter6 / 17 ↓
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The Black-Scholes model used in this illustration relies on the following parameters, each of which must either be observed directly or estimated:
- S: Current stock price ($100) This is directly observable from market data and introduces no estimation error.
- K: Strike price ($100) This is a contractual term that is known exactly.
- T: Time to expiration (0.25 years). This is calculable from contract specifications, though subtleties arise around day count conventions.
- r: Risk-free interest rate (5%). This must be estimated, typically from Treasury yields, and introduces some uncertainty, though generally less than volatility.
- sigma: Volatility of the underlying asset. In this simulation, we treat this as an estimated parameter with uncertainty. This is the dominant source of model risk for option pricing because volatility is not directly observable and must be inferred from historical data or implied from market prices.