8. Case Studies (Real-World Applications)
Case Study 1: Stock Option Pricing
Situation:
An investor wants to determine if a call option is fairly priced.
Approach:
- Uses BSM model with market inputs
Outcome:
- Compares theoretical value with market price
Insight:
Helps identify overvalued or undervalued options.
Case Study 2: Volatility Impact
Situation:
A tech stock becomes highly volatile due to earnings announcements.
Outcome:
- Option prices increase significantly
Insight:
Volatility is one of the most important drivers of option value.
Case Study 3: Time Decay (Theta Effect)
Situation:
An option is close to expiration.
Outcome:
- Option value decreases over time
Insight:
Time works against option buyers as expiry approaches.
Case Study 4: Risk Management in Institutions
Situation:
A financial institution needs to price and manage thousands of options.
Approach:
- Uses BSM model for consistent valuation
Insight:
Provides a standardized pricing framework across markets.
9. Limitations of the Model
The Black–Scholes–Merton model assumes:
- Constant volatility
- No transaction costs
- Continuous trading
- European-style exercise only
Reality:
Markets are more complex, so adjustments are often needed.
10. Key Takeaways
- BSM is a foundational model for option pricing
- Option value depends heavily on volatility and time
- Provides a benchmark for fair pricing
- Works best for European options under stable conditions
11. Quick Practice
Scenario:
Two identical call options exist, but one has higher volatility.
Question:
Why does volatility increase option price?
Which option is more valuable?