SOCR EduMaterials Activities ApplicationsActivities BlackScholesOptionPricing
From Socr
Contents |
SOCR Applications Activities - Black-Scholes Option Pricing Model (with Convergence of Binomial)
Description
You can access the Black-Scholes Option Pricing Model applet at the SOCR Applications Site, select Financial Applications --> BlackScholesOptionPricing.
Black-Scholes option pricing formula
The value C of a European call option at time t = 0 is:
Where,
- S0 Price of the stock at time t = 0
- E Exercise price at expiration
- r Continuously compounded risk-free interest
- σ Annual standard deviation of the returns of the stock
- t Time to expiration in years
- Φ(di) Cumulative probability at di of the standard normal distribution N(0,1)
Binomial convergence to Black-Scholes option pricing formula
The binomial formula converges to the Black-Scholes formula when the number of periods n is large. In the example below we value the call option using the binomial formula for different values of n and also using the Black-Scholes formula. We then plot the value of the call (from binomial) against the number of periods n. The value of the call using Black-Scholes remains the same regardless of n. The data used for this example are:
-
, 
, Rf = 0.05, σ = 0.30,
Days to expiration = 40.
- For the binomial option pricing calculations we divided the 40 days into intervals from 1 to 100 (by 1).
- The snapshot below from the SOCR Black Scholes Option Pricing model applet shows the path of the stock.
References
The materials above was partially taken from:
- Modern Portfolio Theory by Edwin J. Elton, Martin J. Gruber, Stephen J. Brown, and William N. Goetzmann, Sixth Edition, Wiley, 2003.
- Options, Futues, and Other Derivatives by John C. Hull, Sixth Edition, Pearson Prentice Hall, 2006.
- SOCR Applications Site
Translate this page:
